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Title: Regression-based reduced-order models to predict transient thermal output for enhanced geothermal systems

Abstract

Reduced-order modeling is a promising approach, as many phenomena can be described by a few parameters/mechanisms. An advantage and attractive aspect of a reduced-order model is that it is computational inexpensive to evaluate when compared to running a high-fidelity numerical simulation. A reduced-order model takes couple of seconds to run on a laptop while a high-fidelity simulation may take couple of hours to run on a high-performance computing cluster. The goal of this paper is to assess the utility of regression-based reduced-order models (ROMs) developed from high-fidelity numerical simulations for predicting transient thermal power output for an enhanced geothermal reservoir while explicitly accounting for uncertainties in the subsurface system and site-specific details. Numerical simulations are performed based on equally spaced values in the specified range of model parameters. Key sensitive parameters are then identified from these simulations, which are fracture zone permeability, well/skin factor, bottom hole pressure, and injection flow rate. We found the fracture zone permeability to be the most sensitive parameter. The fracture zone permeability along with time, are used to build regression-based ROMs for the thermal power output. The ROMs are trained and validated using detailed physics-based numerical simulations. Finally, predictions from the ROMs are then comparedmore » with field data. We propose three different ROMs with different levels of model parsimony, each describing key and essential features of the power production curves. The coefficients in the proposed regression-based ROMs are developed by minimizing a non-linear least-squares misfit function using the Levenberg–Marquardt algorithm. The misfit function is based on the difference between numerical simulation data and reduced-order model. ROM-1 is constructed based on polynomials up to fourth order. ROM-1 is able to accurately reproduce the power output of numerical simulations for low values of permeabilities and certain features of the field-scale data. ROM-2 is a model with more analytical functions consisting of polynomials up to order eight, exponential functions and smooth approximations of Heaviside functions, and accurately describes the field-data. At higher permeabilities, ROM-2 reproduces numerical results better than ROM-1, however, there is a considerable deviation from numerical results at low fracture zone permeabilities. ROM-3 consists of polynomials up to order ten, and is developed by taking the best aspects of ROM-1 and ROM-2. ROM-1 is relatively parsimonious than ROM-2 and ROM-3, while ROM-2 overfits the data. ROM-3 on the other hand, provides a middle ground for model parsimony. Based on R 2-values for training, validation, and prediction data sets we found that ROM-3 is better model than ROM-2 and ROM-1. For predicting thermal drawdown in EGS applications, where high fracture zone permeabilities (typically greater than 10 –15 m 2) are desired, ROM-2 and ROM-3 outperform ROM-1. As per computational time, all the ROMs are 10 4 times faster when compared to running a high-fidelity numerical simulation. In conclusion, this makes the proposed regression-based ROMs attractive for real-time EGS applications because they are fast and provide reasonably good predictions for thermal power output.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1];  [1]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1375165
Report Number(s):
LA-UR-16-22095
Journal ID: ISSN 0375-6505
Grant/Contract Number:
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Geothermics
Additional Journal Information:
Journal Volume: 70; Journal Issue: C; Journal ID: ISSN 0375-6505
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; Earth Sciences; Energy Sciences; enhanced geothermal systems, reduced-order models, thermal drawdown, data-limited problems; Enhanced Geothermal Systems (EGS); Reduced-Order Models (ROMs); thermal draw39 down; regression.

Citation Formats

Mudunuru, Maruti Kumar, Karra, Satish, Harp, Dylan Robert, Guthrie, Jr., George Drake, and Viswanathan, Hari S. Regression-based reduced-order models to predict transient thermal output for enhanced geothermal systems. United States: N. p., 2017. Web. doi:10.1016/j.geothermics.2017.06.013.
Mudunuru, Maruti Kumar, Karra, Satish, Harp, Dylan Robert, Guthrie, Jr., George Drake, & Viswanathan, Hari S. Regression-based reduced-order models to predict transient thermal output for enhanced geothermal systems. United States. doi:10.1016/j.geothermics.2017.06.013.
Mudunuru, Maruti Kumar, Karra, Satish, Harp, Dylan Robert, Guthrie, Jr., George Drake, and Viswanathan, Hari S. Mon . "Regression-based reduced-order models to predict transient thermal output for enhanced geothermal systems". United States. doi:10.1016/j.geothermics.2017.06.013.
@article{osti_1375165,
title = {Regression-based reduced-order models to predict transient thermal output for enhanced geothermal systems},
author = {Mudunuru, Maruti Kumar and Karra, Satish and Harp, Dylan Robert and Guthrie, Jr., George Drake and Viswanathan, Hari S.},
abstractNote = {Reduced-order modeling is a promising approach, as many phenomena can be described by a few parameters/mechanisms. An advantage and attractive aspect of a reduced-order model is that it is computational inexpensive to evaluate when compared to running a high-fidelity numerical simulation. A reduced-order model takes couple of seconds to run on a laptop while a high-fidelity simulation may take couple of hours to run on a high-performance computing cluster. The goal of this paper is to assess the utility of regression-based reduced-order models (ROMs) developed from high-fidelity numerical simulations for predicting transient thermal power output for an enhanced geothermal reservoir while explicitly accounting for uncertainties in the subsurface system and site-specific details. Numerical simulations are performed based on equally spaced values in the specified range of model parameters. Key sensitive parameters are then identified from these simulations, which are fracture zone permeability, well/skin factor, bottom hole pressure, and injection flow rate. We found the fracture zone permeability to be the most sensitive parameter. The fracture zone permeability along with time, are used to build regression-based ROMs for the thermal power output. The ROMs are trained and validated using detailed physics-based numerical simulations. Finally, predictions from the ROMs are then compared with field data. We propose three different ROMs with different levels of model parsimony, each describing key and essential features of the power production curves. The coefficients in the proposed regression-based ROMs are developed by minimizing a non-linear least-squares misfit function using the Levenberg–Marquardt algorithm. The misfit function is based on the difference between numerical simulation data and reduced-order model. ROM-1 is constructed based on polynomials up to fourth order. ROM-1 is able to accurately reproduce the power output of numerical simulations for low values of permeabilities and certain features of the field-scale data. ROM-2 is a model with more analytical functions consisting of polynomials up to order eight, exponential functions and smooth approximations of Heaviside functions, and accurately describes the field-data. At higher permeabilities, ROM-2 reproduces numerical results better than ROM-1, however, there is a considerable deviation from numerical results at low fracture zone permeabilities. ROM-3 consists of polynomials up to order ten, and is developed by taking the best aspects of ROM-1 and ROM-2. ROM-1 is relatively parsimonious than ROM-2 and ROM-3, while ROM-2 overfits the data. ROM-3 on the other hand, provides a middle ground for model parsimony. Based on R2-values for training, validation, and prediction data sets we found that ROM-3 is better model than ROM-2 and ROM-1. For predicting thermal drawdown in EGS applications, where high fracture zone permeabilities (typically greater than 10–15 m2) are desired, ROM-2 and ROM-3 outperform ROM-1. As per computational time, all the ROMs are 104 times faster when compared to running a high-fidelity numerical simulation. In conclusion, this makes the proposed regression-based ROMs attractive for real-time EGS applications because they are fast and provide reasonably good predictions for thermal power output.},
doi = {10.1016/j.geothermics.2017.06.013},
journal = {Geothermics},
number = C,
volume = 70,
place = {United States},
year = {Mon Jul 10 00:00:00 EDT 2017},
month = {Mon Jul 10 00:00:00 EDT 2017}
}

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