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Title: New Heat Flow Models in Fractured Geothermal Reservoirs - Final Report

Abstract

This study developed new analytical models for predicting the temperature distribution within a geothermal reservoir following reinjection of water having a temperature different from that of the reservoir. The study consisted of two parts: developing new analytical models for the heat conduction rate into multi-dimensional, parallelepiped matrix blocks and developing new analytical models for the advance of the thermal front through the geothermal reservoir. In the first part of the study, a number of semi-empirical models for the multi-dimensional heat conduction were developed to overcome the limitations to the exact solutions. The exact solution based on a similarity solution to the heat diffusion equation is the best model for the early-time period, but fails when thermal conduction fronts from opposing sides of the matrix block merge. The exact solution based on an infinite series solution was found not to be useful because it required tens of thousands of terms to be include d for accuracy. The best overall model for the entire conduction time was a semi-empirical model based on an exponential conduction rate. In the second part of the study, the early-time period exact solution based on similarity methods and the semi-empirical exponential model were used to develop newmore » analytical models for the location of the thermal front within the reservoir during injection. These equations were based on an energy balance on the water in the fractured network. These convective models allowed for both dual and triple porosity reservoirs, i.e., one or two independent matrix domains. A method for incorporating measured fracture spacing distributions into these convective models was developed. It was found that there were only minor differences in the predicted areal extent of the heated zone between the dual and triple porosity models. Because of its simplicity, the dual porosity model is recommended. These new models can be used for preliminary reservoir studies. Although they are not as accurate as numerical simulators, they are simple, easy and inexpensive to use. These new models can be used to get general information about reservoir behavior before committing to the considerable greater expense of numerical simulation.« less

Authors:
Publication Date:
Research Org.:
Reis and Associates, Prescott Valley, AZ (US)
Sponsoring Org.:
USDOE Office of Energy Efficiency and Renewable Energy (EE) (US)
OSTI Identifier:
782011
Report Number(s):
DOE/ID/13746
TRN: AH200124%%241
DOE Contract Number:  
FG07-99ID13746
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: 31 Mar 2001
Country of Publication:
United States
Language:
English
Subject:
15 GEOTHERMAL ENERGY; ACCURACY; DIFFUSION; ENERGY BALANCE; FRACTURES; HEAT FLUX; POROSITY; SIMULATION; SIMULATORS; TEMPERATURE DISTRIBUTION; THERMAL CONDUCTION; WATER; Geothermal Legacy; GEOTHERMAL RESERVOIR; REINJECTION; ANALYTICAL MODELS; THERMAL FRONT; NUMERICAL SIMULATION; DUAL POROSITY MODEL

Citation Formats

Reis, John. New Heat Flow Models in Fractured Geothermal Reservoirs - Final Report. United States: N. p., 2001. Web. doi:10.2172/782011.
Reis, John. New Heat Flow Models in Fractured Geothermal Reservoirs - Final Report. United States. https://doi.org/10.2172/782011
Reis, John. 2001. "New Heat Flow Models in Fractured Geothermal Reservoirs - Final Report". United States. https://doi.org/10.2172/782011. https://www.osti.gov/servlets/purl/782011.
@article{osti_782011,
title = {New Heat Flow Models in Fractured Geothermal Reservoirs - Final Report},
author = {Reis, John},
abstractNote = {This study developed new analytical models for predicting the temperature distribution within a geothermal reservoir following reinjection of water having a temperature different from that of the reservoir. The study consisted of two parts: developing new analytical models for the heat conduction rate into multi-dimensional, parallelepiped matrix blocks and developing new analytical models for the advance of the thermal front through the geothermal reservoir. In the first part of the study, a number of semi-empirical models for the multi-dimensional heat conduction were developed to overcome the limitations to the exact solutions. The exact solution based on a similarity solution to the heat diffusion equation is the best model for the early-time period, but fails when thermal conduction fronts from opposing sides of the matrix block merge. The exact solution based on an infinite series solution was found not to be useful because it required tens of thousands of terms to be include d for accuracy. The best overall model for the entire conduction time was a semi-empirical model based on an exponential conduction rate. In the second part of the study, the early-time period exact solution based on similarity methods and the semi-empirical exponential model were used to develop new analytical models for the location of the thermal front within the reservoir during injection. These equations were based on an energy balance on the water in the fractured network. These convective models allowed for both dual and triple porosity reservoirs, i.e., one or two independent matrix domains. A method for incorporating measured fracture spacing distributions into these convective models was developed. It was found that there were only minor differences in the predicted areal extent of the heated zone between the dual and triple porosity models. Because of its simplicity, the dual porosity model is recommended. These new models can be used for preliminary reservoir studies. Although they are not as accurate as numerical simulators, they are simple, easy and inexpensive to use. These new models can be used to get general information about reservoir behavior before committing to the considerable greater expense of numerical simulation.},
doi = {10.2172/782011},
url = {https://www.osti.gov/biblio/782011}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Sat Mar 31 00:00:00 EST 2001},
month = {Sat Mar 31 00:00:00 EST 2001}
}