skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: On the Representation of the Porosity-Pressure Relationship in General Subsurface Flow Codes

Abstract

The governing equations for subsurface flow codes in a deformable porous media are derived from the balance of fluid mass and Darcy's equation. One class of these codes, which we call general subsurface flow codes (GSFs), allow for more general constitutive relations for material properties such as porosity, permeability and density. Examples of GSFs include PFLOTRAN, FEHM, TOUGH2, STOMP, and some reservoir simulators such as BOAST. Depending on the constitutive relations used in GSFs, an inconsistency arises between the standard groundwater flow equation and the governing equation of GSFs, and we clarify that the reason for this inconsistency is because the Darcy's equation used in the GSFs should account for the velocity of fluid with respect to solid. Due to lack of awareness of this inconsistency, users of the GSFs tend to use a porosity-pressure relationship that comes from the standard groundwater flow equation and assumes that the relative velocity is already accounted for. For the Theis problem, we show that using this traditional relationship in the GSFs leads to significantly large errors. In this work, we propose an alternate porosity-pressure relationship that is consistent with the derivation of the governing equations in the GSFs where the solid velocity ismore » not tracked, and show that, with this relationship, the results are more accurate for the Theis problem. The purpose of this note is to make the users and developers of these GSFs aware of this inconsistency and to advocate that the alternate porosity model derived here should be incorporated in GSFs.« less

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [1]
  1. Univ. of Colorado, Boulder, CO (United States)
  2. 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 National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
OSTI Identifier:
1595657
Report Number(s):
LA-UR-20-20361; LA-UR-17-28739
Journal ID: ISSN 0043-1397
Grant/Contract Number:  
89233218CNA000001; EAR-152084; AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Water Resources Research
Additional Journal Information:
Journal Volume: 54; Journal Issue: 2; Journal ID: ISSN 0043-1397
Publisher:
American Geophysical Union (AGU)
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; porosity; groundwater flow equation; flow and transport models; specific storage; porous media compressibility; petroleum engineering

Citation Formats

Birdsell, Daniel T., Karra, Satish, and Rajaram, Harihar. On the Representation of the Porosity-Pressure Relationship in General Subsurface Flow Codes. United States: N. p., 2018. Web. doi:10.1002/2017WR022001.
Birdsell, Daniel T., Karra, Satish, & Rajaram, Harihar. On the Representation of the Porosity-Pressure Relationship in General Subsurface Flow Codes. United States. doi:10.1002/2017WR022001.
Birdsell, Daniel T., Karra, Satish, and Rajaram, Harihar. Thu . "On the Representation of the Porosity-Pressure Relationship in General Subsurface Flow Codes". United States. doi:10.1002/2017WR022001. https://www.osti.gov/servlets/purl/1595657.
@article{osti_1595657,
title = {On the Representation of the Porosity-Pressure Relationship in General Subsurface Flow Codes},
author = {Birdsell, Daniel T. and Karra, Satish and Rajaram, Harihar},
abstractNote = {The governing equations for subsurface flow codes in a deformable porous media are derived from the balance of fluid mass and Darcy's equation. One class of these codes, which we call general subsurface flow codes (GSFs), allow for more general constitutive relations for material properties such as porosity, permeability and density. Examples of GSFs include PFLOTRAN, FEHM, TOUGH2, STOMP, and some reservoir simulators such as BOAST. Depending on the constitutive relations used in GSFs, an inconsistency arises between the standard groundwater flow equation and the governing equation of GSFs, and we clarify that the reason for this inconsistency is because the Darcy's equation used in the GSFs should account for the velocity of fluid with respect to solid. Due to lack of awareness of this inconsistency, users of the GSFs tend to use a porosity-pressure relationship that comes from the standard groundwater flow equation and assumes that the relative velocity is already accounted for. For the Theis problem, we show that using this traditional relationship in the GSFs leads to significantly large errors. In this work, we propose an alternate porosity-pressure relationship that is consistent with the derivation of the governing equations in the GSFs where the solid velocity is not tracked, and show that, with this relationship, the results are more accurate for the Theis problem. The purpose of this note is to make the users and developers of these GSFs aware of this inconsistency and to advocate that the alternate porosity model derived here should be incorporated in GSFs.},
doi = {10.1002/2017WR022001},
journal = {Water Resources Research},
number = 2,
volume = 54,
place = {United States},
year = {2018},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:

Works referenced in this record:

The relation between the lowering of the Piezometric surface and the rate and duration of discharge of a well using ground-water storage
journal, January 1935


Relationship between Horizontal Strain near a Well and Reverse Water Level Fluctuation
journal, December 1970


Estimating Hydraulic Parameters When Poroelastic Effects Are Significant
journal, January 2011


TOUGH2 User's Guide Version 2
report, November 1999

  • Pruess, K.; Oldenburg, C.M.; Moridis, G.J.
  • LBNL--43134
  • DOI: 10.2172/751729

On the flow of water in an elastic artesian aquifer
journal, January 1940


On Storage Coefficient and Vertical Strain
journal, May 2006


A note on the meaning of storage coefficient
journal, April 1980


Storage Coefficient Revisited: Is Purely Vertical Strain a Good Assumption?
journal, May 2001