ASTM D5719-95(2000)
(Guide)Standard Guide for Simulation of Subsurface Airflow Using Ground-Water Flow Modeling Codes
Standard Guide for Simulation of Subsurface Airflow Using Ground-Water Flow Modeling Codes
SCOPE
1.1 This guide covers the use of a ground-water flow modeling code to simulate the movement of air in the subsurface. This approximation is possible because the form of the ground-water flow equations are similar in form to airflow equations. Approximate methods are presented that allow the variables in the airflow equations to be replaced with equivalent terms in the ground-water flow equations. The model output is then transformed back to airflow terms.
1.2 This guide illustrates the major steps to take in developing an airflow model using an existing ground-water flow modeling code. This guide does not recommend the use of a particular model code. Most ground-water flow modeling codes can be utilized, because the techniques described in this guide require modification to model input and not to the code.
1.3 This guide is not intended to be all inclusive. Other similar techniques may be applicable to airflow modeling, as well as more complex variably saturated ground-water flow modeling codes. This guide does not preclude the use of other techniques, but presents techniques that can be easily applied using existing ground-water flow modeling codes.
1.4 This guide is one of a series of standards on ground-water model applications, including Guides D5447 and D5490. This guide should be used in conjunction with Guide D5447. Other standards have been prepared on environmental modeling, such as Practice E978.
1.5 The values stated in SI units are to be regarded as the standard.
1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
1.7 This guide offers an organized collection of information or a series of options and does not recommend a specific course of action. This document cannot replace education or experience and should be used in conjunction with professional judgment. Not all aspects of this guide may be applicable in all circumstances. This ASTM standard is not intended to represent or replace the standard of care by which the adequacy of a given professional service must be judged, nor should this document be applied without consideration of a project's many unique aspects. The word "Standard" in the title of this document means only that the document has been approved through the ASTM consensus process.
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Designation: D 5719 – 95 (Reapproved 2000)
Standard Guide for
Simulation of Subsurface Airflow Using Ground-Water Flow
Modeling Codes
This standard is issued under the fixed designation D5719; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope circumstances. This ASTM standard is not intended to repre-
sent or replace the standard of care by which the adequacy of
1.1 This guide covers the use of a ground-water flow
a given professional service must be judged, nor should this
modeling code to simulate the movement of air in the subsur-
document be applied without consideration of a project’s many
face. This approximation is possible because the form of the
unique aspects. The word “Standard” in the title of this
ground-water flow equations are similar in form to airflow
document means only that the document has been approved
equations. Approximate methods are presented that allow the
through the ASTM consensus process.
variables in the airflow equations to be replaced with equiva-
lent terms in the ground-water flow equations. The model
2. Referenced Documents
output is then transformed back to airflow terms.
2.1 ASTM Standards:
1.2 This guide illustrates the major steps to take in devel-
D653 Terminology Relating to Soil, Rock, and Contained
oping an airflow model using an existing ground-water flow
Fluids
modeling code. This guide does not recommend the use of a
D5447 Guide for Application of a Ground-Water Flow
particular model code. Most ground-water flow modeling
Model to a Site-Specific Problem
codes can be utilized, because the techniques described in this
D5490 Guide for Comparing Ground-Water Flow Model
guide require modification to model input and not to the code.
Simulations to Site-Specific Information
1.3 This guide is not intended to be all inclusive. Other
E978 Practice for Evaluating Environmental Fate Models
similar techniques may be applicable to airflow modeling, as
of Chemicals
well as more complex variably saturated ground-water flow
modeling codes. This guide does not preclude the use of other
3. Terminology
techniques, but presents techniques that can be easily applied
3.1 Definitions:
using existing ground-water flow modeling codes.
3.1.1 boundary condition—a mathematical expression of a
1.4 This guide is one of a series of standards on ground-
stateofthephysicalsystemthatconstrainstheequationsofthe
water model applications, including Guides D 5447 and
mathematical model.
D5490. This guide should be used in conjunction with Guide
3.1.2 computer code (computer program)—the assembly of
D5447. Other standards have been prepared on environmental
numerical techniques, bookkeeping, and control language that
modeling, such as Practice E978.
represents the model from acceptance of input data and
1.5 The values stated in SI units are to be regarded as the
instructions to delivery of output.
standard.
3.1.3 ground-water flow model—application of a math-
1.6 This standard does not purport to address all of the
ematical model to represent a site-specific ground-water flow
safety concerns, if any, associated with its use. It is the
system.
responsibility of the user of this standard to establish appro-
3.1.4 mathematical model—( a) mathematical equations
priate safety and health practices and determine the applica-
expressing the physical system and including simplifying
bility of regulatory limitations prior to use.
assumptions, (b) the representation of a physical system by
1.7 This guide offers an organized collection of information
mathematical expressions from which the behavior of the
or a series of options and does not recommend a specific
system can be deduced with known accuracy.
course of action. This document cannot replace education or
3.1.5 model—an assembly of concepts in the form of
experienceandshouldbeusedinconjunctionwithprofessional
mathematical equations that portray understanding of a natural
judgment. Not all aspects of this guide may be applicable in all
phenomenon.
ThisguideisunderthejurisdictionofASTMCommitteeD18onSoilandRock
and is the direct responsibility of Subcommittee D18.21 on Ground Water and Annual Book of ASTM Standards, Vol 04.08.
Vadose Investigations. Annual Book of ASTM Standards, Vol 04.09.
Current edition approved April 15, 1995. Published June 1995. Annual Book of ASTM Standards, Vol 11.04.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D 5719
3.2 For definitions of other terms used in this guide, see 4.2.1 If the problem is formulated in terms of air pressure-
Terminology D653. squared, the square root of the model-computed dependent
3.3 Symbols:Symbols and Dimensions: variable is computed at each cell;
3.3.1 A—cross-sectional area of cell [cm ]. 4.2.2 Flow rates computed by the pressure-squared ap-
proach must be transformed into equivalent airflow terms for
3.3.2 g—acceleration due to gravity [cm/s ].
3.3.3 h—air-phase or water phase head [cm]. volumetric flow rates (q ) or mass flow rates ( q ).
v m
4.2.3 No transformation of the output is required by the
3.3.4 k—air phase permeability [cm ].
pressure substitution technique, although the pressures may be
3.3.5 K—hydraulic conductivity [cm/s].
converted to more convenient units.
3.3.6 P—air phase pressure [g/cm-s ].
3.3.7 P —reference air-phase pressure [g/cm-s ].
5. Significance and Use
3.3.8 q —specific discharge vector for air [cm/s].
s
5.1 The use of vapor extraction systems (VES), also called
3.3.9 q—volumetric flow of water through cell [cm /s].
soil vapor extraction (SVE) or venting systems, is becoming a
3.3.10 q*—model-computed term related to airflow in units
2 4
common remedial technology applicable to sites contaminated
g -cm/s .
with volatile compounds (3, 4). A vapor extraction system is
3.3.11 q —volumetric airflow [cm /s].
v
composed of wells or trenches screened within the vadose
3.3.12 q —mass airflow [g/s].
m
7 2 2
zone. Air is extracted from these wells to remove organic
3.3.13 R—universal gas constant=8.314 310 [g-cm /s -
compoundsthatreadilypartitionbetweensolidorliquidphases
mol-K].
−1
into the gas phase. The volatile contaminants are removed in
3.3.14 S —specific storage of the porous material [cm ].
s
the gas phase and treated or discharged to the atmosphere. In
3.3.15 t—time [s].
many cases, the vapor extraction system also incorporates
3.3.16 T—temperature [K].
−1
wells open to the atmosphere that act as air injection wells.
3.3.17 W—volumetric flux per unit volume [s ].
3.3.18 z—elevation head [cm].
NOTE 1—Few model codes are available that allow simulation of the
3.3.19 ]h—hydraulic head difference [cm]. movement of air, water, and nonaqueous liquids through the subsurface.
Those model codes that are available (5, 6), require inordinate compute
3.3.20 ]l—length of model cell [cm].
hardware, are complicated to use, and require collection of field data that
3.3.21 r—density of air [g/cm ].
may be difficult or expensive to obtain. In the future, as computer
3.3.22 u—air-filled porosity [nd].
capabilities expand, this may not be a significant problem. Today,
2 2 2
3.3.23 f—pressure-squared (P ) [(g/cm-s ) ].
however, these complex models are not applied routinely to the design of
3.3.24 v—average molecular weight of air [g/mol].
vapor extraction systems.
3.3.25 µ—dynamic viscosity of air [g/cm-s].
5.2 This guide presents approximate methods to efficiently
simulate the movement of air through the vadose zone. These
4. Summary of Guide
methods neglect the presence of water and other liquids in the
4.1 The flow of gas (air in this case) through unsaturated
vadose zone; however, these techniques are much easier to
porous media can be approximated using ground-water flow
apply and require significantly less computer hardware than
modeling codes. This is accomplished through substitution of
more robust numerical models.
air-phase parameters and variables into the ground-water flow
5.3 This guide should be used by ground-water modelers to
equations. There are two substitution techniques discussed in
approximately simulate the movement of air in the vadose
thisguide,thepressure-squaredtechnique (1),andthepressure
zone.
substitution technique (2). These substitutions are summarized
5.4 Use of this guide to simulate subsurface air movement
as follows:
does not guarantee that the airflow model is valid. This guide
4.1.1 The dependent variable, usually head, in the ground-
simply describes mathematical techniques for simulating sub-
water flow equation becomes pressure or pressure-squared; surface air movement with ground-water modeling codes. As
4.1.2 Saturated hydraulic conductivity ( K), both horizontal
with any modeling study, the modeler must have a thorough
and vertical components, becomes air permeability (k or understanding of site conditions with supporting data in order
intrinsic permeability) in the pressure-squared technique and
to properly apply the techniques presented in this guide.
an equivalent air hydraulic conductivity in the pressure substi-
6. Pressure-Squared Substitution Procedure
tution technique.
4.1.3 Storage coefficient (S) becomes the air storage coeffi- 6.1 The pressure-squared substitution procedure is adapted
cient (S );
from Baehr and Joss (1). The technique allows simulation of
a
4.1.4 The Vadose zone is considered a confined aquifer; the flow of gas (air in this case) through porous media using
and,
ground-water flow modeling codes. This is accomplished
4.1.5 All boundary conditions are expressed in terms of air through substitution of air-phase parameters and variables into
pressure-squared, although constant flux boundary conditions the ground-water flow equations. These substitutions are sum-
may be used in the pressure substitution technique. marized as follows:
4.2 The ground-water modeling code is executed using 6.2 Airflow Equation—The following presentation outlines
these parameter and variable substitutions. The model results the essential assumptions of the airflow equation. A more
must then be transformed to values representative of air.These detailed presentation providing justification of the various
calculations are summarized as follows: assumptions is provided by Baehr and Hult (7).
D 5719
6.2.1 The conservation of mass equation for airflow in an difference is less than 0.8 atm. When substituting pressure
unsaturated porous medium is given by the following: (insteadofpressure-squared)forhead,theerrorsaresimilarfor
pressure differences less than 0.2 atm, but are quite large for
]
~ru!1π·~r; q ! 50 (1)
s pressure differences greater than 0.5 atm. In most cases, the
]t
pressure differences will be less than 0.2 atm; therefore, either
6.2.2 Darcy’s Law for airflow is assumed as follows:
substitution may be used in environmental modeling (see
rg
Section 7 for a description of the pressure substitution tech-
; q 52 ' k πh (2)
s
µ
nique).
6.2.9 Eq 7 can be directly compared to the linear ground-
6.2.3 Hubbert (1940) defined the head for a compressible
water flow equation. The simplifying assumptions needed to
fluid as follows:
arrive at this linear airflow equation are summarized as
1 P1
h 5 z 1 dP (3)
follows:
*
g r
P
6.2.9.1 Darcy’s law is valid for airflow;
6.2.4 The Ideal Gas Law is assumed to relate pressure and
6.2.9.2 The elevation component of pneumatic head is
density and thus provides a model for air compressibility as
neglected;
follows:
6.2.9.3 Temperature effects are neglected;
vP
6.2.9.4 The Ideal Gas law is a valid model for compress-
r5 (4)
RT
ibility;
6.2.9.5 The Klinkenberg slip effect is neglected;
6.2.5 Substituting Eq 4 into Eq 3, assuming v and T are
6.2.9.6 Water movement and consolidation are neglected,
constant, neglecting the elevation component of head (that is
therefore porosity is constant with respect to time; and
small for air compared to the pressure component) and
1/2
substituting into Eq 2 gives the following expression for 6.2.9.7 f = P in definition of storage coefficient S .
atm a
Darcy’s Law in terms of P: 6.2.10 BaehrandHult(7)examinedtheconsequencesofthe
assumptions presented in 6.2.9. The authors found that the
; q 52 ' k πP (5)
s linearairflowmodelgivenbyEq7isagoodworkingmodelfor
µ
essentially all environmental applications.
6.2.6 Substituting Eq 4 and Eq 5 into Eq 1, and then using
6.3 Ground-Water Flow Equation—The following ground-
the following linearizing change of variable suggested by
water flow equation is solved by many ground-water flow
Muskat and Botset (8) for airflow:
models:
f5 P (6)
] ]h ] ]h ] ]h ]h
K 1 K 1 K 2 W 5 S (9)
S D S D S D
xx yy zz s
]x ]x ]y ]y ]z ]z ]t
yields the following three-dimensional airflow equation in
Cartesian coordinates that is analogous in form to the ground-
where: x, y,and zareCartesiancoordinatesalignedalongthe
waterflowequationsolvedbymanyground-waterflowmodels
major axes of the hydraulic conductivity tensor with diagonal
(MODFLOW (9), for example):
components K , K ,K .
xx yy zz
] ]f ] ]f ] ]f ]f 6.3.1 Thepurposeoftheprocedurepresentedinthisguideis
k 1 k 1 k 5 S (7)
S D S D S D
xx yy zz a
]x ]x ]y ]y ]z ]z ]t to facilitate airflow simulations by matching Eq 7 and Eq 9 so
thatthenumericalsolutioncodedinground-waterflowmodels
where, x, y,and zareCartesiancoordinatesalignedalongthe
canbeusedtosolvetheairflowequation.Thisisaccomplished
major axes of the permeability tensor with diagonal compo-
with the following parameter matches:
nents k , k , and k .
xx yy zz
h⇒ f (10)
6.2.7 Air-phase permeability is assumed to be independent
of P, therefore, the Klinkenberg slip effect (10) can only be
K⇒ k (11)
modeled as constant with respect to P. The coefficient S is the
a
S ⇒ S (12)
s a
pneumatic equivalent of specific storage and if air-filled
6.3.2 The parameter matching allows the hydraulic head
porosity is constant with respect to time (that is, water
and flow output from the ground-water model to be interpreted
movement is neglected) then:
for the airflow model in accordance with 6.3.
uµ
6.4 Boundary Conditions—There are only two permissible
S 5 (8)
a
=f
types of boundary conditions when using the pressure-squared
6.2.8 The change of variable f= P results in a linear substitution described above. These include constant pressure
and no-flow boundaries.
equation for steady-state airflow. The transient equation is
1/2
linearized by assuming f = P in the definition of S , 6.4.1 Constant pressure cells are actually constant pressure-
atm a
where P is the prevailing atmospheric pressure. squared cells. Constant
...
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