ASTM D5719-95(2006)
(Guide)Standard Guide for Simulation of Subsurface Airflow Using Groundwater Flow Modeling Codes
Standard Guide for Simulation of Subsurface Airflow Using Groundwater Flow Modeling Codes
SIGNIFICANCE AND USE
The use of vapor extraction systems (VES), also called soil vapor extraction (SVE) or venting systems, is becoming a common remedial technology applicable to sites contaminated with volatile compounds (3, 4). A vapor extraction system is composed of wells or trenches screened within the vadose zone. Air is extracted from these wells to remove organic compounds that readily partition between solid or liquid phases into the gas phase. The volatile contaminants are removed in the gas phase and treated or discharged to the atmosphere. In many cases, the vapor extraction system also incorporates wells open to the atmosphere that act as air injection wells.
Note 1—Few model codes are available that allow simulation of the movement of air, water, and nonaqueous liquids through the subsurface. Those model codes that are available (5, 6), require inordinate compute hardware, are complicated to use, and require collection of field data that may be difficult or expensive to obtain. In the future, as computer capabilities expand, this may not be a significant problem. Today, however, these complex models are not applied routinely to the design of vapor extraction systems.
This guide presents approximate methods to efficiently simulate the movement of air through the vadose zone. These methods neglect the presence of water and other liquids in the vadose zone; however, these techniques are much easier to apply and require significantly less computer hardware than more robust numerical models.
This guide should be used by groundwater modelers to approximately simulate the movement of air in the vadose zone.
Use of this guide to simulate subsurface air movement does not guarantee that the airflow model is valid. This guide simply describes mathematical techniques for simulating subsurface air movement with groundwater modeling codes. As with any modeling study, the modeler must have a thorough understanding of site conditions with supporting data in order to properly appl...
SCOPE
1.1 This guide covers the use of a groundwater flow modeling code to simulate the movement of air in the subsurface. This approximation is possible because the form of the groundwater 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 groundwater 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 groundwater flow modeling code. This guide does not recommend the use of a particular model code. Most groundwater 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 groundwater flow modeling codes. This guide does not preclude the use of other techniques, but presents techniques that can be easily applied using existing groundwater flow modeling codes.
1.4 This guide is one of a series of standards on groundwater 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 standard. No other units of measurement are included in this 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 ...
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Designation:D5719 −95(Reapproved 2006)
Standard Guide for
Simulation of Subsurface Airflow Using Groundwater 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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope 1.7 This guide offers an organized collection of information
or a series of options and does not recommend a specific
1.1 This guide covers the use of a groundwater flow
course of action. This document cannot replace education or
modeling code to simulate the movement of air in the subsur-
experienceandshouldbeusedinconjunctionwithprofessional
face. This approximation is possible because the form of the
judgment. Not all aspects of this guide may be applicable in all
groundwater flow equations are similar in form to airflow
circumstances. This ASTM standard is not intended to repre-
equations. Approximate methods are presented that allow the
sent or replace the standard of care by which the adequacy of
variables in the airflow equations to be replaced with equiva-
a given professional service must be judged, nor should this
lent terms in the groundwater flow equations. The model
document be applied without consideration of a project’s many
output is then transformed back to airflow terms.
unique aspects. The word “Standard” in the title of this
1.2 This guide illustrates the major steps to take in devel-
document means only that the document has been approved
oping an airflow model using an existing groundwater flow
through the ASTM consensus process.
modeling code. This guide does not recommend the use of a
particularmodelcode.Mostgroundwaterflowmodelingcodes
2. Referenced Documents
can be utilized, because the techniques described in this guide
2.1 ASTM Standards:
require modification to model input and not to the code.
D653Terminology Relating to Soil, Rock, and Contained
1.3 This guide is not intended to be all inclusive. Other
Fluids
similar techniques may be applicable to airflow modeling, as
D5447GuideforApplicationofaGroundwaterFlowModel
well as more complex variably saturated groundwater flow
to a Site-Specific Problem
modeling codes. This guide does not preclude the use of other
D5490Guide for Comparing Ground-Water Flow Model
techniques, but presents techniques that can be easily applied
Simulations to Site-Specific Information
using existing groundwater flow modeling codes.
E978Practice for Evaluating Mathematical Models for the
Environmental Fate of Chemicals (Withdrawn 2002)
1.4 This guide is one of a series of standards on groundwa-
ter model applications, including Guides D5447 and D5490.
3. Terminology
This guide should be used in conjunction with Guide D5447.
Other standards have been prepared on environmental
3.1 Definitions:
modeling, such as Practice E978.
3.1.1 boundary condition—a mathematical expression of a
stateofthephysicalsystemthatconstrainstheequationsofthe
1.5 The values stated in SI units are to be regarded as
mathematical model.
standard. No other units of measurement are included in this
standard.
3.1.2 computer code (computer program)—the assembly of
numerical techniques, bookkeeping, and control language that
1.6 This standard does not purport to address all of the
represents the model from acceptance of input data and
safety concerns, if any, associated with its use. It is the
instructions to delivery of output.
responsibility of the user of this standard to establish appro-
priate safety and health practices and determine the applica- 3.1.3 groundwater flow model—application of a mathemati-
bility of regulatory limitations prior to use. calmodeltorepresentasite-specificgroundwaterflowsystem.
1 2
ThisguideisunderthejurisdictionofASTMCommitteeD18onSoilandRock For referenced ASTM standards, visit the ASTM website, www.astm.org, or
and is the direct responsibility of Subcommittee D18.21 on Groundwater and contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Vadose Zone Investigations. Standards volume information, refer to the standard’s Document Summary page on
Current edition approved July 1, 2006. Published August 2006. Originally the ASTM website.
approved in 1995. Last previous edition approved in 2000 as D5719–95 (2000). The last approved version of this historical standard is referenced on
DOI: 10.1520/D5719-95R06. www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5719−95 (2006)
3.1.4 mathematical model—( a) mathematical equations 4.1.2 Saturated hydraulic conductivity (K), both horizontal
expressing the physical system and including simplifying and vertical components, becomes air permeability (k or
assumptions, (b) the representation of a physical system by intrinsic permeability) in the pressure-squared technique and
mathematical expressions from which the behavior of the an equivalent air hydraulic conductivity in the pressure substi-
system can be deduced with known accuracy. tution technique.
4.1.3 Storage coefficient (S) becomes the air storage coeffi-
3.1.5 model—an assembly of concepts in the form of
cient (S );
mathematical equations that portray understanding of a natural a
4.1.4 The Vadose zone is considered a confined aquifer;
phenomenon.
and,
3.2 For definitions of other terms used in this guide, see
4.1.5 All boundary conditions are expressed in terms of air
Terminology D653.
pressure-squared, although constant flux boundary conditions
3.3 Symbols and Dimensions:
may be used in the pressure substitution technique.
3.3.1 A—cross-sectional area of cell [cm ].
4.2 Thegroundwatermodelingcodeisexecutedusingthese
3.3.2 g—acceleration due to gravity [cm/s ].
parameter and variable substitutions. The model results must
3.3.3 h—air-phase or water phase head [cm].
then be transformed to values representative of air. These
calculations are summarized as follows:
3.3.4 k—air phase permeability [cm ].
4.2.1 If the problem is formulated in terms of air pressure-
3.3.5 K—hydraulic conductivity [cm/s].
squared, the square root of the model-computed dependent
3.3.6 P—air phase pressure [g/cm-s ].
variable is computed at each cell;
3.3.7 P —reference air-phase pressure [g/cm-s ].
4.2.2 Flow rates computed by the pressure-squared ap-
3.3.8 q —specific discharge vector for air [cm/s]. proach must be transformed into equivalent airflow terms for
s
volumetric flow rates (q ) or mass flow rates (q ).
3.3.9 q—volumetric flow of water through cell [cm /s]. v m
4.2.3 No transformation of the output is required by the
3.3.10 q*—model-computed term related to airflow in units
pressure substitution technique, although the pressures may be
2 4
g -cm/s .
converted to more convenient units.
3.3.11 q —volumetric airflow [cm /s].
v
3.3.12 q —mass airflow [g/s].
5. Significance and Use
m
7 2 2
3.3.13 R—universal gas constant=8.314×10 [g-cm /s -
5.1 The use of vapor extraction systems (VES), also called
mol-K].
soil vapor extraction (SVE) or venting systems, is becoming a
−1
3.3.14 S —specific storage of the porous material [cm ]. common remedial technology applicable to sites contaminated
s
with volatile compounds (3, 4). A vapor extraction system is
3.3.15 t—time [s].
composed of wells or trenches screened within the vadose
3.3.16 T—temperature [K].
zone. Air is extracted from these wells to remove organic
−1
3.3.17 W—volumetric flux per unit volume [s ].
compoundsthatreadilypartitionbetweensolidorliquidphases
3.3.18 z—elevation head [cm]. into the gas phase. The volatile contaminants are removed in
the gas phase and treated or discharged to the atmosphere. In
3.3.19 ∂h—hydraulic head difference [cm].
many cases, the vapor extraction system also incorporates
3.3.20 ∂l—length of model cell [cm].
3 wells open to the atmosphere that act as air injection wells.
3.3.21 ρ—density of air [g/cm ].
3.3.22 θ—air-filled porosity [nd].
NOTE 1—Few model codes are available that allow simulation of the
2 2 2
movement of air, water, and nonaqueous liquids through the subsurface.
3.3.23 φ—pressure-squared (P ) [(g/cm-s ) ].
Those model codes that are available (5, 6), require inordinate compute
3.3.24 ω—average molecular weight of air [g/mol].
hardware, are complicated to use, and require collection of field data that
3.3.25 µ—dynamic viscosity of air [g/cm-s].
may be difficult or expensive to obtain. In the future, as computer
capabilities expand, this may not be a significant problem. Today,
4. Summary of Guide
however, these complex models are not applied routinely to the design of
vapor extraction systems.
4.1 The flow of gas (air in this case) through unsaturated
porous media can be approximated using groundwater flow
5.2 This guide presents approximate methods to efficiently
modeling codes. This is accomplished through substitution of
simulate the movement of air through the vadose zone. These
air-phase parameters and variables into the groundwater flow
methods neglect the presence of water and other liquids in the
equations. There are two substitution techniques discussed in
vadose zone; however, these techniques are much easier to
this guide, the pressure-squared technique (1), and the pres-
apply and require significantly less computer hardware than
sure substitution technique (2). These substitutions are sum-
more robust numerical models.
marized as follows:
5.3 This guide should be used by groundwater modelers to
4.1.1 The dependent variable, usually head, in the ground-
approximately simulate the movement of air in the vadose
water flow equation becomes pressure or pressure-squared;
zone.
5.4 Use of this guide to simulate subsurface air movement
The boldface numbers in parentheses refer to a list of references at the end of
this standard. does not guarantee that the airflow model is valid. This guide
D5719−95 (2006)
simply describes mathematical techniques for simulating sub- 6.2.7 Air-phase permeability is assumed to be independent
surface air movement with groundwater modeling codes. As of P, therefore, the Klinkenberg slip effect (10) can only be
with any modeling study, the modeler must have a thorough modeled as constant with respect to P.The coefficient S is the
a
understanding of site conditions with supporting data in order pneumatic equivalent of specific storage and if air-filled
to properly apply the techniques presented in this guide. porosity is constant with respect to time (that is, water
movement is neglected) then:
6. Pressure-Squared Substitution Procedure
θµ
6.1 The pressure-squared substitution procedure is adapted
S 5 (8)
a
=φ
from Baehr and Joss (1). The technique allows simulation of
the flow of gas (air in this case) through porous media using
6.2.8 The change of variable φ= P results in a linear
groundwater flow modeling codes. This is accomplished
equation for steady-state airflow. The transient equation is
through substitution of air-phase parameters and variables into
1/2
linearized by assuming φ = P in the definition of S ,
atm a
the groundwater flow equations. These substitutions are sum-
where P is the prevailing atmospheric pressure.
atm
marized as follows:
6.2.8.1 Massmann (2)describestheerrorsinvolvedwiththe
6.2 Airflow Equation—The following presentation outlines
pressure-squared substitution described above, as well as
the essential assumptions of the airflow equation. A more
simplysubstitutingpressureforhead.Theerrorinthepressure-
detailed presentation providing justification of the various
squared substitution is less than 1% when the pressure
assumptions is provided by Baehr and Hult (7).
difference between any two points in the flow field is less than
6.2.1 The conservation of mass equation for airflow in an
0.2 atmospheres (atm) and less than 5% when the pressure
unsaturated porous medium is given by the following:
difference is less than 0.8 atm. When substituting pressure
(insteadofpressure-squared)forhead,theerrorsaresimilarfor
]
~ρθ!1π·~ρ;q ! 50 (1)
s
pressure differences less than 0.2 atm, but are quite large for
]t
pressure differences greater than 0.5 atm. In most cases, the
6.2.2 Darcy’s Law for airflow is assumed as follows:
pressure differences will be less than 0.2 atm; therefore, either
ρg
substitution may be used in environmental modeling (see
;q 52 'k πh (2)
s
µ
Section 7 for a description of the pressure substitution tech-
nique).
6.2.3 Hubbert (1940) defined the head for a compressible
6.2.9 Eq 7 can be directly compared to the linear ground-
fluid as follows:
water flow equation. The simplifying assumptions needed to
1 P1
h 5 z1 dP (3) arrive at this linear airflow equation are summarized as
*
P
g ρ
follows:
6.2.4 The Ideal Gas Law is assumed to relate pressure and
6.2.9.1 Darcy’s law is valid for airflow;
density and thus provides a model for air compressibility as
6.2.9.2 The elevation component of pneumatic head is
follows:
neglected;
ωP
6.2.9.3 Temperature effects are neglected;
ρ 5 (4)
RT
6.2.9.4 The Ideal Gas law is a valid model for compress-
6.2.5 Substituting Eq 4 into Eq 3, assuming ω and T are
ibility;
constant, neglecting the elevation component of head (that is
6.2.9.5 The Klinkenberg slip effect is neglected;
small for air compared to the pressure component) and
6.2.9.6 Water movement and consolidation are neglected,
substituting into Eq 2 gives the following expression for
therefore porosity is constant with respect to time; and
Darcy’s Law in terms of P:
1/2
6.2.9.7 φ = P in definition of storage coefficient S .
atm a
6.2.10 BaehrandHult (7)examinedtheconsequencesofthe
;q 52 'k πP (5)
s
µ
assumptions presented in 6.2.9. The authors found that the
linearairflowmodelgivenbyEq7isagoodworkingmodelfor
6.2.6 Substituting Eq 4 and Eq 5 into Eq 1, and then using
essentially all environmental applications.
the following linearizing change of variable suggested by
Muskat and Botset (8) for airflow:
6.3 Groundwater Flow Equation—The following ground-
water flow equation is solved by many groundwater flow
φ 5 P (6)
models:
yields the following three-dimensional airflow equation in
] ]h ] ]h ] ]h ]h
Cartesian coordinates that is analogous in form to the ground-
K 1 K 1 K 2 W 5 S (9)
S D S D S D
xx yy zz s
water flow equation solved by many groundwater flow models ]x ]x ]y ]y ]z ]z ]t
(MODFLOW (9), for example):
where: x, y,and zareCartesiancoordinatesalignedalongthe
] ]φ ] ]φ ] ]φ ]φ
major axes of the hydraulic conductivity tensor with diagonal
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
components K , K ,K .
xx yy zz
where x, y, and z are Cartesian coordinates aligned along the 6.3.1
...
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