1、Designation: D 5719 95 (Reapproved 2006)Standard Guide forSimulation of Subsurface Airflow Using Ground-Water FlowModeling Codes1This standard is issued under the fixed designation D 5719; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revi
2、sion, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This guide covers the use of a ground-water flowmodeling code to simulate the movement of air in th
3、e subsur-face. This approximation is possible because the form of theground-water flow equations are similar in form to airflowequations. Approximate methods are presented that allow thevariables in the airflow equations to be replaced with equiva-lent terms in the ground-water flow equations. The m
4、odeloutput is then transformed back to airflow terms.1.2 This guide illustrates the major steps to take in devel-oping an airflow model using an existing ground-water flowmodeling code. This guide does not recommend the use of aparticular model code. Most ground-water flow modelingcodes can be utili
5、zed, because the techniques described in thisguide require modification to model input and not to the code.1.3 This guide is not intended to be all inclusive. Othersimilar techniques may be applicable to airflow modeling, aswell as more complex variably saturated ground-water flowmodeling codes. Thi
6、s guide does not preclude the use of othertechniques, but presents techniques that can be easily appliedusing existing ground-water flow modeling codes.1.4 This guide is one of a series of standards on ground-water model applications, including Guides D 5447 andD 5490. This guide should be used in c
7、onjunction with GuideD 5447. Other standards have been prepared on environmentalmodeling, such as Practice E 978.1.5 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.6 This standard does not purport to address all of thesafety
8、concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.1.7 This guide offers an organized collection of informationor a series of opt
9、ions and does not recommend a specificcourse of action. This document cannot replace education orexperience and should be used in conjunction with professionaljudgment. Not all aspects of this guide may be applicable in allcircumstances. This ASTM standard is not intended to repre-sent or replace th
10、e standard of care by which the adequacy ofa given professional service must be judged, nor should thisdocument be applied without consideration of a projects manyunique aspects. The word “Standard” in the title of thisdocument means only that the document has been approvedthrough the ASTM consensus
11、 process.2. Referenced Documents2.1 ASTM Standards:2D 653 Terminology Relating to Soil, Rock, and ContainedFluidsD 5447 Guide for Application of a Ground-Water FlowModel to a Site-Specific ProblemD 5490 Guide for Comparing Ground-Water Flow ModelSimulations to Site-Specific InformationE 978 Practice
12、 for Evaluating Mathematical Models for theEnvironmental Fate of Chemicals33. Terminology3.1 Definitions:3.1.1 boundary conditiona mathematical expression of astate of the physical system that constrains the equations of themathematical model.3.1.2 computer code (computer program)the assembly ofnume
13、rical techniques, bookkeeping, and control language thatrepresents the model from acceptance of input data andinstructions to delivery of output.3.1.3 ground-water flow modelapplication of a math-ematical model to represent a site-specific ground-water flowsystem.3.1.4 mathematical model(a) mathemat
14、ical equations ex-pressing the physical system and including simplifying as-sumptions, (b) the representation of a physical system bymathematical expressions from which the behavior of thesystem can be deduced with known accuracy.1This guide is under the jurisdiction ofASTM Committee D18 on Soil and
15、 Rockand is the direct responsibility of Subcommittee D18.21 on Ground Water andVadose Zone Investigations.Current edition approved July 1, 2006. Published August 2006. Originallyapproved in 1995. Last previous edition approved in 2000 as D 5719 95 (2000).2For referenced ASTM standards, visit the AS
16、TM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Withdrawn.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428
17、-2959, United States.3.1.5 modelan assembly of concepts in the form ofmathematical equations that portray understanding of a naturalphenomenon.3.2 For definitions of other terms used in this guide, seeTerminology D 653.3.3 Symbols and Dimensions:3.3.1 Across-sectional area of cell cm2.3.3.2 gacceler
18、ation due to gravity cm/s2.3.3.3 hair-phase or water phase head cm.3.3.4 kair phase permeability cm2.3.3.5 Khydraulic conductivity cm/s.3.3.6 Pair phase pressure g/cm-s2.3.3.7 P0reference air-phase pressure g/cm-s2.3.3.8 qsspecific discharge vector for air cm/s.3.3.9 qvolumetric flow of water throug
19、h cell cm3/s.3.3.10 q*model-computed term related to airflow in unitsg2-cm/s4.3.3.11 qvvolumetric airflow cm3/s.3.3.12 qmmass airflow g/s.3.3.13 Runiversal gas constant = 8.314 3 107g-cm2/s2-mol-K.3.3.14 Ssspecific storage of the porous material cm1.3.3.15 ttime s.3.3.16 Ttemperature K.3.3.17 Wvolum
20、etric flux per unit volume s1.3.3.18 zelevation head cm.3.3.19 hhydraulic head difference cm.3.3.20 llength of model cell cm.3.3.21 rdensity of air g/cm3.3.3.22 uair-filled porosity nd.3.3.23 fpressure-squared (P2) (g/cm-s2)2.3.3.24 vaverage molecular weight of air g/mol.3.3.25 dynamic viscosity of
21、air g/cm-s.4. Summary of Guide4.1 The flow of gas (air in this case) through unsaturatedporous media can be approximated using ground-water flowmodeling codes. This is accomplished through substitution ofair-phase parameters and variables into the ground-water flowequations. There are two substituti
22、on techniques discussed inthis guide, the pressure-squared technique (1),4and the pres-sure substitution technique (2). These substitutions are sum-marized as follows:4.1.1 The dependent variable, usually head, in the ground-water flow equation becomes pressure or pressure-squared;4.1.2 Saturated hy
23、draulic conductivity (K), both horizontaland vertical components, becomes air permeability (k orintrinsic permeability) in the pressure-squared technique andan equivalent air hydraulic conductivity in the pressure substi-tution technique.4.1.3 Storage coefficient (S) becomes the air storage coeffi-c
24、ient (Sa);4.1.4 The Vadose zone is considered a confined aquifer;and,4.1.5 All boundary conditions are expressed in terms of airpressure-squared, although constant flux boundary conditionsmay be used in the pressure substitution technique.4.2 The ground-water modeling code is executed usingthese par
25、ameter and variable substitutions. The model resultsmust then be transformed to values representative of air. Thesecalculations are summarized as follows:4.2.1 If the problem is formulated in terms of air pressure-squared, the square root of the model-computed dependentvariable is computed at each c
26、ell;4.2.2 Flow rates computed by the pressure-squared ap-proach must be transformed into equivalent airflow terms forvolumetric flow rates (qv) or mass flow rates (qm).4.2.3 No transformation of the output is required by thepressure substitution technique, although the pressures may beconverted to m
27、ore convenient units.5. Significance and Use5.1 The use of vapor extraction systems (VES), also calledsoil vapor extraction (SVE) or venting systems, is becoming acommon remedial technology applicable to sites contaminatedwith volatile compounds (3, 4). A vapor extraction system iscomposed of wells
28、or trenches screened within the vadosezone. Air is extracted from these wells to remove organiccompounds that readily partition between solid or liquid phasesinto the gas phase. The volatile contaminants are removed inthe gas phase and treated or discharged to the atmosphere. Inmany cases, the vapor
29、 extraction system also incorporateswells open to the atmosphere that act as air injection wells.NOTE 1Few model codes are available that allow simulation of themovement of air, water, and nonaqueous liquids through the subsurface.Those model codes that are available (5, 6), require inordinate compu
30、tehardware, are complicated to use, and require collection of field data thatmay be difficult or expensive to obtain. In the future, as computercapabilities expand, this may not be a significant problem. Today,however, these complex models are not applied routinely to the design ofvapor extraction s
31、ystems.5.2 This guide presents approximate methods to efficientlysimulate the movement of air through the vadose zone. Thesemethods neglect the presence of water and other liquids in thevadose zone; however, these techniques are much easier toapply and require significantly less computer hardware th
32、anmore robust numerical models.5.3 This guide should be used by ground-water modelers toapproximately simulate the movement of air in the vadosezone.5.4 Use of this guide to simulate subsurface air movementdoes not guarantee that the airflow model is valid. This guidesimply describes mathematical te
33、chniques for simulating sub-surface air movement with ground-water modeling codes. Aswith any modeling study, the modeler must have a thoroughunderstanding of site conditions with supporting data in orderto properly apply the techniques presented in this guide.6. Pressure-Squared Substitution Proced
34、ure6.1 The pressure-squared substitution procedure is adaptedfrom Baehr and Joss (1). The technique allows simulation ofthe flow of gas (air in this case) through porous media usingground-water flow modeling codes. This is accomplished4The boldface numbers in parentheses refer to a list of reference
35、s at the end ofthis standard.D 5719 95 (2006)2through substitution of air-phase parameters and variables intothe ground-water flow equations. These substitutions are sum-marized as follows:6.2 Airflow EquationThe following presentation outlinesthe essential assumptions of the airflow equation. A mor
36、edetailed presentation providing justification of the variousassumptions is provided by Baehr and Hult (7).6.2.1 The conservation of mass equation for airflow in anunsaturated porous medium is given by the following:tru! 1r;qs! 5 0 (1)6.2.2 Darcys Law for airflow is assumed as follows:; qs52rg k h (
37、2)6.2.3 Hubbert (1940) defined the head for a compressiblefluid as follows:h 5 z 11g*P0P1rdP (3)6.2.4 The Ideal Gas Law is assumed to relate pressure anddensity and thus provides a model for air compressibility asfollows:r5vPRT(4)6.2.5 Substituting Eq 4 into Eq 3, assuming v and T areconstant, negle
38、cting the elevation component of head (that issmall for air compared to the pressure component) andsubstituting into Eq 2 gives the following expression forDarcys Law in terms of P:; qs521 k P (5)6.2.6 Substituting Eq 4 and Eq 5 into Eq 1, and then usingthe following linearizing change of variable s
39、uggested byMuskat and Botset (8) for airflow:f5P2(6)yields the following three-dimensional airflow equation inCartesian coordinates that is analogous in form to the ground-water flow equation solved by many ground-water flow models(MODFLOW (9), for example):xSkxxfxD1ySkyyfyD1zSkzzfzD5 Saft(7)where x
40、, y, and z are Cartesian coordinates aligned along themajor axes of the permeability tensor with diagonal compo-nents kxx, kyy, and kzz.6.2.7 Air-phase permeability is assumed to be independentof P, therefore, the Klinkenberg slip effect (10) can only bemodeled as constant with respect to P. The coe
41、fficient Sais thepneumatic equivalent of specific storage and if air-filledporosity is constant with respect to time (that is, watermovement is neglected) then:Sa5u=f(8)6.2.8 The change of variable f = P2results in a linearequation for steady-state airflow. The transient equation islinearized by ass
42、uming f1/2= Patmin the definition of Sa,where Patmis the prevailing atmospheric pressure.6.2.8.1 Massmann (2) describes the errors involved with thepressure-squared substitution described above, as well assimply substituting pressure for head. The error in the pressure-squared substitution is less t
43、han 1 % when the pressuredifference between any two points in the flow field is less than0.2 atmospheres (atm) and less than 5 % when the pressuredifference is less than 0.8 atm. When substituting pressure(instead of pressure-squared) for head, the errors are similar forpressure differences less tha
44、n 0.2 atm, but are quite large forpressure differences greater than 0.5 atm. In most cases, thepressure differences will be less than 0.2 atm; therefore, eithersubstitution may be used in environmental modeling (seeSection 7 for a description of the pressure substitution tech-nique).6.2.9 Eq 7 can b
45、e directly compared to the linear ground-water flow equation. The simplifying assumptions needed toarrive at this linear airflow equation are summarized asfollows:6.2.9.1 Darcys law is valid for airflow;6.2.9.2 The elevation component of pneumatic head isneglected;6.2.9.3 Temperature effects are neg
46、lected;6.2.9.4 The Ideal Gas law is a valid model for compress-ibility;6.2.9.5 The Klinkenberg slip effect is neglected;6.2.9.6 Water movement and consolidation are neglected,therefore porosity is constant with respect to time; and6.2.9.7 f1/2= Patmin definition of storage coefficient Sa.6.2.10 Baeh
47、r and Hult (7) examined the consequences of theassumptions presented in 6.2.9. The authors found that thelinear airflow model given by Eq 7 is a good working model foressentially all environmental applications.6.3 Ground-Water Flow EquationThe following ground-water flow equation is solved by many g
48、round-water flowmodels:xSKxxhxD1ySKyyhyD1zSKzzhzD2 W 5 Ssht(9)where: x, y, and z are Cartesian coordinates aligned along themajor axes of the hydraulic conductivity tensor with diagonalcomponents Kxx, Kyy,Kzz.6.3.1 The purpose of the procedure presented in this guide isto facilitate airflow simulati
49、ons by matching Eq 7 and Eq 9 sothat the numerical solution coded in ground-water flow modelscan be used to solve the airflow equation. This is accomplishedwith the following parameter matches:hf (10)Kk (11)SsSa(12)6.3.2 The parameter matching allows the hydraulic headand flow output from the ground-water model to be interpretedfor the airflow model in accordance with 6.3.6.4 Boundary ConditionsThere are only two permissibletypes of boundary condition
