D. Johnson Wright_2010_Dense, viscous brine behavior in heterogeneous porous medium systems

Dense,viscous brine behavior in heterogeneous porous medium systems

D.Johnson Wright a ,J.A.Pedit a ,S.

E.Gasda a ,M.W.Farthing b ,L.L.Murphy c ,S.R.Knight d ,G.R.Brubaker d ,https://www.doczj.com/doc/134439707.html,ler a ,?

a Department of Environmental Sciences and Engineering,University of North Carolina,Chapel Hill,NC 27599-7431,USA

b U.S.Army Engineer Research and Development Center,Vicksburg,MS 39180-6199,USA

c CH2M Hill,Atlanta,GA 30346,USA d

AECOM,Morrisville,NC 27560,USA

a r t i c l e i n f o a

b s t r a

c t

Article history:

Received 15December 2009

Received in revised form 30March 2010Accepted 31March 2010

Available online 14April 2010The behavior of dense,viscous calcium bromide brine solutions used to remediate systems contaminated with dense nonaqueous phase liquids (DNAPLs)is considered in laboratory and ?eld porous medium systems.The density and viscosity of brine solutions are experimentally investigated and functional forms ?t over a wide range of mass fractions.A density of 1.7times,and a corresponding viscosity of 6.3times,that of water is obtained at a calcium bromide mass fraction of 0.53.A three-dimensional laboratory cell is used to investigate the establishment,persistence,and rate of removal of a strati ?ed dense brine layer in a controlled system.Results from a ?eld-scale experiment performed at the Dover National Test Site are used to investigate the ability to establish and maintain a dense brine layer as a component of a DNAPL recovery strategy,and to recover the brine at suf ?ciently high mass fractions to support the economical reuse of the brine.The results of both laboratory and ?eld experiments show that a dense brine layer can be established,maintained,and recovered to a signi ?cant extent.Regions of unstable density pro ?les are shown to develop and persist in the ?eld-scale experiment,which we attribute to regions of low hydraulic conductivity.The saturated –unsaturated,variable-density groundwater ?ow simulation code SUTRA is modi ?ed to describe the system of interest,and used to compare simulations to experimental observations and to investigate certain unobserved aspects of these complex systems.The model results show that the standard model formulation is not appropriate for capturing the behavior of sharp density gradients observed during the dense brine experiments.

?2010Elsevier B.V.All rights reserved.

Keywords:DNAPL

Remediation Instabilities Fingering Modeling

1.Introduction

The effective,ef ?cient,and economical remediation of subsurface systems contaminated with DNAPLs remains a signi ?cant environmental challenge.Over the last several years,the use of dense-brine methods have been explored as a means to control DNAPL movement during mobilization-based remediation approaches.We refer collectively to these approaches as brine-based remediation technologies (BBRTs).The basic premise behind BBRTs is that a dense brine can be used to increase the density of the aqueous phase and inhibit downward migration of DNAPL in the presence of DNAPL mobilizing ?ushing solutions,such as surfactants,or to induce upward mobilization of brine by increasing buoy-ancy forces.

An example application of BBRTs involves the establish-ment of a dense brine layer above a low permeability layer and beneath a DNAPL-contaminated region,lowering of the water table to increase gravity forces acting on the DNAPL to mobilize the DNAPL downward,vertical ?ushing with a surfactant solution to further mobilize the DNAPL downward,

Journal of Contaminant Hydrology 115(2010)46–63

?Corresponding author.

E-mail addresses:nomad12@https://www.doczj.com/doc/134439707.html, (D.J.Wright),

pedit@https://www.doczj.com/doc/134439707.html, (J.A.Pedit),sgasda@https://www.doczj.com/doc/134439707.html, (S.E.Gasda),matthew.w.farthing@https://www.doczj.com/doc/134439707.html, (M.W.Farthing),

llmurph@https://www.doczj.com/doc/134439707.html, (L.L.Murphy),sknight@https://www.doczj.com/doc/134439707.html, (S.R.Knight),GBrubaker@https://www.doczj.com/doc/134439707.html, (G.R.Brubaker),casey_miller@https://www.doczj.com/doc/134439707.html, (C.T.

Miller).

0169-7722/$–see front matter ?2010Elsevier B.V.All rights reserved.doi:

10.1016/j.jconhyd.2010.03.005

Contents lists available at ScienceDirect

Journal of Contaminant Hydrology

j o u r n a l h o m e p a g e :w ww.e l s ev i e r.c o m /l o c a t e /j c o n hyd

collection of the mobilized DNAPL from the top of the brine layer,and secondary treatment of the residual DNAPL remaining in the unsaturated zone using,for example,vapor extraction.Such an approach has proven effective in three-dimensional,heterogeneous laboratory systems(Johnson et al.,2004).

Laboratory experiments to investigate a range of BBRTs have been performed in one-,two-,and three-dimensional porous medium systems,and heterogeneous systems have been the focus of these experiments(Miller et al.,2000;Hill et al.,2001;Johnson et al.,2004).Encouraging results have been reported based upon these experiments,including the ef?cient removal of the high fractions of DNAPL from heterogeneous,three-dimensional systems(Hill et al.,2001; Johnson et al.,2004).

The encouraging results of laboratory investigations of BBRTs notwithstanding,many open fundamental issues must be resolved before a determination of the feasibility of using BBRTs for active source-zone remediation at the?eld scale can be made.One set of these open issues deals with the behavior of the dense brine solutions of which relatively little is known.For example,the viscosity of calcium bromide solutions has not been carefully measured and functionally described for a complete range of mass fractions.In addition, relatively little work has been done to understand?ow and transport phenomena in porous medium systems for solu-tions that have the range of density and viscosity variations of interest for BBRTs.It is known that non-ideal dispersion behavior exists for other non-dilute brine systems,although the appropriate model to describe such systems is an open issue(Hassanizadeh and Leijnse,1995;Landman et al., 2007b).As with any system that exhibits the range of density and viscosity variations characteristic of BBRTs,both gravity and viscous?ngering instabilities are a potential concern depending upon displacement patterns and medium char-acteristics.As a result of these complexities,no mechanistic simulation model has been developed to simulate brine behavior during the application of BBRTs.

The fundamental open issues with dense brine behavior are more than intellectual curiosities if one wishes to carefully assess the practicality of BBRTs.For example,it is important to understand:the expected density of a brine layer that can be achieved,which affects the DNAPLs for which movement can be controlled;the time scale of the stability of a brine layer,which impacts methods needed to maintain the integrity of a brine barrier;the fraction of the brine that can be recovered as a function of mass fraction, which impacts economical ef?ciency and the potential for reuse;the rate of removal of relatively dilute brine solutions, which may not be reusable but may be required to ensure environmental compliance;and strategies and limitations for emplacing and removing brine effectively in complex systems,which will determine the number,con?guration, and use the schedule of injection and removal wells.

The overall goal of this study is to investigate some of the open scienti?c and practical issues associated with dense, viscous brine behavior in heterogeneous porous medium systems.The speci?c objectives of this work include:(1)to determine the density and viscosity of calcium bromide solutions over a wide range of mass fractions;(2)to determine the feasibility of establishing and maintaining a high-density layer in a heterogeneous porous medium at the laboratory scale;(3)to assess the rate of brine recovery from a heterogeneous laboratory system;(4)to assess the scalability of experimental results achieved in the laboratory to a heterogeneous?eld-scale system;(5)to evaluate the role of instabilities in brine layer emplacement,maintenance,and removal at the?eld-scale;(6)to develop a numerical simulation model to describe dense brine movement;(7)to apply the numerical model to support the understanding of laboratory and?eld observations;and(8)to assess remaining issues requiring resolution to achieve a mature level of understanding of dense brine behavior in heterogeneous porous medium systems.

2.Background

2.1.Overview

The dense,viscous?uids of concern in this work can exhibit complex patterns of?ow and transport in porous medium systems that depend upon?uid properties,solid medium properties,and displacement patterns(Sudicky, 1986;Voss and Souza,1987;Schincariol and Schwartz, 1990;Welty and Gelhar,1991,1992;Schincariol et al., 1994).While such systems are of signi?cant recent interest due to applications that include waste disposal(Nordbotten et al.,2004;Rumynin et al.,2005),DNAPL remediation(Miller et al.,2000;Hill et al.,2001;Johnson et al.,2004),and saltwater intrusion(Zhang et al.,2001;Held et al.,2005; Abarca et al.,2007;Brovelli et al.,2007;Goswami and Clement,2007),our understanding of such systems is not complete.In the sections that follow,we brie?y summarize the state of knowledge regarding equations of state,density effects,viscous effects,porous medium property effects, model formulation,and simulators.

2.2.Equations of state

Fluid?ow through a porous medium depends on the density and viscosity of the?uid.In systems with a wide range of variability in these properties,equations of state have to be established to effectively model the system.Although there is a lack of published data for calcium bromide,several functional forms for density,ρ,and dynamic viscosity,μ, have been proposed for sodium chloride.The most commonly used non-dilute forms are for density(Kolditz et al.,1998; Diersch and Kolditz,2002;Watson et al.,2002),

ρ=ρ0expγω

eTe1Twhereρ0is the reference density,γis a?tting parameter,and ωis the salt mass fraction;and for viscosity(Watson et al., 2002;Zhou et al.,2005;Johannsen et al.,2006)

μ=μ01+Aω+Bω2+Cω3

;e2Twhereωis the salt mass fraction and A,B,and C are?tting parameters.

However,several other studies have used laboratory or?eld data to?t a range of empirical expressions for density and viscosity relations(Rowe and Chou,1970;Mercer et al.,1975; Phillips et al.,1981;Gill,1982;Kemp et al.,1989;McCain,1991;

47

D.J.Wright et al./Journal of Contaminant Hydrology115(2010)46–63

Batzle and Wang,1992;Palliser and McKibbin,1998).These functional forms,all of which were derived for sodium chloride with the exception of Gill(1982)and McCain(1991),were compared by Adams and Bachu(2002).They found that several different functional forms for density and viscosity represented the available data for sodium chloride adequately for a range of conditions depending on salinity,pressure,and temperature. They also found that both density and viscosity differences between estimated values increased with increasing mass fraction with a difference in density of up to20%,and a difference in viscosity of up to50%noted between different estimation methods at high mass fractions.Such differences suggest that care must be taken in choosing an appropriate equation of state. The density and viscosity properties of calcium bromide,and their respective equations of state,have not been reported over the wide range of mass fractions of interest for BBRTs.

2.3.Density effects

Fluid densities change as a function of?uid pressures, temperatures,and chemical composition.The primary causes of density-dependent?ow are due to temperature changes and compositional effects.Both of these motivating conditions have been the source of a substantial amount of recent research(Ackerer et al.,1999;Schotting et al.,1999;Simmons et al.,2001,2002;Diersch and Kolditz,2002;Prasad and Simmons,2003;Jiao and H?tzl,2004;Wood et al.,2004;Dentz et al.,2006;Nigam and Woods,2006;Graf and Therrien,2007; Flowers and Hunt,2007;Landman and Schotting,2007). When nonuniform densities exist in a porous medium system, a gravitational driving force gives rise to preferential?ow of a more dense?uid overlying a less dense?uid in the vertical direction and can result in gravity?ngering(Welty and Gelhar,1991;Schincariol et al.,1994,1997;Simmons and Narayan,1997;Simmons et al.,2001;Prasad and Simmons, 2003;Woods and Carey,2007).Density-dependent?ow will occur until either an impermeable boundary is encountered or the?uid properties,hence density,change to remove the density gradient.In other words,such systems tend toward a stable state.For the non-isothermal case,this implies stability when an isothermal condition has been obtained,or con-versely that unstable conditions and?uid motion can persist in certain cases,such as in a classical Raleigh–Bernard convection system(Gebhart et al.,1988).

For compositionally-motivated density-dependent?ow,a different situation results.The thermodynamic equilibrium condition for a closed system is a solution of uniform composition and density.However,gravitational forces result in a quasi-stable distribution,which can be a relatively sharply strati?ed system with a thin transition region for cases in which the pore space is?lled with sources of two?uids that differ substantially in density.The time scale to achieve a quasi-stable strati?ed con?guration are in general much shorter than the time scale needed to achieve the thermodynamic equilibrium typi?ed by uniform composition,since diffusive and dispersive transport is relatively slow in such non-ideal systems.

2.4.Viscous effects

The standard Darcy approximation of the momentum equation predicts that speci?c discharge is inversely propor-tional to the viscosity.The generally small change in viscosity that results from compositional changes in most systems has led to a tendency to consider viscosity constant,even in systems for which density variation is of a concern(Fried, 1975;Ophori,1998).This seems reasonable for many systems and is a convenient assumption.

Viscosity variations can be important and give rise to both interesting and complex issues.For certain compositional systems,such as the dense brines of focus in this work, viscosities can be several times that of water,which greatly exceeds the contrasts observed in typical saltwater intrusion applications.Changes in the viscosity of this magnitude can signi?cantly affect?ow and transport phenomena.Viscosity variations lead to the potential to develop unstable?ngering when a less viscous solution displaces a more viscous solution (Heller,1966;Wooding,1969;Paterson,1985;Welty and Gelhar,1991;Juanes and Blunt,2006;Nagatsu et al.,2007).In addition,when compositional variations lead to signi?cant changes in both density and viscosity,interactions between viscous and gravity instabilities will result(Jiao and H?tzl, 2004;Flowers and Hunt,2007).The nature of these interactions has not been completely elucidated for dense viscous brines.

2.5.Porous medium property effects

The effects of density gradients on groundwater?ow have been widely studied in recent years,so have the effects of heterogeneity in hydraulic properties of porous media on ?ow and transport(Smith and Freeze,1979;Schincariol and Schwartz,1990;Simmons and Narayan,1997;Schincariol, 1998;Shikaze et al.,1998;Elfeki and Dekking,2001; Simmons et al.,2001;Prasad and Simmons,2003;Scanlon et al.,2003;Juanes and Blunt,2006).Investigations of the effects of heterogeneity on density-dependent?ow have demonstrated a dependence of instability onset and growth or decay on the magnitude of spatial variability in subsurface characteristics,such as hydraulic conductivity(Schincariol and Schwartz,1990;Simmons et al.,2001).

The onset and growth of density instabilities in heteroge-neous media is complex.While local perturbations in the permeability?eld may induce the formation and growth of instabilities,continued?ow through heterogeneous media may in turn reduce growth and increase stabilization of perturbations due to mixing caused by dispersion(Schincariol and Schwartz,1990;Schincariol et al.,1997).In addition,the existence of low permeable regions such as clay lenses can dampen instability growth and in cases where the density contrast is low stabilize perturbations(Schincariol et al., 1997).In addition,simulations conducted by Schincariol et al. (1997)suggested that low permeability regions can dampen the upward migration of https://www.doczj.com/doc/134439707.html,paratively,much less is known about systems for which both large changes in density and viscosity occur in heterogeneous systems.

2.6.Model formulation

While mechanistic macroscale models based upon phase and species conservation of mass equations are well estab-lished and the standard basis for formulations involving density-dependent?ow in porous medium systems(e.g., Hassanizadeh and Gray,1979;Voss,1984;Voss and Souza,

48 D.J.Wright et al./Journal of Contaminant Hydrology115(2010)46–63

1987Bear and Bachmat,1991),the adequacy of the closure of such models is in question.As noted above,relations for densities and viscosities as functions of mass fractions are not well established and have yet to be detailed for the calcium bromide solutions of focus in this work.Without accurate relations for such key variables,model formulations and the resultant simulations will be inaccurate as well.

In addition,high-concentration brine solutions are non-ideal solutions.The signi?cance of this observation is manifest in the failure of traditional advective–dispersive models to describe the observed movement and dispersion of brine fronts.Formal averaging(Hassanizadeh and Leijnse, 1995;Schotting et al.,1999;Watson et al.,2002)and homogenization approaches(Landman et al.,2007b)have been used to advance models to describe such systems,but the appropriate model formulation is considered an open issue.Recent work by Gray and Miller(2009)has advanced a new class of models that appear promising,but these models have not yet been compared to the experimental data.

Experimental observations have been made to support the non-ideal nature of the dense brine porous medium systems and to provide a basis for the development of the improved model formulations.High-concentration brines have been shown to deviate from the Fickian dispersion.Gravitational effects have been shown to have a stabilizing effect on upward displacement of brine in column studies decreasing the observed amount of dispersion relative to an ideal,dilute tracer.This phenomena result in a decrease in the length of the mixing zone(Hassanizadeh and Leijnse,1995).Changes in dispersive properties have been shown to depend upon ?ow rates(Schotting et al.,1999;Watson et al.,2002; Landman et al.,2007b),density,viscosity,and concentration gradients(Welty and Gelhar,1991),porous medium proper-ties(Watson et al.,2002;Landman et al.,2007b),and the magnitude of the density contrast(Landman et al.,2007b).

2.7.Simulators

Several production-level?nite-element-and?nite-volume-based simulators have been developed to model variable-density subsurface?ow and transport.These include,but are not limited to,SUTRA(Voss,1984),FEFLOW(Diersch,2005), TOUGH2(Oldenburg and Pruess,1995),FEMWATER(Lin et al., 1997),and ROCKFLOW(Kolditz et al.,2001).Nonlinear compositional effects and their interaction with the heteroge-neous porous media mean that analytical or semi-analytical solutions are available in only limited,highly idealized cases (Verruijt,1968;van Duijn et al.,1998).As a result,a series of benchmark problems are typically used to evaluate model performance for some subset of the challenges associated with the density-dependent?ow and transport.

Available benchmarks range from stable displacements with low-density contrasts(Henry,1964)to highly unstable free-convection problems(Elder,1967).To be more speci?c, common test problems include the classical Henry saltwater intrusion problem(Henry,1964),the HYDROCOIN salt dome problem(Oldenburg and Pruess,1995;Konikow et al.,1997), and the low-density version of the three-dimensional salt pool problem(Oswald and Kinzelbach,2004).Stable dis-placement con?gurations with high-density contrasts are considered in column experiments(Hassanizadeh and Leijnse,1995;Schotting et al.,1999)as well as a high-density saltpool experiment(Oswald and Kinzelbach,2004).On the other hand,benchmarks like the salt lake(Simmons et al., 1999)and Elder(Elder,1967)problems involve con?gura-tions with dense?uid overlying less dense?uid and so exhibit highly unstable?ngering and solutions that are qualitatively different depending on the mesh resolution and numerical approximation(Frolkovic and De Schepper,2001;Diersch and Kolditz,2002).

Collectively these benchmarks highlight the particular challenges of modeling density-dependent?ow and trans-port.In addition to the basic complication of nonlinear closure relations for density and viscosity and potentially non-ideal dispersion behavior,density-dependent coupling places a premium on accurate,stable resolution of solution fronts and accurate velocity approximations(Diersch and Kolditz,2002;Mazzia and Putti,2002;Ackerer and Younes, 2008).For problems with gravity or viscous?ngering instabilities,mesh resolution has proven critical.In compar-isons among multiple simulators,a number of discrepancies have come to the forefront.Discretization effects have resulted from different mesh types and re?nement levels. For the Elder problem,several researchers have found varying results on whether the central?ow element is upwelling or downwelling due to changes in the mesh resolution(Voss and Souza,1987;Oldenburg and Pruess,1995;Kolditz et al., 1998;Ackerer et al.,1999;Diersch and Kolditz,2002;Woods et al.,2003;Park and Aral,2007).Similar in?uences of mesh discretization on the speed of propagating density?ngers and the number of these perturbations have been found with the salt lake problem as well(Wooding et al.,1997;Simmons et al.,1999;Diersch and Kolditz,2002).Some have even concluded that the Elder problem is not an appropriate benchmark problem due to the in?uence of the boundary conditions(Simpson and Clement,2003).

Recent efforts have been aimed at improving numerical methods to more accurately simulate the Elder problem as a benchmark(Ackerer and Younes,2008).More broadly, unstable systems and problems with sharp interfaces contin-ue to challenge and motivate research into improved numerical methods(Johannsen et al.,2006;Gotovac et al., 2007;Landman et al.,2007a;Younes et al.,2009).It seems clear that high-resolution simulation of dense,viscous?uids in complex porous medium systems remains dif?cult and that care is needed in applying existing simulators to such systems.

3.Approach

3.1.Overview

The work undertaken to meet the objectives of this study included characterization of solution properties,selecting and characterizing porous media,performance of three-dimen-sional laboratory cell experiments of brine emplacement and recovery,performance of a?eld-scale experiment of brine emplacement and recovery,and the modi?cation and appli-cation of a numerical model to simulate density and viscosity-dependent?ow and transport phenomena in heterogeneous porous medium systems.We detail the approach used for each of these components in the subsections that follow.

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3.2.Calcium bromide equations of state

Calcium bromide was chosen as the brine source because it is readily available in large quantities in a concentrated form of53%by weight(Synergy Fluids,Houston,Texas).In addition,the density of concentrated calcium bromide solutions can exceed the density of most DNAPLs,which allows the use of such solutions for controlling bulk DNAPL movement.This property is essential for BBRTs.

The objective of this aspect of the study was to develop equations of state for density and viscosity of high-concentration calcium bromide solutions.To do this,measurements of both

properties were made for a range of mass fractions.The density of calcium bromide solutions with mass fractions up to0.53was measured using an Anton Paar DMA48density meter.The meter measures density from0–3±0.0001g/cm3.All samples were measured at20°C.Viscosity was measured with a Haake Model B falling ball viscometer.All samples were measured at20°C and at mass fractions that corresponded with the measured density values.Several measurements were collected for each mass fraction sample due to measurement variations.The standard deviation ranged from0.0074cP at a mass fraction of zero to 0.0108cP at a mass fraction of0.53.

https://www.doczj.com/doc/134439707.html,boratory cell experiments

Laboratory experiments were undertaken to meet two objectives:(1)to determine the feasibility of establishing and maintaining a high-density brine layer with minimal dilution effects,and(2)to assess the rate at which brine can be removed from a system.The importance of the?rst objective is that the density of the brine layer that can be established determines the range of DNAPLs for which free-phase?ow can be controlled.The importance of the second objective is that the brines are expensive so it is advantageous to recycle these brines,and most?eld-scale applications of BBRTs will require removal of a substantial fraction of the brines after remediation is accomplished.The rate and mass fractions at which these brines can be recovered bear upon the ef?cacy of recycling of the brine and the overall cost of such technol-ogies.Because such aspects of these systems have not been investigated to date,it was appropriate to start with controlled laboratory studies.

Two laboratory experiments were conducted in a three-dimensional cell that measured22.5-cm long×16.5-cm wide×24-cm tall and was?tted with an aluminum cover. The cell was?lled with porous media to a height of approximately21cm.Each experiment was packed with a different medium.One experiment consisted of a quartz sand mix(QS),which was based on sieve analysis of the Dover sand(DS)and consisted of several Unimin Accusands(12/20, 20/30,30/40,and40/50)and two U.S.Silica sands(AFS50/70 and F95),and was packed as a homogenized mix.The other experiment was packed as a correlated random?eld with DS collected from the Dover National Test Site(DNTS)in Dover. The properties of each porous medium are provided in Table1.

To create a correlated random?eld for the DS experiment, the DS was sieved into12different sized fractions,all with a diameter less than2mm.The DS was packed into the laboratory cell using a21-layer heterogeneous packing based on a correlated random?eld model assuming aniso-tropic exponential covariance conditions and a log-normal particle size distribution(Christakos,1992;Deutsch and Journel,1992).Each layer consisted of cubes of homogeneous sands obtained from the sieved fractions of1.5-cm length and width and1-cm height.Correlation lengths of7.5and5.0cm for the horizontal and vertical planes,respectively,were used to match the scale of the tank used in the experiment.The mean and standard deviation of the log of particle size were ?0.789ln(mm)and2.39,respectively.

Both experiments contained a series of injection and extraction ports as well as sampling ports for monitoring in situ density during all phases of the BBRT.Stainless steel tubing(2.21-mm i.d.and 3.05-mm o.d.)was used for injecting and extracting brine from locations0.5and4.5cm above the bottom of the cell.The layout of the port locations is represented in Fig.1.All injection and extraction ports were point sources and sinks,respectively.All boundaries of the cell were no?ow boundaries,but the top of the cell was vented to the atmosphere.Ports labeled with a“B”in Fig.1 were located4.5cm from the bottom of the cell and ports labeled with an“L”were located0.5cm from the bottom of the cell.Stainless steel tubing(0.51-mm i.d.and0.82-mm o.d.)was used as sampling ports.The cell was packed with sand,the ports inserted,the system sealed using a gasket-lined aluminum lid,and the cell vibrated to consolidate the media.The system was?ushed with CO2gas prior to injecting de-aired deionized(DDI)water through the deepest ports to saturate the system.

The phases of the BBRT emulated in the laboratory experiments included establishing a brine barrier by injecting brine with a mass fraction of0.53g/g(ρ=1.7098g/cm3)near the bottom of the cell and displacing freshwater upward, pumping near the brine barrier interface as it would be done during the implementation of a remedial strategy,dewater-ing of the cell and bulk brine removal,and?ushing of the residual brine remaining with freshwater to reduce in situ densities and the total dissolved solids(TDS)concentrations. Table2provides a summary of injection and extraction locations,pore volumes(PV),as well as sampling locations during each stage of the implemented BBRT.Ef?uent and in situ density samples were collected and analyzed during the entire process.

For the QS experiment,?uid was extracted through an upper port(E1)until air was present in the ef?uent.Fluid extraction was continued through the lower ports(L1–L4), again until air was present in the ef?uent.The system was partially re?lled with DDI water through the lower ports until the medium surrounding the upper ports appeared to be fully Table1

Porous medium properties.

Property Dover sand(DS)Quartz sand(QS) d50(mm)0.470.30

Uniformity coef?cient(d60/d10) 2.79 4.30

Particle density(g/cm3) 2.63 2.66

Porosity0.440.33

Pore volume 3.775L 2.604L

Packing Corr.random?eld Homogenized

50 D.J.Wright et al./Journal of Contaminant Hydrology115(2010)46–63

saturated.The system was then ?ushed by injecting DDI water into the lowest ports on one side of the tank (L3–L4)and extracting from the lowest ports on the other side (L1–

L2).Additional ?ushing was conducted by injecting DDI water into the upper ports (B1–B6)and extracting from the lower ports (L1–L4).

Brine was injected into the lowest ports of the DS cell to minimize mixing due to density inversions and establish the brine layer more ef ?ciently.Once the brine layer was established,the calcium bromide was recovered initially by extracting ?uid through E1,E2,B3,and B4during the pumping and the initial dewatering stage.Then,?uid was extracted through the lower ports (L1–L4)and the system partially re ?lled and ?ushed from side to side.

A volume fraction of less than 0.005of tetrachloroethylene was injected into the DS cell.This low volume fraction of organic liquid was con ?ned to the upper portions of the cell and was assumed to have a negligible effect on the brine aspects of this work,which is the focus of this work.3.4.Field experiment

A ?eld-scale experiment was performed at the Dover National Test Site (DNTS)to assess the scalability of the experimental results achieved in the laboratory to a hetero-geneous ?eld-scale system.Of special interest was an assessment of the brine barrier density that could be achieved and maintained,and the nature of the brine mass recovery as a function of mass fraction.While tetrachlorethylene was injected in the ?eld study,this aspect of the work is not a focus of this manuscript.Because the volume fraction of tetrachlorethylene injected was less than 0.005,it had a negligible effect on the brine aspects of the study.

The DNTS site consists of a water table aquifer overlying an extensive clay formation.The permeable sands extend from the ground surface to a depth of 11-to 14-m below ground surface (bgs)and are comprised of ?ne to medium sands with occasional discontinuous clay and silt lenses (ARA Inc.,1996).The ambient water table is approximately 8-to 11-m bgs,giving a saturated thickness of the water table aquifer of about 3m.The vertically averaged hydraulic conductivity of the aquifer is 2.6m/https://www.doczj.com/doc/134439707.html,anic matter,soluble salts,and clay contents of the aquifer are low.The clay formation consists of gray,?rm,dense marine clays and is approximately 6-m thick with a hydraulic conductivity of 2.6×10?3m/day (ARA Inc.,1996).

Test Cell 3was used in this study and was enclosed using double-walled W275Waterloo Barrier ?Sheet Piles driven into the subsurface and keyed into a con ?ning aquitard approximately 14-m bgs.Test Cell 3was equipped with injection/extraction wells,multilevel micro-samplers (MLS),and contaminant injection points.The layout of these locations is displayed in Fig.2.The test cell area was covered to prevent precipitation from in ?ltrating into the cell.The cell was 4.6m×3m in the horizontal plane.The average depth to the clay layer was approximately 12.3-m bgs with the highest clay elevation at 11.7-m bgs.The elevation of the top of the clay layer was irregular as is shown in Fig.3,adding complications to both the physical experiment and computer simulations.Previous studies in this cell included a cosolvent tracer study (Brooks et al.,2002),a cosolvent solubilization study (Brooks et al.,2004),a surfactant solubilization study (Childs et al.,2006),and a cyclodextrin solubilization study (Tick et al.,2003

).

Fig.1.Top and side view layout of brine injection and extraction ports for the three-dimensional laboratory cell.

Table 2

Summary of laboratory experiments during brine barrier establishment and maintenance.Stage

Brine barrier establishment Pumping and dewatering Medium

QS DS QS DS Injection ports B1–B6L1–L4B1–B6,L3–L4L1–L4Extraction ports

––E1,L1–L4E1–E2,B3–B4,L1–L4Sample locations

Q1–Q12D1–D6Q1–Q7D1–D6Injection/extraction (PV)

0.65

0.42

0.30

0.16

51

D.J.Wright et al./Journal of Contaminant Hydrology 115(2010)46–63

A calcium bromide solution was injected into the test cell using two injection phases to establish a brine barrier at approximately11.6-m bgs.The brine barrier interface(BBI)is terminology used to represent the region in which a transition from a relatively dilute solution to a concentrated brine solution occurs;the BBI varied in location in response to injection and withdrawal.The intended design location for the BBI was0.9m above the average clay layer elevation and 0.3m above the highest clay elevation.

The establishment of the brine barrier was divided into two phases using a series of screened wells that had been packed off and relying on the clay layer and sides of the cell as no?ow boundaries to control the?ow of brine.Brine was primarily injected below11.58-m bgs into the center of the test cell during Phase1.Brine was injected at the same depth but on the left and right sides of the test cell during Phase2. Details of the set up of each stage is summarized in Table3,which contains information on the location of injection and extraction wells during brine barrier establishment.Phase1 of the?eld study involved injecting brine into four locations to concentrate brine into the center,deeper part of the cell. Wells45,46,55,and56(refer to Fig.2for well locations) were chosen for Phase1.Brine was injected into the bottom of these wells,which were packed off at11.4-m bgs.Packing off the wells forced brine into the deepest portions of the cell, which promoted a stable displacement of freshwater upward and limited brine mixing and dilution,which would decrease the ef?ciency of brine injection.The displaced water was then removed using wells41,42,44,51,53,and54by placing pumps at approximately10.3-m bgs.The water table at the beginning of brine injection was located at9.3-m bgs.

After injecting approximately2440L of brine over9days during Phase1,the brine injection/water extraction locations were reversed such that brine was injected below11.4-m

bgs

Fig.2.Dover Test Cell3

layout.

Fig.3.Geometry of the con?ning clay layer beneath Test Cell3and line sources for brine injection,where red locations represent Phase1and yellow locations Phase2injections.

52 D.J.Wright et al./Journal of Contaminant Hydrology115(2010)46–63

into wells41,42,44,51,53,and54and displaced?uids were removed at10.3-m bgs from wells45,46,55,and56.This switch to Phase2of the brine injection strategy allowed the perimeter of the cell to?ll with brine and provided time for relaxation of the hydraulic mounds formed around Phase1 injection wells.Phase2continued until another6440L of brine was injected,which occurred over a period of27days. During both brine injection phases,and the rest of the study, the?uid density was monitored in situ using multilevel samplers,through ef?uent sampling from wells,and through periodic bailing of wells.These data assisted in understanding how the brine propagated through the system,as well as determining the temporal pro?le of brine recovery.

Once the brine barrier was adequately established,brine continued to be injected to maintain the brine barrier in the cell.Brine injection was accomplished using the Phase2 injection wells,however these wells were simultaneously pumped by packing off locations above the BBI.To minimize brine loss,packers were installed below the pumped portion of the well screens to prevent excess brine depletion.During this48-day period,approximately4000L of brine was injected to maintain the brine barrier.

At the end of the injection period,pumps were lowered to the bottom of the wells to remove bulk brine.To achieve an ef?cient removal of?uids,pumps were relocated to more productive wells when?uid recoveries from wells dimin-ished due to low water levels.The remainder of the study was devoted to?ushing the residual brine by adding freshwater to the system.Based on the density measurements from the multilevel samplers,pumps and freshwater injection loca-tions were rotated to target high?uid density regions.

3.5.Modeling approach

Our intent with the modeling was to determine if the brine recovery process could be simulated to mimic the laboratory experiment and to use the model to evaluate the effects of density and viscosity variations and heterogeneity of the intrinsic permeability at the?eld scale.Another purpose of the simulations,although not discussed herein, was to assist the execution of the?eld experiment by running preliminary and real-time simulations to guide the brine injection and the removal design that was implemented. Because of the dif?culty of modeling dense brine behavior,we view the simulation work as preliminary in nature.

We chose SUTRA,a simulator distributed by the United States Geological Survey,to carry out these objectives.SUTRA can be used to simulate saturated or unsaturated density-dependent groundwater?ow and transport in three-dimensional systems. It uses a hybrid?nite-element mesh discretization and an implicit,?rst-order,?nite-difference time-stepping method to approximate the conservation equations(Voss and Provost, 2002).There is a user option of solving either(1)the conservation of mass of a?uid and mass of a solute or(2)the conservation of mass and energy of a?uid,where the?rst option was chosen in this study.The code solves for?uid pressures and solute mass fractions as they change with time.As is true with all discretization-based groundwater modeling applications,the method is approximate in nature and the accuracy depends upon the spatial and temporal discretization,error tolerances of the solvers,and accuracy of the parameter estimates.An additional consideration for these simulations is that,as noted before,the appropriate mathematical model formulation for such systems is considered an open issue.For all of these reasons, our expectation was that SUTRA was an approximate tool that we relied upon to give a semi-quantitative indication of?uid ?ow and species transport.

An assumption made in developing the SUTRA simulator is that solute concentrations do not affect viscosity.The equation of state for density in SUTRA is also of a form that does not match the dense brines of concern in this work. Therefore,modi?ed equations of state for density and viscosity that accurately described concentrated calcium bromide solutions were implemented in the modi?ed SUTRA simulator.The functional form of these equations is discussed later.

A further modi?cation to the SUTRA source code involved altering extraction speci?cations.This change was essential for the brine recovery simulations.The SUTRA model requires a mass rate of input or removal for any external source or sink.However,in the?eld-scale experiment,volumetric injection and extraction rates were used to control the level of the water table in the test cell.Because the mass recovery rate from a well varied with time,it was not convenient to convert a desired volume extraction rate to a mass extraction rate necessary for the SUTRA input.

Source code modi?cations were made such that a volume extraction rate could be speci?ed in the simulation.To make this change,the mass fraction output at each time step in SUTRA,ωt,and the density equation of state were utilized. From a given volumetric extraction rate(E V),the mass extraction rate required by SUTRA at each time step(E m t), was approximated by:

E t m=E Vρt?1ωt?1

h i

e3T

Because the time steps were relatively small compared to the time rate of change of the density,this approach provided an accurate approximation for the desired mass extraction

Table3

Summary of DNTS study during implementation of a BBRT.

Stage Barrier establishment Pumping Dewatering and bulk

brine removal Barrier ?ushing

Phase1Phase2

Injection wells45–46,55–5641–42,44,51,53–5441–42,44,51,53–54Various Various Extraction wells41–42,44,51,53–5445–46,55–5645–46,55–56Various Various CaBr2injected(PV)0.150.400.170.08–

CaBr2removed(PV)0.0020.110.330.180.1253

D.J.Wright et al./Journal of Contaminant Hydrology115(2010)46–63

rate.This change allowed the amount of?uid in the system to be easily controlled in the simulator to match the?eld conditions.

A laboratory system and a?eld-scale system were simulated.Some of the relevant model parameters used in the SUTRA simulations for both the laboratory and?eld-scale simulations are given in Table4.

The laboratory simulation was designed to mimic the laboratory experiment that contained a homogenized mix of

quartz sand.Location of injection,extraction,and sampling ports were selected based upon the corresponding locations in the experiment.Initial conditions used in the simulation correspond to the sharp concentration gradient observed in the experiment once the dense brine layer had been established.The initial mass in place in the simulation was approximately750g of the calcium bromide.Hydrostatic pressure was set to zero at the top of the domain.The simulation included system dewatering,partial re?lling with freshwater,and both horizontal and vertical?ushing to remove the residual brine.

Because of the non-ideal dispersion behavior of dense brines,the effect of different dispersivity coef?cients was explored for this system.Three sets of longitudinal and transverse dispersivity coef?cients were tested,as shown in Table5,with the range varying over three orders of magnitude.The dilute tracer longitudinal dispersivity for this system was estimated to be on the order of0.1cm.

Field-scale laboratory simulations were designed to represent the DNTS test cell during the brine emplacement period.The elevation of the top of an irregularly shaped clay layer was interpolated based on well installation data.The locations of wells and sampling points were based on their locations within the test cell.Minimal information on the heterogeneity of the domain was available,so as a?rst approximation we assumed that the effects of heterogeneity could be evaluated by treating permeability as a log-normally distributed spatial random?eld (SRF)(Freeze,1975;Simmons et al.,2001).Realizations of the three-dimensional permeability?elds were generated using a sequential Gaussian simulation(SGSIM)(Deutsch and Journel, 1992).It was assumed that changes in permeability were gradual and that the domain could be approximated by a Gaussian covariance model.Correlation length scales could not be determined because of a lack of permeability data.The vertical and horizontal correlation length scales(γy andγx,respectively)were assumed to be0.5m and2.5m,respectively.SGSIM was used to create two permeability?elds:a domain heterogeneous in three dimensions,and a vertically layered domain with each layer having a homogeneous permeability.In the latter case, SGSIM was used to generate a packing with a desired vertical correlation length and vertical covariance https://www.doczj.com/doc/134439707.html,rmation on permeability?elds used in each brine simulations is available in Table6.

Initial conditions for the DNTS cell simulations consisted of a solute mass fraction set to zero,and a hydrostatic pressure pro?le with the top of the water table equal to zero. All boundaries where set as no?ow boundaries,which matched the physical system that was contained with sheet piling.Brine was injected into the model system below11.58-m bgs based on the strategy implemented in the?eld study such that Phase1occurred at an average injection rate of 5.34×10?3kg/s over a9-day period and Phase2occurred at an average injection rate of4.75×10?3kg/s over a27-day period.Fluids were extracted from the top of the domain over the36-day period at an average rate of2.95×10?6m3/s.

4.Results

4.1.Equations of state

We measured the density and viscosity of the calcium bromide solutions as a function of mass fraction yielding the results shown in Fig.4.Both relationships exhibited nonlinear behavior that was not well described by standard equations of state.The change of viscosity for calcium bromide was substantial,therefore such changes must be accounted for to model transport phenomena accurately in the systems of concern in this work and for BBRTs in general.

An empirical equation of state for?uid density as a function of calcium bromide mass fraction was estimated from the data using nonlinear least-squares analysis.The third-degree polynomial that accurately describes the mea-sured data is

ρωeT=0:8319ω3+0:4958ω2+0:8417ω+0:9982e4Twhere density is given in g/mL,and0.9982is the reference density.

Table4

SUTRA model parameters for brine simulations of laboratory and?eld experiments.

Model parameter Units Lab value Field value

Freshwater density g/cm30.99820.9982 Freshwater viscosity cP 1.0019 1.0019

Brine source mass fraction g/g0.530.53

Brine source density g/cm3 1.70 1.70

Brine source viscosity cP 6.1 6.1

Porosity[?]0.330.35

Mean intrinsic permeability m28.3×10?123×10?12 Longitudinal dispersivity m0.00480.48 Transverse dispersivity m0.00160.16 Molecular diffusivity[m2/s] 1.22×10?9 1.22×10?9 n(van Genuchten)[?] 2.0 2.0

α(van Genuchten)[?]5×10?55×10?5Table5

Dispersivity coef?cients for laboratory experiment simulations.

SimulationαLαT

T10.048m0.016m

T20.0048m0.0016m T30.00048m0.00016m

Table6

Permeability?elds for?eld-scale simulations.

Simulation Domain Varianceγxγy

F1Homogeneous0––

F2Gaussian SRF1 2.5m0.5m F3Layered2-0.5m

54 D.J.Wright et al./Journal of Contaminant Hydrology115(2010)46–63

An empirical equation of state for ?uid viscosity as a function of calcium bromide mass fraction was estimated from the data and is of the form

μωeT=1:001916:43ω3?5:190ω2

+1:552ω?

e5T

where viscosity is given in cP.

Using Eq.(1)for the density relationship with a γvalue of 0.6923,a value that was originally derived from sodium chloride solution data,would lead to an under prediction of the density of a calcium bromide solution.Estimating the ?tting parameter from the calcium bromide data yields a γvalue of 0.9855and improves the model ?t for Eq.(1).However,the improved relationship over and under predicts density when the mass fraction is less than and greater than 0.4,respectively.The viscosity relationship typically used to model groundwater systems (Eq.(2)),which was ?tted to the calcium bromide data such that A =1.43,B =-6.77,and C =?27.98,under predicts viscosity for mass fractions greater than 0.42relative to the data and the empirically derived Eq.(5).

https://www.doczj.com/doc/134439707.html,boratory study

https://www.doczj.com/doc/134439707.html,boratory cell experiment results

In situ density samples were collected at elevations from 2.0to 7.0cm from the bottom of the tank during the QS experiment.Fig.5shows density as a function of depth and number of pore volumes of brine injected during the establishment of the brine barrier.At early times,sampling locations in close proximity to injection ports had the highest density measurements.This led to large variations in density at a given elevation as can be seen in the data collected after injecting 0.23PV of brine.For example,the density ranged from 1.01–1.52g/cm 3at an elevation of 3.0cm.Density variations at a given elevation greatly diminished after the addition of 0.40PV of brine.After 0.40PV,observed densities from the bottom of the tank to the extraction port at 4.5cm (i.e.,the designated BBI)exceeded the density of trichloro-ethylene (TCE),which has a density of 1.46g/cm 3.After 0.57PV,observed brine densities from the bottom of the tank to the extraction port at 4.5cm exceeded the 1.62g/cm 3,which corresponds to the density of one of the denser DNAPLs of interest,tetrachloroethylene (PCE).

Density sampling during the DS experiment was limited compared to sampling during the QS experiment.Samples were only collected at elevations from 1.0to 3.0cm from the bottom of the tank.Density as a function of depth after the establishment of the brine barrier are shown in Fig.6.Markers in this ?gure represent the average brine density and lines represent the range of observed densities.There was little variation in density in the lower portion of the cell after the addition of 0.42PV of brine.

After establishing a brine barrier,pumping began at the BBI,as it would during implementation of a BBRT.During pumping,brine continued to be injected into the cell through the deepest ports to maintain the brine barrier and counter losses due to pumping.Pumping induced mixing around the extraction wells.Therefore,in situ densities were measured to determine the effect of pumping in the vicinity of the BBI.Densities measured near the end of pumping are shown in Fig.6for the DS medium.After signi ?cant pumping from an elevation of 4.5cm,densities measured at an elevation of 3.0cm ranged from 1.3to 1.7g/cm 3.The lowest densities were observed near the extraction locations.The average density in the brine barrier increased and the variability decreased closer to the bottom of the cell.The results suggest that capillary forces will need to offset the loss of buoyancy

to

Fig.4.Density (left)and viscosity (right)of calcium bromide as a function of mass

fraction.

Fig.5.Density as a function of elevation during the establishment of the brine barrier for the QS laboratory experiment.

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D.J.Wright et al./Journal of Contaminant Hydrology 115(2010)46–63

prevent DNAPLs with densities similar to TCE and PCE from migrating below the extraction elevation,particularly near the extraction points.

In an effort to recover the calcium bromide from the QS experiment,the cell was partially drained,partially re ?lled,and then ?ushed with DDI water.In situ densities were measured during various stages of brine recovery and the results are shown in Fig.7.Dewatering the cell resulted in densities ranging from 1.14g/cm 3at an elevation of 7cm to 1.67g/cm 3near the bottom.The DDI water injected to partially resaturate the cell mixed with the residual brine and resulted in a lower vertical density gradient with densities ranging from 1.22g/cm 3at an elevation of 7cm to 1.45g/cm 3near the bottom.Flushing with less than 2PV of DDI water reduced density to less than 1.00g/cm 3through-out the cell.

Although reducing in situ density is important,the ability to reduce the TDS of the ef ?uent stream is equally important in terms of waste treatment and restoration of the system to its original state.The TDS of the ef ?uent stream are shown in Fig.8.The Secondary Drinking Water Standard for TDS is 500mg/L (U.S.EPA,2009).In the experiment using the QS medium,we achieved a TDS concentration of 789mg/L after ?ushing approximately 2.5PV of DDI water through the portion of the cell originally containing the brine barrier.The QS experiment exhibited a log-linear decrease in TDS with cumulative ?ushing volume.The experiment using the DS medium also exhibited this log-linear nature,but with slight deviations due to changes in ?ow rates during ?ushing.The TDS in the ef ?uent samples from the DS experiment were less than 300mg/L after ?ushing with 3.3PV.Flushing was performed through-out the cell in the DS study whereas ?ushing was limited to the lower half of the cell in the QS study.In addition,the majority of the ?ushing in the QS study consisted of ?ushing from the upper ports to the lower ports while ?ushing in the DS study consisted of ?ushing between lower ports.As a result of the differences in ?ushing strategy and media heterogeneity,less freshwater was needed to reduce the TDS ef ?uent concentrations in the DS study than the QS experiment.Flushing of approximately 3.3PV of freshwater after draining the DS medium resulted in recovery of approximately 98.9%of the injected brine from the DS medium.The mass fraction of 91%of the recovered brine exceeded 0.1,which is the approximate limit for recycling brines economically after reconcentration.

4.2.2.Model results

The modi ?ed SUTRA simulator,which accounts for density and viscosity as functions of calcium bromide mass fraction using Eqs.(4)and (5),was used to simulate the brine recovery process of the QS laboratory experiment.To evaluate the model results,the concentration data in Fig.8were converted to fraction of mass removed and compared with the simulated data.

Examination of Fig.9shows that all three simulations with different values of dispersivity (T1,T2,and T3)overestimate mass removal for the ?rst 0.2PV removed,but then diverge from each other as they progress to the end.As expected,the simulation with the highest dispersivity values (T1)leads to excessive dispersion and dilution of the dense brine layer that result in signi ?cant underprediction of overall mass removal.The simulation with dispersivity values closest to dispersivity for a dilute system (T2)shows good agreement with the experimental data until approximately 1PV ?ushed,but

then

Fig.6.Average density as a function of elevation after the establishment of the brine barrier and during pumping for the DS laboratory

experiment.

Fig.7.Density as a function of elevation during the recovery of the brine barrier for the QS laboratory

experiment.

Fig.8.Ef ?uent TDS concentration during calcium bromide removal from the laboratory experiments,where ○represents the QS medium and represents the DS medium.

56 D.J.Wright et al./Journal of Contaminant Hydrology 115(2010)46–63

begins to underpredict mass removal for the remainder of the simulated period.The ?nal simulation (T3)with the lowest dispersivity values shows overprediction for much of the simulation,however by the end,the total mass removal is less than the experimental value by an order of magnitude.

The simulated results indicate that the model is only adequate in predicting accurate mass removal rates at the very beginning of the ?ushing period.However,the differ-ences in slope after 1.5PV ?ushed suggests that dispersion is an issue.As the simulations progress,the model is not able to maintain a sharp density gradient in the vertical and the dense brine layer becomes diluted,thus hampering effective mass removal.This observation is con ?rmed by the model result of vertical density pro ?le not shown here.Even with an arbitrarily low dispersivity,the mass removal does not match the overall experimental data.

Numerical diffusion in the model results is controlled to the extent possible using a converged grid.However,some of the poor match to the laboratory data can be attributed to numerical diffusion that cannot be completely eliminated,due to the methods employed in the simulator.Despite the presence of some numerical effects,the model results also suggest that the SUTRA model formulation of dispersion,which assumes a dilute system and Fickian dispersion,is not appropriate for modeling high-concentration brines with non-ideal dispersive behavior.Further work is needed to develop appropriate simulators for these types of non-dilute systems.4.3.Field study

4.3.1.Field experiment results

Density samples collected from the multilevel samplers were used to investigate the spatial and temporal distribution of brine within the test cell.In addition,samples were also collected from the ef ?uent stream to maintain a mass balance of the brine during each stage of the BBRT including brine barrier establishment,pumping and dewatering,bulk brine removal,and ?ushing of the residual brine.There was considerable variation in density at all depths at the end of Phase 1as is shown in Fig.10.Densities were greatest near the injection wells and decreased with distance from the injection wells.Phase 2resulted in an increase in density in regions that were low in density at the conclusion of Phase 1.Density variation at all depths decreased by the end of Phase 2.

Density measurements during and at the end of Phase 2indicted that there were regions in the lower portion of the cell where density inversion developed.The localized regions where apparent instabilities persisted were between wells 42and 44and between wells 51and 53.These results suggest there was some heterogeneity effect that leads to a density inversion in these areas.Utilization of extraction wells in the vicinity of these regions did not occur during the pumping and dewatering stage.However,wells were used as extrac-tion wells in regions where suf ?cient brine had been injected to achieve the required density to impede the vertical movement of PCE.Selection of wells away from the unstable regions decreased the possibility of brine barrier deteriora-tion due to mixing induced by pumping in the unstable regions.

To minimize the development of instabilities,extraction pumps were initially placed above the proposed BBI and slowly lowered during the course of pumping until the extraction pumps were at the level of the BBI.This strategy decreased brine losses,reduced mixing at the BBI,and promoted continued stabilization of the brine barrier.After removing 0.68PV —with a pore volume being based on the maximum saturated zone extending from the clay layer to 8.5-m bgs and yielding an approximate ?uid volume of 16,200L of ?uid —from the test cell,densities below the BBI were essentially unchanged compared to densities at the end of Phase 2as shown in Fig.11.The average brine density and range of densities within the brine barrier held relatively constant during vertical ?ushing of the upper portion of the cell.The observed densities over a several month period showed that the brine barrier was a stable feature that could be maintained.Densities above the brine barrier decreased as ?uid was ?ushed downward towards the extraction loca-tions.The large range of densities that existed above the BBI suggest that all areas were not uniformly ?ushed,resulting in the persistence of localized high concentrations of brine above the

BBI.

Fig.9.Experimental and simulated fraction of calcium bromide remaining in the laboratory experiment with quartz sand

medium.

Fig.10.In situ densities after Phase 1and Phase 2brine additions.The depth of extraction is indicated on the plot as a solid horizontal line.The densities of PCE and TCE are provided as a point of reference.

57

D.J.Wright et al./Journal of Contaminant Hydrology 115(2010)46–63

After partial dewatering of the test cell,multilevel sampler data revealed results similar to laboratory observations in that densities in the brine barrier zone were still relatively high (i.e.,exceeded 1.3g/cm 3).Residual brine from the brine establishment phase that had been bypassed during the ?ushing stage contributed to elevated density readings in the upper regions of the domain,but,in general,densities decreased with elevation above the BBI.

Samples collected after re ?lling the cell with water indicated that densities above 12.0-m bgs ranged from 1.01to 1.32g/cm 3with the results shown in Fig.12.Below 12.0-m bgs,the density increased with depth with the exception of the local regions of lower density observed earlier.The test cell was undisturbed for three months after the completion of the primary study.Density samples collected at the end of this period indicated that the wide variation in density at a given depth observed earlier diminished and that the overall vertical density gradient also diminished.Apparent density instabilities in the lower portion of the cell persisted,but were less pronounced.The reductions in variability and vertical gradient were due to diffusion and small-scale ?ow driven by local density instabilities.Drainage from above the water table increased the water level in the cell by 0.63m during the three

month period and the drainage,depending on its density,may have also impacted the density pro ?le.

Ef ?uent samples collected throughout the study revealed changes in the composition of the ef ?uent stream depending on the stage of the BBRT as shown in Fig.13.As brine was injected into the system during establishment of the brine barrier,the thickness of the barrier increased and brine migrated upward toward the extraction elevation leading to an increase in the density of the ef ?uent stream.The extraction pumps were lowered during the addition of the ?ushing solution which resulted in an initial increase in the density of the ef ?uent stream,followed by a slight decline.Further lowering of the extraction pumps during dewatering and bulk brine removal resulted in an increase in the ef ?uent density from 1.3to 1.6g/cm 3.A 0.4PV ?ush with water resulted in a decrease in the density of the ef ?uent to 1.1g/cm 3.

The overall process recovered 92%of the calcium bromide injected into the system.The number of pore volumes of water ?ushed through the ?eld-scale system was only a small fraction of the pore volumes that were ?ushed through the laboratory systems.In addition the rate of ?ushing was higher in the test cell than in the laboratory https://www.doczj.com/doc/134439707.html,boratory systems were re ?lled at a slow rate to try to resaturate the cell.Further ?ushing could have removed additional calcium bromide mass as in the laboratory experiments,but time constraints did not make further ?ushing possible.

It may be possible to recycle brine during the application of a BBRT if the contaminants can be removed and the brine reconcentrated.We may assume that the cost of such a recycling process would be inversely related to the calcium bromide mass fraction of the ef ?uent.Assessing the potential for economic brine recycling includes examining the volume of brine ef ?uent that exceeds a minimal mass fraction (ωmin )that is de ?ned as the mass fraction below which the cost of recycling becomes uneconomical.Fig.14shows that,for example,if ωmin =0.25than more than 50%of the ef ?uent that was collected could be recycled economically.Similarly,if ωmin =0.10,then more than 88%of the collected ef ?uent could be feasibly recycled.The exact mass fraction at which it becomes uneconomical to reconcentrate the brine would likely be

project-dependent.

Fig.11.Average density as a function of depth during implementation of the BBRT remediation strategy.The solid horizontal line represents the brine barrier

interface.

Fig.12.Density as a function of depth at the end of the primary study and 3months

post-study.

Fig.13.Ef ?uent density as a function of ef ?uent volume during (1)brine injection,(2)?ushing solution addition,(3)dewatering,(4)bulk brine removal,and (5)brine barrier ?ushing.

58 D.J.Wright et al./Journal of Contaminant Hydrology 115(2010)46–63

4.3.2.Model results

Field-scale simulations were also conducted to investigate the formation of a density inversion (or instability)during the injection of brine to form the brine barrier.Since minimal information was available on the porous media properties,three permeability ?elds were used in the simulations:a homogeneous ?eld,a ?eld based on a Gaussian covariance model,and a layered permeability ?eld (see Table 6).The areally-averaged results of the simulations are shown in Fig.15.The completion of Phase 1,which corresponds to brine injection into the center 4wells and deeper zone of the test cell (see Fig.3),shows a stable and relatively sharp density pro ?le in the simulations with homogeneous and Gaussian permeability ?elds.However,the simulation with the layered permeability ?eld developed a density inversion early in this phase.Inspection of the permeability ?eld in the instability region for the layered system indicates that the permeability decreases by more than two orders of magni-tude between 12-m bgs and the bottom of the domain (see Fig.15).The low permeability inhibited the migration of brine into this region.

Density instabilities were found to develop in each of the simulated systems by the end of Phase 2.The inversion that developed during Phase 1for the layered permeability system persisted through Phase 2.In addition,the simulations for the homogeneous and Gaussian permeability ?elds also devel-oped slight density inversions beneath 12-m bgs,although not as pronounced as the layered permeability ?eld system.The initiation and persistence of the density inversion during this phase for the homogeneous and Gaussian cases is largely due to the location of the Phase 2injection wells,which were along the outer edges of the cell where the topography of the bottom surface becomes shallower (Fig.3).In addition,Phase 2injection was three times as long as Phase 1,which resulted in most of the total calcium bromide mass being injected in shallower zones.This also caused circulation of fresh water into the deeper zones,diluting the dense brine injected during Phase 1.Thus,stable density gradients existed locally but at different elevations,and therefore the apparent density inversion in Fig.15is an artifact of averaging.Additional simulations showed that after the system equilibrates for a number of days,the brine migrates slowly into the deeper zones for the simulations with homogeneous and Gaussian permeability ?elds,and the apparent density instability in Fig.15for these two cases stabilized.The density instability for the layered permeability ?eld persisted as expected due to the strong permeability contrast in the deeper region.

Compared with the ?eld-scale experiment observations shown in Fig.11,the simulated results with the layered permeability ?eld best approximates the observed average density gradient at the end of Phase 2.This indicates that a low permeability zone likely exists along the top of the clay layer as discussed earlier.Near the top of the observed BBI between ?10.8and ?11.8m (bgs),the simulated results show a density gradient not as sharp as observed in the test cell and with lower average concentrations.Despite the use of a converged grid,this is likely due to numerical dispersion,and the underlying assumption of Fickian diffusion.These results further reveal the overall inadequacy of the simulator to maintain sharp density gradients over time as observed in both the laboratory and ?eld

experiments.

Fig.14.The volume of ef ?uent exceeding a minimum mass fraction (ωmin

).

Fig.15.(Left)simulated average densities with depth for different permeability ?elds in the ?eld-scale simulations,where F 1is the homogeneous,F 2is the Gaussian,and F 3is the layered permeability ?eld.(Right)average permeability with depth for the Gaussian and layered permeability ?elds.

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D.J.Wright et al./Journal of Contaminant Hydrology 115(2010)46–63

5.Discussion

Knowledge of the?uid properties of a high-concentration calcium bromide solution is essential for understanding the dynamics of a BBRT based upon such a solution.This was of particular importance because the density was1.7times and the viscosity was6times that of water at the mass fraction used in the BBRT studies.Changes in the density and viscosity over the range of mass fractions experienced during imple-mentation of a BBRT can result in a72%decrease in hydraulic conductivity.

Although laboratory studies conducted to date have implemented brine barrier strategies,the properties of such brine barriers have not been investigated.We monitored in situ brine densities during all stages of a BBRT https://www.doczj.com/doc/134439707.html,boratory studies showed effective establishment of dense brine barriers that achieved densities in excess of a variety of chlorinated solvents.These densities were main-tained with some localized reductions in density near extraction wells.With adequate brine barrier thickness, localized reductions in density due to mixing near extraction wells should not affect the effectiveness of a brine barrier at arresting downward migration of most DNAPLs.

With adequate?ushing,more than98%of the injected brine was recovered from the laboratory systems.High recoveries are needed if in situ calcium bromide concentra-tions are going to be substantially reduced.The ability to reduce calcium bromide concentrations is particularly im-portant in natural systems that may eventually serve as sources for drinking water.

Some of the primary differences between the laboratory and?eld studies,other than the domain size,were the degree of heterogeneity,the source and sink type(i.e.the laboratory experiments had point sources and sinks while the?eld experiment had line sources and sinks),and the presence of residual?uids from previous studies in the?eld test cell. Obstacles that arose during brine injection and maintenance in the?eld setting included brine mounding around wells and density instabilities within the medium,which were inves-tigated in more detail using a modi?ed SUTRA simulator.Any remnants remaining from the prior studies had a minimal effect on density and viscosity in comparison to the brine solution since initial measurements were found to be comparable to water.A more likely in?uence of the remnants would be pore clogging as the solutions serve as food for bacteria,which would inhibit brine migration in such areas if it occurred.

Hydraulic issues were encountered during the dewatering and bulk brine removal phase of the?eld-scale study.We were unable to achieve the degree of dewatering of the brine barrier that we had achieved in the laboratory systems,which made removal of the residual brine more dif?cult.Based on its areal extent and porosity,the test cell had approximately 4850L of pore space volume per meter of depth.Lowering the water table resulted in the?uid recovery of water that corresponded to approximately a third of the pore space volume per thickness of medium.This inef?cient?uid recovery was partly due to the slow drainage of the unsaturated zone relative to the time frame of the?eld experiment.Reductions in the thickness of the saturated zone diminished the ef?ciency of the bladder pumps used in the wells,which also contributed to the inef?cient?uid recovery. Although reductions in?uid recovery occurred,we were able to recover a high fraction of the injected brine and expect that with further freshwater?ushing additional mass removal was feasible.

We modi?ed SUTRA to include the density and viscosity relationships for calcium bromide.SUTRA's mass-based extraction scheme was converted to a volume-based extrac-tion scheme,which made simulating BBRTs easier.There was general agreement between the SUTRA simulation and ef?uent measurements from the laboratory system during the early period of brine-barrier?ushing.However,excessive numerical dispersion,even for very low dispersivity values, led to excessive mixing and poor brine recovery in the latter part of the simulation.SUTRA simulations also provided insight to?eld-scale observations including the role of density-and viscosity-dependent?ow,and the interaction of the two properties during brine barrier?ushing.

Density inversions were observed in the?eld study as well as in simulations of the?eld study.Simulated density instabilities were found near areas of low permeability, which were found in the deeper portions of the system. Density instabilities may have arisen from the decreased permeability because such conditions existed in the deeper portions of the test cell that were in close proximity to the clay layer.These instabilities persisted in both the?eld and simulated studies further suggesting their existence was due to areas of low permeability.The formation of localized density inversions in low permeability regions may not pose a problem with respect to the performance of BBRTs.If the permeability is low enough to limit the migration of brine,the low permeability regions are likely not accessible to a DNAPL either,at least prior to a DNAPL coming into contact with a solution that promotes mobilization.

The ability to accurately monitor and predict in situ densities in a?eld setting is dif?cult.Fluids in wells stratify quickly relative to?uids in the adjoining medium so monitoring density in wells can be unreliable,particularly when density inversions exist in the medium.Discrete interval sampling within wells or multilevel samplers can be used to alleviate density sampling dif?culties.Model simulations can be used to describe the density within a brine barrier,but modeling requires detailed knowledge of the porous medium properties,particularly if it is hoped that the model will capture localized inversions.A conservative brine barrier strategy would be to increase the thickness of the barrier to ensure control of mobilized DNAPL,but such an approach may lead to signi?cant amounts of DNAPL trapped below the brine barrier interface where recovery would be dif?cult.

Although we have gained insight into the behavior and application of brine barriers,we believe there are still a number of relevant issues that should be considered to mature our understanding.These issues include the following items: (1)Model development and simulators.Density-dependent

models and simulators are still an active area of research.

As the theory,model,and numerics continue to develop,

so will a more mature scienti?c understanding of the

systems of concern,the role of sharp fronts,and density

and viscosity induced instabilities.

60 D.J.Wright et al./Journal of Contaminant Hydrology115(2010)46–63

(2)Behavior in the absence of hydraulic controls.Installation

of sheet piles may be unrealistic at some sites so wells

must be used to control brine migration.Well

placement would have to be optimized to minimize

migration and loss of brine outside of the contaminat-

ed region.Such systems would require larger volumes

of brine,which emphasizes the importance of being

able to recycle and reuse brine on site.

(3)Horizontal?ushing of remedial?uids.The impact of

horizontal?ushing with remedial?uids,such as

surfactants and cosolvents,on brine barrier stability

has not been investigated.Horizontal?ushing is more

common than vertical?ushing,but it may increase

mixing at the brine barrier interface.The impact of

such a?ushing strategy on brine barrier maintenance

needs some consideration.

(4)Barrier thickness.We observed persistent density

inversions during the?eld experiment.Consequently,

the brine barrier thickness in some locations was less

than the desired thickness.The minimal thickness of a

brine barrier needed to control mobilization needs to

be assessed.It is expected that this thickness will be a

function of distance from an extraction or injection

well,?ow rates,density difference between the brine

and the DNAPL,and the DNAPL and medium properties.

(5)Clay effects.Due to the length of time a brine barrier

may overlay a clay layer,it is important to determine

the impact of brine on the structural integrity of the

clay layer.In addition,the rate of loss of brine into the

underlying clay layer needs to be investigated.Diffu-

sion of brine back out of the clay layer after removal of

the bulk brine is also a concern as it could pose a long-

term source of dissolved salt into the aquifer.

We believe that resolution of these issues will require substantial work,but such a resolution would bene?t future applications of BBRTs.

6.Conclusions

We characterized and de?ned the relationship of the density and viscosity of calcium bromide solutions over a range of mass fractions that were observed during the implementation of a https://www.doczj.com/doc/134439707.html,monly used approaches for representing these relationships were unable to adequately describe our data over the entire mass fraction range. Therefore,we developed equations of state to better represent the relationships between density and viscosity as a function of calcium bromide mass fraction.

We observed changes in the density within a brine barrier as a function of space and time while establishing and maintaining a brine barrier in laboratory cells.We found that a brine barrier could be effectively established by injecting about0.4PV of brine into the con?ned cell.The brine barrier could also be maintained during the course of a BBRT experiment.

It is feasible to recover high percentages of brine at the end of a BBRT.In the laboratory setting we were able to recover more than98%of the injected brine,of which more than90% had a mass fraction exceeding0.1,which is the lower limit at which it is economically viable to reconcentrate and recycle the ef?uent.Focusing?ushing on the lower portion of the laboratory cell,or primarily the region where the brine barrier existed,is more ef?cient in reducing calcium bromide concentrations than?ushing the entire cell.Freshwater ?ushing of the brine barrier region was found to require less than half of the pore volumes of freshwater needed to reduce the calcium bromide concentration to a similar level when?ushing the entire system.

A BBRT was implemented at the?eld-scale.We were able to successfully establish and maintain a brine barrier,and recover approximately92%of the injected brine.Instabilities were encountered in the?eld due to the complex hetero-geneities that existed near an underlying clay layer.These instabilities were persistent through the course of the study. We do not believe the instabilities posed a major problem because they existed in locations that were not likely to be easily penetrated by mobilized DNAPL. Acknowledgements

This work was supported by the National Institute of Environmental Health Sciences grant P42ES05948,AECOM, and the Dead Sea Bromine Group.The Dover National Environmental Technology Test Site is established and managed by the Strategic Environmental Research and Development Program.The demonstration complied with prescribed NETTS protocols and guidelines for quality assurance,health and safety,technical completeness,and regulatory compliance.The support of the NETTS facilities and test location manager and staff are gratefully acknowledged. References

Abarca,E.,Carrera,J.,Sanchez-Vila,X.,Dentz,M.,2007.Anisotropic dispersive Henry problem.Advances in Water Resources30(4),913–926. Ackerer,P.,Younes,A.,2008.Ef?cient approximations for the simulation of density driven?ow in porous media.Advances in Water Resources31

(1),15–27.

Ackerer,P.,Younes,A.,Mose,R.,1999.Modeling variable density?ow and solute transport in porous medium I.Numerical model and veri?cation.

Transport in Porous Media35,345–373.

Adams,J.J.,Bachu,S.,2002.Equations of state for basin geo?uids:algorithm review and intercomparison for brines.Geo?uids2(4),257–271.

ARA Inc.,1996.Groundwater remediation?eld laboratory-GRFL:hydro-geology characterization and site development.Volume I:site charac-terization and development.Tech.rep.,prepared by Applied Research Associates,Inc.for Armstrong Laboratory.

Batzle,M.,Wang,Z.J.,1992.Seismic properties of pore?uids.Geophysics57

(11),1396–1408.

Bear,J.,Bachmat,Y.,1991.Introduction to Modeling of Transport Phenomena in Porous Media.Kluwer Academic Publishers,Dordrecht,The Netherlands.

Brooks,M.C.,Annable,M.D.,Rao,P.S.C.,Hat?eld,K.,Jawitz,J.W.,Wise,W.R., Wood,A.L.,En?eld,C.G.,2002.Controlled release,blind tests of DNAPL characterization using partitioning tracers.Journal of Contaminant Hydrology59(3–4),187–210.

Brooks,M.C.,Annable,M.D.,Rao,P.S.C.,Hat?eld,K.,Jawitz,J.W.,Wise,W.R., Wood,A.L.,En?eld,C.G.,2004.Controlled release,blind test of DNAPL remediation by ethanol?ushing.Journal of Contaminant Hydrology69 (3–4),281–297.

Brovelli,A.,Mao,X.,Barry,D.A.,2007.Numerical modeling of tidal in?uence on density-dependent contaminant transport.Water Resources Re-search43.

Childs,J.,Acosta,E.,Annable,M.D.,Brooks,M.C.,En?eld,C.G.,Harwell,J.H., Hasegawa,M.,Knox,R.C.,Rao,P.S.C.,Sabatini,D.A.,Shiau,B.,Szekeres,E., Wood,A.L.,2006.Field demonstration of surfactant-enhanced solubili-zation of DNAPL at Dover Air Force Base,Delaware.Journal of Contaminant Hydrology82(1–2),1–22.

61

D.J.Wright et al./Journal of Contaminant Hydrology115(2010)46–63

Christakos,G.,1992.Random Field Models in the Earth Sciences.Academic Press,San Diego,CA.

Dentz,M.,Tartakovsky,D.M.,Abarca,E.,Guadagnini,A.,Sanchez-Vila,X., Carrera,J.,2006.Variable-density?ow in porous media.Journal of Fluid Mechanics561,209–235.

Deutsch,C.V.,Journel,A.G.,1992.GSLIB:Geostatistical Software Library and User's Guide.Oxford University Press,New York.

Diersch,H.-J.G.,2005.FEFLOW Finite Element Subsurface Flow&Transport Simulation System Reference Manual.WASY GmbH,Berlin,Germany.

Tech.rep.

Diersch,H.J.G.,Kolditz,O.,2002.Variable-density?ow and transport in porous media:approaches and challenges.Advances in Water Resources 25(8–12),899–944.

Elder,J.W.,1967.Transient convection in a porous medium.Journal of Fluid Mechanics27,609–623.

Elfeki, A.,Dekking,M.,2001.A Markov chain model for subsurface characterization:theory and applications.Mathematical Geology33

(5),569–589.

Flowers,T.C.,Hunt,J.R.,2007.Viscous and gravitational contributions to mixing during vertical brine transport in water-saturated porous media.

Water Resources Research43(1).

Freeze,R.A.,1975.A stochastic-conceptual analysis of one-dimensional groundwater?ow in nonuniform homogeneous media.Water Resources Research11(5),725–741.

Fried,J.J.,1975.Groundwater pollution.In:Fried,J.J.(Ed.),The Experimental Determination of Groundwater Pollution Parameters.Elsevier Scienti?c Publishing Co.,Amsterdam,pp.59–113.

Frolkovic,P.,De Schepper,H.,2001.Numerical modelling of convection dominated transport coupled with density driven?ow in porous media.

Advances in Water Resources24(1),63–72.

Gebhart,B.,Jaluria,Y.,Mahajan,R.,Sammakia,B.,1988.Buoyancy Induced Flows And Transport.Hemisphere,New York.

Gill,A.E.,1982.Atmosphere-ocean dynamics.Academic Press,New York. Goswami,R.R.,Clement,T.P.,https://www.doczj.com/doc/134439707.html,boratory-scale investigation of saltwater intrusion dynamics.Water Resources Research43(4). Gotovac,H.,Andricevic,R.,Gotovac, B.,2007.Multi-resolution adaptive modeling of groundwater?ow and transport problems.Advances in Water Resources30(5),1105–1126.

Graf,T.,Therrien,R.,2007.Variable-density groundwater?ow and solute transport in irregular2D fracture networks.Advances in Water Resources30(3),455–468.

Gray,W.G.,Miller,C.T.,2009.Thermodynamically constrained averaging theory approach for modeling?ow and transport phenomena in porous medium systems:5.Single-?uid-phase transport.Advances in Water Resources32(5),681–711.

Hassanizadeh,S.M.,Gray,W.G.,1979.General conservation equations for multi-phase systems: 1.Averaging procedure.Advances in Water Resources2(3),131–144.

Hassanizadeh,S.M.,Leijnse, A.,1995.A non linear theory of high-concentration-gradient dispersion in porous media.Advances in Water Resources18(4),203–215.

Held,R.,Attinger,S.,Kinzelbach,W.,2005.Homogenization and effective parameters for the henry problem in heterogeneous formations.Water Resources Research41(11).

Heller,J.P.,1966.Onset of instatbility patterns between miscible?uids in porous media.Journal of Applied Physics37(4),1566–1579.

Henry,H.R.,1964.Effects of dispersion on salt encroachment in coastal aquifers.U.S.Geological Survey.Tech.rep.

Hill,E.H.,Moutier,M.,Alfaro,J.,Miller,C.T.,2001.Remediation of DNAPL pools using dense-brine barrier strategies.Environmental Science& Technology35(14),3031–3039.

Jiao,C.Y.,H?tzl,H.,2004.An experimental study of miscible displacements in porous media with variation of?uid density and viscosity.Transport in Porous Media54(2),125–144.

Johannsen,K.,Oswald,S.,Held,R.,Kinzelbach,W.,2006.Numerical simulation of three-dimensional saltwater–freshwater?ngering instabilities observed in a porous medium.Advances in Water Resources 29(11),1690–1704.

Johnson,D.N.,Pedit,J.A.,Miller,C.T.,2004.Ef?cient,near-complete removal of DNAPL from three-dimensional,heterogeneous porous media using a novel combination of treatment technologies.Environmental Science& Technology38(19),5149–5156.

Juanes,R.,Blunt,M.J.,2006.Analytical solutions to multiphase?rst-contact miscible models with viscous?ngering.Transport in Porous Media64

(3),339–373.

Kemp,N.P.,Thomas,D.C.,Atkinson,G.,Atkinson,B.L.,1989.Density modeling for brines as a function of composition,temperature,and pressure.SPE Production Engineering4,394–400.

Kolditz,O.,Habbar,A.,Kaiser,R.,Rother,T.,Thorenz,C.,M.K.,Moenickes,S., 2001.ROCKFLOW Numerical Modeling of Fluid Flow,Mass and Heat

Transport in Subsurface Systems,Version 3.5.Institute of Fluid Mechanics and Computer Applications in Civil Engineering,University of Hannover,Hannover,Germany.Tech.rep.

Kolditz,O.,Ratke,R.,Diersch,H.J.G.,Zielke,W.,1998.Coupled groundwater ?ow and transport:1.Veri?cation of variable density?ow and transport models.Advances in Water Resources21(1),27–46.

Konikow,L.F.,Sanford,W.E.,Campbell,P.J.,1997.Constant-concentration boundary condition:lessons from the HYDROCOIN varible-density groundwater benchmark problem.Water Resources Research33(10), 2253–2261.

Landman, A.J.,Johannsen,K.,Schotting,R.,2007.Density-dependent dispersion in heterogeneous porous media part I:a numerical study.

Advances in Water Resources30(12),2467–2480.

Landman,A.J.,Schotting,R.,Egorov,A.,Demidov,D.,2007.Density-dependent dispersion in heterogeneous porous media part II:comparison with nonlinear models.Advances in Water Resources30(12),2481–2498. Landman, A.J.,Schotting,R.J.,2007.Heat and brine transport in porous media:the Oberbeck–Boussinesq approximation revisited.Transport in Porous Media70(3),355–373.

Lin,H.-C.J.,Richards, D.R.,Yeh,G.-T.,Cheng,J.-R.,Cheng,H.-P.,1997.

FEMWATER:A Three-Dimensional Finite Element Computer Model for Simulating Density-Dependent Flow and Transport In Variably Saturated Media.U.S.Army Corps of Engineers Waterways Experiment Station, Vicksburg,MS.Tech.rep.

Mazzia, A.,Putti,M.,2002.Mixed-?nite element and?nite volume discretization for heavy brine simulations in groundwater.Jounal of Computational and Applied Mathematics147,191–213.

McCain,J.W.,1991.Reservoir?uid property correlations—state of the art.

SPE Production Engineering6,266–272.

Mercer,J.W.,Pinder,G.F.,Donaldson,I.G.,1975.Galerkin-?nite element analysis of hydrothermal system at Wairakei,New Zealand.Journal of Geophysical Research80(17),2608–2621.

Miller,C.T.,Hill,E.H.,Moutier,M.,2000.Remediation of DNAPL-contaminated subsurface systems using density-motivated mobilization.Environmen-tal Science&Technology34(4),719–724.

Nagatsu,Y.,Matsuda,K.,Kato,Y.,Tada,Y.,2007.Experimental study on miscible viscous?ngering involving viscosity changes induced by variations in chemical species concentrations due to chemical reactions.

Journal of Fluid Mechanics571,475–493.

Nigam,M.S.,Woods,A.W.,2006.The in?uence of buoyancy contrasts on miscible source-sink?ows in a porous medium with thermal inertia.

Journal of Fluid Mechanics549,253–271.

Nordbotten,J.M.,Celia,M.A.,Bachu,S.,2004.Analytical solutions for leakage rates through abandoned wells.Water Resources Research40(4). Oldenburg,C.M.,Pruess,K.,1995.Dispersive transport dynamics in a strongly coupled groundwater brine?ow system.Water Resources Research31

(2),289–302.

Ophori,D.U.,1998.The signi?cance of viscosity in density-dependent?ow of groundwater.Journal of Hydrology204(1–4),261–270.

Oswald,S.E.,Kinzelbach,W.,2004.Three-dimensional physical benchmark experiments to test variable-density?ow models.Journal of Hydrology 290(1–2),22–42.

Palliser,C.,McKibbin,R.,1998.A model for deep geothermal brines,ii: thermodynamic properties—density.Transport in Porous Media33(1–

2),129–154.

Park,C.H.,Aral,M.M.,2007.Sensitivity of the solution of the Elder problem to density,velocity and numerical perturbations.Journal of Contaminant Hydrology92(1–2),33–47.

Paterson,L.,1985.Fingering with miscible?uids in a Hele Shaw cell.Journal of Chemical Engineering Data28(1),26–30.

Phillips,S.L.,Igbene,A.,Fair,J.A.,Ozbek,H.,Tavana,M.,1981.A technical databook for geothermal energy https://www.doczj.com/doc/134439707.html,wrence Berkeley Labora-tory Report..Tech.rep.

Prasad,A.,Simmons,C.T.,2003.Unstable density-driven?ow in heteroge-neous porous media:a stochastic study of the Elder[1967b]“short heater”problem.Water Resources Research39(1),1–21.

Rowe,A.M.,Chou,J.C.S.,1970.Pressure–volume–temperature–concentration relation of aqueous NaCl solutions.Journal of Chemical Engineering Data 15,61–66.

Rumynin,V.G.,Konosavsky,P.K.,Hoehn, E.,2005.Experimental and modeling study of adsorption–desorption processes with application to

a deep-well injection radioactive waste disposal site.Journal of

Contaminant Hydrology76(1–2),19–46.

Scanlon,B.R.,Mace,R.E.,Barrett,M.E.,Smith,B.,2003.Can we simulate regional groundwater?ow in a karst system using equivalent porous media models?Case study,Barton Springs Edwards aquifer,USA.Journal of Hydrology276(1–4),137–158.

Schincariol,R.A.,1998.Dispersive mixing dynamics of dense miscible plumes:natural perturbation initiation by local-scale heterogeneities.

Journal of Contaminant Hydrology34(3),247–271.

62 D.J.Wright et al./Journal of Contaminant Hydrology115(2010)46–63

Schincariol,R.A.,Schwartz,F.W.,1990.An experimental investigation of variable density?ow and mixing in homogeneous and heterogeneous media.Water Resources Research26(10),2317–2329.

Schincariol,R.A.,Schwartz,F.W.,Mendoza,C.A.,1994.On the generation of instabilities in variable density?ow.Water Resources Research30(4), 913–927.

Schincariol,R.A.,Schwartz,F.W.,Mendoza,C.A.,1997.Instabilities in variable density?ows:stability and sensitivity analyses for homogeneous and heterogeneous media.Water Resources Research33(1),31–41. Schotting,R.J.,Moser,H.,Hassanizadeh,S.M.,1999.High-concentration-gradient dispersion in porous media:experiments,analysis and approximations.Advances in Water Resources22(7),665–680. Shikaze,S.G.,Sudicky,E.A.,Schwartz,F.W.,1998.Density-dependent solute transport in discretely-fractured geologic media:is prediction possible?

Journal of Contaminant Hydrology34(3),273–291.

Simmons, C.T.,Fenstemaker,T.R.,Sharp,J.M.,2001.Variable-density groundwater?ow and solute transport in heterogeneous porous media:approaches,resolutions and future challenges.Journal of Contaminant Hydrology52(1–4),245–275.

Simmons,C.T.,Narayan,K.A.,1997.Mixed convection processes below a saline disposal basin.Journal of Hydrology194(1–4),263–285. Simmons,C.T.,Narayan,K.A.,Wooding,R.A.,1999.On a test case for density-dependent groundwater?ow and solute transport models:the salt lake problem.Water Resources Research35(12),3607–3620.

Simmons,C.T.,Pierini,M.L.,Hutson,J.L.,https://www.doczj.com/doc/134439707.html,boratory investigation of variable–density?ow and solute transport in unsaturated-saturated porous media.Transport in Porous Media47(2),215–244.

Simpson,M.J.,Clement,T.P.,2003.Theoretical analysis of the worthiness of Henry and Elder problems as benchmarks of density-dependent groundwater?ow models.Advances in Water Resources26(1),17–31. Smith,L.,Freeze,R.A.,1979.Stochastic analysis of steady state groundwater ?ow in a bounded domain:1.One-dimensional simulations.Water Resources Research15(3),521–528.

Sudicky,E.A.,1986.A natural gradient experiment on solute transport in a sand aquifer:spatial variability of hydraulic conductivity and its role in the dispersion process.Water Resources Research22(13),2069–2082. Tick,G.R.,Lourenso, F.,Wood, A.L.,Brusseau,M.L.,2003.Pilot-scale demonstration of cyclodextrin as a solubility-enhancement agent for remediation of a tetrachloroethene-contaminated aquifer.Environmen-tal Science&Technology37(24),5829–5834.

U.S.EPA,2009.MCL—National Primary Drinking Water Regulations.EPA, Washington,D.C.816-F-09-0004.

van Duijn,C.J.,Peletier,L.A.,Schotting,R.J.,1998.Brine transport in porous media:self-similar solutions.Advances in Water Resources22(3), 285–297.

Verruijt,A.,1968.A note on the Ghyben–Herzberg formula.Bulletin of the International Association of Scienti?c Hydrology XIII4,43–46.Voss,C.I.,1984.A?nite-element simulation model for saturated–unsaturated,?uid-density-dependent ground-water?ow with energy transport or chemically-reactive single-species solute transport.U.S.Geological Survey Water-Resources Investigations Report84-4369.U.S.Geological Survey.

Tech.Rep.

Voss,C.I.,Provost,A.M.,2002.SUTRA—A Model for Saturated,Variable-Density Ground-Water Flow with Solute or Energy Transport.U.S.Geological Survey, Reston,VA.Tech.rep.

Voss,C.I.,Souza,W.R.,1987.Variable density?ow and solute transport simulation of regional aquifers containing a narrow freshwater–saltwater transition zone.Water Resources Research23(10),1851–1866.

Watson,S.J.,Barry,D.A.,Schotting,R.J.,Hassanizadeh,S.M.,2002.Validation of classical density-dependent solute transport theory for stable,high-concentration-gradient brine displacements in coarse and medium sands.Advances in Water Resources25(6),611–635.

Welty,C.,Gelhar,L.W.,1991.Stochastic analysis of the effects of?uid density and viscosity variability on macrodispersion in heterogeneous porous media.Water Resources Research27(8),2061–2075.

Welty,C.,Gelhar,L.W.,1992.Simulation of large-scale transport of variable density and viscosity?uids using a stochastic mean model.Water Resources Research28(3),815–827.

Wood,M.,Simmons,C.T.,Hutson,J.L.,2004.A breakthrough curve analysis of unstable density-driven?ow and transport in homogeneous porous media.Water Resources Research40(3).

Wooding,R.A.,1969.Growth of?ngers at an unstable diffusing interface in a porous medium or Hele-Shaw cell.Journal of Fluid Mechanics39, 477–495.

Wooding,R.A.,Tyler,S.W.,White,I.,Anderson,P.A.,1997.Convection in groundwater below an evaporating salt lake.2.Evolution of?ngers or plumes.Water Resources Research33(6),1219–1228.

Woods,J.A.,Carey,G.F.,2007.Upwelling and downwelling behavior in the Elder–Voss–Souza benchmark.Water Resources Research43(12). Woods,J.A.,Teubner,M.D.,Simmons,C.T.,Narayan,K.A.,2003.Numerical error in groundwater?ow and solute transport simulation.Water Resources Research39(6).

Younes,A.,Fahs,M.,Ahmed,S.,2009.Solving density driven?ow problems with ef?cient spatial discretizations and higher-order time integration methods.Advances in Water Resources32(3),303–486.

Zhang,Q.,Volker,R.E.,Lockington,D.A.,2001.In?uence of seaward boundary condition on contaminant transport in uncon?ned coastal aquifers.

Journal of Contaminant Hydrology49(3–4),201–215.

Zhou,Q.L.,Bear,J.,Bensabat,J.,2005.Saltwater upconing and decay beneath a well pumping above an interface zone.Transport in Porous Media61(3), 337–363.

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D.J.Wright et al./Journal of Contaminant Hydrology115(2010)46–63

软件开发模型介绍与对比分析

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软件工程复习题及答案

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FLAC3D学习笔记(自己总结版)

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常见的软件开发模型

常见的软件开发模型 软件开发模型是软件开发全部过程、活动和任务的结构框架。 1.软件开发模型是对软件过程的建模，即用一定的流程将各个环节连接起来，并可用规范的方式操作全过程，好比工厂的流水线。 2.软件开发模型能清晰、直观地表达软件开发全部过程，明确规定要完成的主要活动和任务，它用来作为软件项目工作的基础。 3.软件开发模型应该是稳定和普遍适用的 软件开发模型的选择应根据： 1.项目和应用的特点 2.采用的方法和工具 3.需要控制和交付的特点 软件工程之软件开发模型类型 1.边做边改模型 2.瀑布模型 3.快速原型模型 4.增量模型 5.螺旋模型 6.喷泉模型 边做边改模型（Build-and-Fix Model） 国内许多软件公司都是使用"边做边改"模型来开发的。在这种模型中，既没有规格说明，也没有经过设计，软件随着客户的需要一次又一次地不断被修改. 在这个模型中，开发人员拿到项目立即根据需求编写程序，调试通过后生成软件的第一个版本。在提供给用户使用后，如果程序出现错误，或者用户提出新的要求，开发人员重新修改代码，直到用户满意为止。 这是一种类似作坊的开发方式，对编写几百行的小程序来说还不错，但这种方法对任何规模的开发来说都是不能令人满意的，其主要问题在于：（1）缺少规划和设计环节，软件的结构随着不断的修改越来越糟，导致无法继续修改； （2）忽略需求环节，给软件开发带来很大的风险； （3）没有考虑测试和程序的可维护性，也没有任何文档，软件的维护十分困难。

瀑布模型（Waterfall Model） 1970年Winston Royce提出了著名的"瀑布模型"，直到80年代早期，它一直是唯一被广泛采用的软件开发模型。瀑布模型将软件生命周期划分为制定计划、需求分析、软件设计、程序编写、软件测试和运行维护等六个基本活动，并且规定了它们自上而下、相互衔接的固定次序，如同瀑布流水，逐级下落。 在瀑布模型中，软件开发的各项活动严格按照线性方式进行，当前活动接受上一项活动的工作结果，实施完成所需的工作内容。当前活动的工作结果需要进行验证，如果验证通过，则该结果作为下一项活动的输入，继续进行下一项活动，否则返回修改。 瀑布模型强调文档的作用，并要求每个阶段都要仔细验证。但是，这种模型的线性过程太理想化，已不再适合现代的软件开发模式，几乎被业界抛弃，其主要问题在于： （1）各个阶段的划分完全固定，阶段之间产生大量的文档，极大地增加了工作量； （2）由于开发模型是线性的，用户只有等到整个过程的末期才能见到开发成果，从而增加了开发的风险； （3）早期的错误可能要等到开发后期的测试阶段才能发现，进而带来严重的后果。 我们应该认识到，"线性"是人们最容易掌握并能熟练应用的思想方法。当人们碰到一个复杂的"非线性"问题时，总是千方百计地将其分解或转化为一系列简单的线性问题，然后逐个解决。一个软件系统的整体可能是复杂的，而单个子程序总是简单的，可以用线性的方式来实现，否则干活就太累了。线性是一种简洁，简洁就是美。当我们领会了线性的精神，就不要再呆板地套用线性模型的外表，而应该用活它。例如增量模型实质就是分段的线性模型，螺旋模型则是接连的弯曲了的线性模型，在其它模型中也能够找到线性模型的影子. 快速原型模型（Rapid Prototype Model） 快速原型模型的第一步是建造一个快速原型，实现客户或未来的用户与系统的交互，用户或客户对原型进行评价，进一步细化待开发软件的需求。通过逐步调整原型使其满足客户的要求，开发人员可以确定客户的真正需求是什么；第二步则在第一步的基础上开发客户满意的软件产品。 显然，快速原型方法可以克服瀑布模型的缺点，减少由于软件需求不明确带来的开发风险，具有显著的效果。 快速原型的关键在于尽可能快速地建造出软件原型，一旦确定了客户的真正需求，所建造的原型将被丢弃。因此，原型系统的内部结构并不重要，重要的是必须迅速建立原型，随之迅速修改原型，以反映客户的需求。 增量模型（Incremental Model） 又称演化模型。与建造大厦相同，软件也是一步一步建造起来的。在增量模型中，软件被作为一系列的增量构件来设计、实现、集成和测试，每一个构件是由多种相互作用的模块所形成的提供特定功能的代码片段构成. 增量模型在各

常用软件开发模型比较分析

常用软件开发模型比较分析 2007-09-26 20:21 正如任何事物一样，软件也有其孕育、诞生、成长、成熟和衰亡的生存过程，一般称其为“软件生命周期”。软件生命周期一般分为6个阶段，即制定计划、需求分析、设计、编码、测试、运行和维护。软件开发的各个阶段之间的关系不可能是顺序且线性的，而应该是带有反馈的迭代过程。在软件工程中，这个复杂的过程用软件开发模型来描述和表示。 软件开发模型是跨越整个软件生存周期的系统开发、运行和维护所实施的全部工作和任务的结构框架，它给出了软件开发活动各阶段之间的关系。目前，常见的软件开发模型大致可分为如下3种类型。 ① 以软件需求完全确定为前提的瀑布模型（Waterfall Model）。 ② 在软件开发初始阶段只能提供基本需求时采用的渐进式开发模型，如螺旋模型（Spiral Model）。 ③ 以形式化开发方法为基础的变换模型（T ransformational Model）。 本节将简单地比较并分析瀑布模型、螺旋模型和变换模型等软件开发模型。 1.2.1 瀑布模型瀑布模型即生存周期模型，其核心思想是按工序将问题化简，将功能的实现与设计分开，便于分工协作，即采用结构化的分析与设计方法将逻辑实现与物理实现分开。瀑布模型将软件生命周期划分为软件计划、需求分析和定义、软件设计、软件实现、软件测试、软件运行和维护这6个阶段，规定了它们自上而下、相互衔接的固定次序，如同瀑布流水逐级下落。采用瀑布模型的软件过程如图1-3所示。

图1-3 采用瀑布模型的软件过程 瀑布模型是最早出现的软件开发模型，在软件工程中占有重要的地位，它提供了软件开发的基本框架。瀑布模型的本质是一次通过，即每个活动只执行一次，最后得到软件产品，也称为“线性顺序模型”或者“传统生命周期”。其过程是从上一项活动接收该项活动的工作对象作为输入，利用这一输入实施该项活动应完成的内容给出该项活动的工作成果，并作为输出传给下一项活动。同时评审该项活动的实施，若确认，则继续下一项活动；否则返回前面，甚至更前面的活动。瀑布模型有利于大型软件开发过程中人员的组织及管理，有利于软件开发方法和工具的研究与使用，从而提高了大型软件项目开发的质量和效率。然而软件开发的实践表明，上述各项活动之间并非完全是自上而下且呈线性图式的，因此瀑布模型存在严重的缺陷。 ① 由于开发模型呈线性，所以当开发成果尚未经过测试时，用户无法看到软件的效果。这样软件与用户见面的时间间隔较长，也增加了一定的风险。 ② 在软件开发前期末发现的错误传到后面的开发活动中时，可能会扩散，进而可能会造成整个软件项目开发失败。 ③ 在软件需求分析阶段，完全确定用户的所有需求是比较困难的，甚至可以说是不太可能的。 1.2.2 螺旋模型螺旋模型将瀑布和演化模型（Evolution Model）结合起来，它不仅体现了两个模型的优点，而且还强调了其他模型均忽略了的风险分析。这

自定义本构模型

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常见软件开发模型

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软件测试和运行维护等六个基本活动，并且规定了它们自上而下、相互衔接的固定次序，如 同瀑布流水，逐级下落。 在瀑布模型中，软件开发的各项活动严格按照线性方式进行，当前活动接受上一项活动的工作结果，实施完成所需的工作内容。当前活动的工作结果需要进行验证，如果验证通过，则该结果作为下一项活动的输入，继续进行下一项活动，否则返回修改。 瀑布模型强调文档的作用，并要求每个阶段都要仔细验证。但是，这种模型的线性过程太理想化，已不再适合现代的软件开发模式，几乎被业界抛弃，其主要问题在于： （1）各个阶段的划分完全固定，阶段之间产生大量的文档，极大地增加了工作量； （2）由于开发模型是线性的，用户只有等到整个过程的末期才能见到开发成果，开发的风 从而增加了险； （3）早期的错误可能要等到开发后期的测试阶段才能发现，进而带来严重的后果。 快速原型模型（Rapid Prototype Model ） 快速原型模型的第一步是建造一个快速原型，实现客户或未来的用户与系统的交互，用户或客户对原型进行评价，进一步细化待开发软件的需求。通过逐步调整原型使其满足客户的要求，开发人员可以确定客户的真正需求是什么； 第二步则在第一步的基础上开发客户满意的软件产品。 显然，快速原型方法可以克服瀑布模型的缺点，减少由于软件需求不明确带来的开发风险，具有显著的效果。快速 原型的关键在于尽可能快速地建造出软件原型，一旦确定了客户的真 正需求，所建造的原型将被丢弃。因此，原型系统的内部结构并不重要，重要的是必须迅速 建立原型，随之迅速修改原型，以反映客户的需求。

常用软件开发模型

常用软件开发模型比较分析 正如任何事物一样，软件也有其孕育、诞生、成长、成熟和衰亡的生存过程，一般称其为“软件生命周期”。软件生命周期一般分为6个阶段，即制定计划、需求分析、设计、编码、测试、运行和维护。软件开发的各个阶段之间的关系不可能是顺序且线性的，而应该是带有反馈的迭代过程。在软件工程中，这个复杂的过程用软件开发模型来描述和表示。 软件开发模型是跨越整个软件生存周期的系统开发、运行和维护所实施的全部工作和任务的结构框架，它给出了软件开发活动各阶段之间的关系。目前，常见的软件开发模型大致可分为如下3种类型。 ①以软件需求完全确定为前提的瀑布模型（Waterfall Model）。 ②在软件开发初始阶段只能提供基本需求时采用的渐进式开发模型，如螺旋模型（Spiral Model）。 ③以形式化开发方法为基础的变换模型（Transformational Model）。 本节将简单地比较并分析瀑布模型、螺旋模型和变换模型等软件开发模型。 1.2.1 瀑布模型 瀑布模型即生存周期模型，其核心思想是按工序将问题化简，将功能的实现与设计分开，便于分工协作，即采用结构化的分析与设计方法将逻辑实现与物理实现分开。瀑布模型将软件生命周期划分为软件计划、需求分析和定义、软件设计、软件实现、软件测试、软件运行和维护这6个阶段，规定了它们自上而下、相互衔接的固定次序，如同瀑布流水逐级下落。采用瀑布模型的软件过程如图1-3所示。 图1-3 采用瀑布模型的软件过程 瀑布模型是最早出现的软件开发模型，在软件工程中占有重要的地位，它提供了软件开发的基本框架。瀑布模型的本质是一次通过，即每个活动只执行一次，最后得到软件产品，

常用软件开发模型比较分析

1.2 常用软件开发模型比较分析 正如任何事物一样，软件也有其孕育、诞生、成长、成熟和衰亡的生存过程，一般称其为“软件生命周期”。软件生命周期一般分为6个阶段，即制定计划、需求分析、设计、编码、测试、运行和维护。软件开发的各个阶段之间的关系不可能是顺序且线性的，而应该是带有反馈的迭代过程。在软件工程中，这个复杂的过程用软件开发模型来描述和表示。 软件开发模型是跨越整个软件生存周期的系统开发、运行和维护所实施的全部工作和任务的结构框架，它给出了软件开发活动各阶段之间的关系。目前，常见的软件开发模型大致可分为如下3种类型。 ① 以软件需求完全确定为前提的瀑布模型（Waterfall Model）。 ② 在软件开发初始阶段只能提供基本需求时采用的渐进式开发模型，如螺旋模型（S piral Model）。 ③ 以形式化开发方法为基础的变换模型（Transformational Model）。 本节将简单地比较并分析瀑布模型、螺旋模型和变换模型等软件开发模型。 1.2.1 瀑布模型 瀑布模型即生存周期模型，其核心思想是按工序将问题化简，将功能的实现与设计分开，便于分工协作，即采用结构化的分析与设计方法将逻辑实现与物理实现分开。瀑布模型将软件生命周期划分为软件计划、需求分析和定义、软件设计、软件实现、软件测试、软件运行和维护这6个阶段，规定了它们自上而下、相互衔接的固定次序，如同瀑布流水逐级下落。采用瀑布模型的软件过程如图1-3所示。

空间维： 把MIS的实体（系统）划分为若干个子系统。按垂直方向如分解为战略决策与计划，管理控制和执行处理三个层次；再按水平方向分解，如划分为：生产管理，材料管理，财会管理等子系统。 常用方法： 把系统按空间维分成若干个子系统，分期开发子系统，子系统的开发再遵循时间维的分解，按开发工程分步骤开发。 1.2.2 螺旋模型 螺旋模型将瀑布和演化模型（Evolution Model）结合起来，它不仅体现了两个模型的优点，而且还强调了其他模型均忽略了的风险分析。这种模型的每一个周期都包括需求定义、风险分析、工程实现和评审4个阶段，由这4个阶段进行迭代。软件开发过程每迭代一次，软件开发又前进一个层次。采用螺旋模型的软件过程如图1-4所示。 图1-4 采用螺旋模型的软件过程 螺旋模型基本做法是在“瀑布模型”的每一个开发阶段前引入一个非常严格的风险识别、风险分析和风险控制，它把软件项目分解成一个个小项目。每个小项目都标识一个或多个主要风险，直到所有的主要风险因素都被确定。 螺旋模型强调风险分析，使得开发人员和用户对每个演化层出现的风险有所了解，继而做出应有的反应，因此特别适用于庞大、复杂并具有高风险的系统。对于这些系统，

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和经管过程规范，分别适用于软件开发过程中的技术性活动和经管性活动。 1.5 软件开发过程模型 本规范所采用的软件开发过程模型为简化的RUP开发过程模型；软件开发过程是体系结构为中心，用例驱动和风险驱动相结合的过程迭代。 1.6 开发过程划分 开发过程包括多次迭代，每次迭代的目标和侧重点不同；较早的迭代侧重于业务建模和需求建模；而后的迭代则侧重于分析设计和编码。 2. 技术过程规范部分 2.1 概述 本规范中将软件开发的整个技术过程分为四个顺序实施的阶段，分别为业务建模阶段、需求阶段、分析设计阶段和实现阶段。在对技术过程规范的描述，按阶段内部的活动和产物对四个阶段分别说明。 在本规范中对阶段内活动的说明，是按顺序性活动和持续性活动两类分别进行说明。对于顺序性活动是按该阶段中活动的总体顺序进行的描述，而在实际工作中，从各活动的具体实施的细节来看，各活动之间的顺序是不断交叉变化的。对于持续性活动主要是对贯穿该阶段过程始终的技术活动进行说明。 规范中所提到的可选文档是指在其所属阶段，可根据具体情况灵活掌握，开发团队自主决定是否开发的文档产物。而提交文档则是指在工程开发过程中必须开发的文档产物，但可根据具体工程情况，在软件开发计划中明确规定是否要形成正式文档并提交。 规范中各阶段提到的技术评审，具体参见《评审规范》中所对应技术性评审的详细描述。 2.2 业务建模阶段 2.2.1 顺序性活动描述 1)开始初步调研，获取初始业务需求，进行问题定义，形成《业务概览》并建立《术语表》； 2)制定《调研记录表册》，实施详细的业务调研，建立初始的业务用例模型和《业务用例 规格》； 3)分析业务过程，取出可以实现自动化的用例，分析业务部门和实体对象，形成初始的业 务对象模型； 4)根据初始业务对象模型和初始业务用例模型，分析并提取与系统实现相关的用例和模 型，建立系统域模型； 5)精化域模型中的初始用例，详细描述业务流程，分析业务规则，建立精化的业务用例模 型，形成《业务规则》和《业务用例规格》； 6)精化域模型中的初始对象，进行详细的对象描述，分析对象职责和对象间关系，建立精 化的业务对象模型，形成《业务对象纵览》； 7)分析业务上的非功能性需求，形成《增补业务规格》； 8)应用业务对象，实现业务用例，制定《业务用例实现规格》，以验证业务对象与业务用 例的正确性，根据验证结果，修正业务对象、业务用例及相关文档； 9)汇总《业务规则》《业务用例规格》《业务对象纵览》《增补业务规格》和《业务用例 实现规格》形成《业务架构文档》。

课题_软件开发模式简介

软件开发模式简介 1. 边做边改模型（Build-and-Fix Model） 好吧，其实现在许多产品实际都是使用的“边做边改”模型来开发的，特别是很多小公司产品周期压缩的太短。在这种模型中，既没有规格说明，也没有经过设计，软件随着客户的需要一次又一次地不断被修改。 在这个模型中，开发人员拿到项目立即根据需求编写程序，调试通过后生成软件的第一个版本。在提供给用户使用后，如果程序出现错误，或者用户提出新的要求，开发人员重新修改代码，直到用户和测试等等满意为止。 这是一种类似作坊的开发方式，边做边改模型的优点毫无疑问就是前期出成效快。 对编写逻辑不需要太严谨的小程序来说还可以对付得过去，但这种方法对任何规模的开发来说都是不能令人满意的，其主要问题在于： 1）缺少规划和设计环节，软件的结构随着不断的修改越来越糟，导致无法继续修改； 2）忽略需求环节，给软件开发带来很大的风险； 3）没有考虑测试和程序的可维护性，也没有任何文档，软件的维护十分困难。 2. 瀑布模型（Waterfall Model） 瀑布模型是一种比较老旧的软件开发模型，1970年温斯顿·罗伊斯提出了著名的“瀑布模型”，直到80年代都还是一直被广泛采用的模型。 瀑布模型将软件生命周期划分为制定计划、需求分析、软件设计、程序编写、软件测试和运行维护等六个基本活动，并且规定了它们自上而下、相互衔接的固定次序，如同瀑布流水，逐级下落。 在瀑布模型中，软件开发的各项活动严格按照线性方式进行，当前活动接受上一项活动的工作结果，实施完成所需的工作内容。当前活动的工作结果需要进行验证，如验证通过，则该结果作为下一项活动的输入，继续进行下一项活动，否则返回修改。 瀑布模型优点是严格遵循预先计划的步骤顺序进行，一切按部就班比较严谨。 瀑布模型强调文档的作用，并要求每个阶段都要仔细验证。但是，这种模型的线性过程太理想化，已不再适合现代的软件开发模式，几乎被业界抛弃，其主要问题在于： 1）各个阶段的划分完全固定，阶段之间产生大量的文档，极大地增加了工作量； 2）由于开发模型是线性的，用户只有等到整个过程的末期才能见到开发成果，从而增加了开发的风险； 3）早期的错误可能要等到开发后期的测试阶段才能发现，进而带来严重的后果。 4）各个软件生命周期衔接花费时间较长，团队人员交流成本大。 5）瀑布式方法在需求不明并且在项目进行过程中可能变化的情况下基本是不可行的。 3. 迭代模型（stagewise model）（也被称作迭代增量式开发或迭代进化式开发） ，是一种与传统的瀑布式开发相反的软件开发过程，它弥补了传统开发方式中的一些弱点，具有更高的成功率和生产率。 在迭代式开发方法中，整个开发工作被组织为一系列的短小的、固定长度（如3周）的小项目，被称为一系列的迭代。每一次迭代都包括了需求分析、设计、实现与测试。采用这种方法，开发工作可以在需求被完整地确定之前启动，并在一次迭代中完成系统的一部分功能或业务逻辑的开发工作。再通过客户的反馈来细化需求，并开始新一轮的迭代。 教学中，对迭代和版本的区别，可理解如下：迭代一般指某版本的生产过程，包括从需求分析到测试完成；版本一般指某阶段软件开发的结果，一个可交付使用的产品。 与传统的瀑布模型相比较，迭代过程具有以下优点： 1）降低了在一个增量上的开支风险。如果开发人员重复某个迭代，那么损失只是这一个开发有误的迭代的花费。 2）降低了产品无法按照既定进度进入市场的风险。通过在开发早期就确定风险，可以尽早来解决而不至于在开发后期匆匆忙忙。 3）加快了整个开发工作的进度。因为开发人员清楚问题的焦点所在，他们的工作会更有效率。 4）由于用户的需求并不能在一开始就作出完全的界定，它们通常是在后续阶段中不断细化的。因此，迭代过程这种模式使适应需求的变化会更容易些。因此复用性更高 4. 快速原型模型（Rapid Prototype Model） 快速原型模型的第一步是建造一个快速原型，实现客户或未来的用户与系统的交互，用户或客户对原型进行评价，进一步细化待开发软件的需求。通过逐步调整原型使其满足客户的要求，开发人员可以确定客户的真正需求是什么；第二步则在第一步的基础上开发客户满意的软件产品。 显然，快速原型方法可以克服瀑布模型的缺点，减少由于软件需求不明确带来的开发风险，具有显著的效果。 快速原型的关键在于尽可能快速地建造出软件原型，一旦确定了客户的真正需求，所建造的原型将被丢弃。因此，原型系统的内部结构并不重要，重要的是必须迅速建立原型，随之迅速修改原型，以反映客户的需求。 快速原型模型有点整合“边做边改”与“瀑布模型”优点的意味。 5、增量模型（Incremental Model） 与建造大厦相同，软件也是一步一步建造起来的。在增量模型中，软件被作为一系列的增量构件来设计、实现、集成和测试，每一个构件是由多种相互作用的模块所形成的提供特定功能的代码片段构成。 增量模型在各个阶段并不交付一个可运行的完整产品，而是交付满足客户需求的一个子集的可运行产品。整个产品被分解成若干个构件，开发人员逐个构件地交付产品，这样做的好处是软件开发可以较好地适应变化，客户可以不断地看到所开发的软件，从而降低开发风险。但是，增量模型也存在以下缺陷： 1）由于各个构件是逐渐并入已有的软件体系结构中的，所以加入构件必须不破坏已构造好的系统部分，这需要软件具备开放式的体系结构。 2）在开发过程中，需求的变化是不可避免的。增量模型的灵活性可以使其适应这种变化的能力大大优于瀑布模型和快速原型模型，但也很容易退化为边做边改模型，从而是软件过程的控制失去整体性。 在使用增量模型时，第一个增量往往是实现基本需求的核心产品。核心产品交付用户使用后，经过评价形成下一个增量的开发计划，它包括对核心产品的修改和一些新功能的发布。这个过程在每个增量发布后不断重复，直到产生最终的完善产品。 例如，使用增量模型开发字处理软件。可以考虑，第一个增量发布基本的文件管理、编辑和文档生成功能，第二个增量发布更加完善的编辑和文档生成功能，第三个增量实现拼写和文法检查功能，第四个增量完成高级的页面布局功能。 6. 螺旋模型（Spiral Model）