Mass transport in an artificial heterogeneous aquifer: Experiments and numerical modelling

Transcription

1 Contaminant Transport in Grounwater, Kobus & Kinzelbach (es) 1989 Balkema, Rotteram SBN Mass transport in an artificial heterogeneous aquifer: xperiments an numerical moelling GSchafer & HKobus Jnstitutfiir Wasserbau, Universitiit Stuttgart, FR Germany ABSTRACT: n orer to generate a ata base for the numerical stuy of ispersion processes in a well efine heterogeneous porous meium, a laboratory tank of 14 m in length, 5 m in height an 13 m in with has been constructe, which is compose of 81 ifferent elements of exactly known geometry an hyraulic properties n ispersion experiments using salt as tracer, breakthrough curves are observe at 8 points in 8 vertical sections A comparison of three types of numerical moels with the experimental ata shows how well the moels of various complexity escribe the avection an ispersion processes an how in these cases the various ispersion parameters epen upon the moels use NTRODUCTON Mass transport in grounwater is strongly etermine by the heterogeneities of the aquifer n epth-average moels, the isregare vertical velocity variation results in an increase of isperision coefficients with the transport scale (Mercao, 1967; Gelhar an Axness, 1983) A more etaile moelling approach woul require etaile information about the aquifer structure, which is usually not available A systematical experimental investigation in a large scale moel aquifer has been carrie out in orer to generate a etaile ata base for numerical stuies n ispersion experiments, the observe breakthrough curves reflect the transport behaviour ue to the heterogeneous aquifer structure The effects of permeability ifferences upon the longituinal spreaing have been stuie using a continuous injection of tracer as well as a pulse injection The main objective of this paper is to outline the experimental stuies performe in the artificial heterogeneous aquifer an to escribe the mass transport with ifferent types of numerical moels While the transport moelling with a 2D finite ifference moel contains the aquifer structure in all its known etails, a simplifie moelling approach using a two-layer moel takes into account only characteristic parts of the aquifer Further, the performance of the classical one-imensional avectionispersion equation, as the simplest approach for the interpretation of transport processes, is checke against the available experimental ata 2 PHYSCAL MODL AND AQUFR The laboratory moel consists of a steel flume with a transparent frontage having internal imensions of 14 m x 5 m x 13 m (figure 1) Figl Physical moel 229

2 All measurement evices are mounte at the backwall of the tank in 8 vertical sections at istances of 5, 125, 375, 45, 525, 875, 125 an 135 m from the inlet section (figure 2) The inlet an outlet of the flume are screene over the entire cross-section n orer to avoi chanelling on the top part of the sans, a silicon film was presse into the sans by a constantly applie pressure xactly controlle piezometric hea bounaries at both ens of the moel guarantee a constant ischarge through the aquifer The hyraulic graient can be varie over a range from 3 to 13 percent The flume was packe using six moel layers in orer to construct a layere system with abrupt iscontinuities of iniviual layers in the manner shown in figure 2 The experimental setup was esigne by making numerical stuies using a vertically 2 transport moel (ScMfer,l987) Layer A is a heterogeneous region compose of iniviual layers A 1, A2 an A3; layer B is more permeable than A, but similarly mae up of three layers B 1, B2 an B3 (see figure 2) The average hyraulic conuctivity of layer B is about seven times higher than the one of layer A The arrangements were mae such that the epth-average permeability is constant, over the entire moel aquifer n orer to built up moel layers with ifferent hyraulic properties, three silicate sans an two types of porous ceramic plates were use San 1 an 2 are uniform homogeneous sans with a mean grain size of 38 an 57m; san 3 is a nonuniform heterogeneous san with a mean grain size of 1 5 m The components of san 3 are three uniform sans with mean grain sizes of 57, 15 an 25 m an volume ratios of 4, 25 an 35 percent The Darcy coefficients of the use sans were experimentally etermine to be m/s (san 1 ), m/s (san 2) an m/s (san 3) n orer to represent ranomly istribute heterogeneities, low- an high-permeability ceramic plates (8 x 1 x 5 m) with Darcy coefficients of m/s respectively 5 1 m/s were use The local ispersivities range from 6 m (san ) to 24 m (san 3) These values confirm the functional relationship between mean grain size an ispersivity of the soli matrix (Pfannkuch,1963) While layer A2 an B2 are built up with homogeneous silicate san an 2, layers A3 an B3 are mixtures of sans 2 an 3, respectively, an ranomly istribute porous ceramic plates n the case of layer A3 the permeability of the inclusions is about two times higher than that of the surrouning san Layer B3, however, inclues ceramic plates with a lower permeability of only 5 percent compare to silicate san 2 n both cases the pore volume of the ceramic plates per total pore volume is approximately 13 percent Layer A 1 is a composition of fine layers of high permeabiltiy (silicate san 2) an low permeability (silicate san ) As to layer B, it contains only silicate san 3 The permeability, porosity an ispersivity of each moel layer was teste in separate test series (Schlifer, 1987) n orer to stuy the transport behaviour in the given aquifer, both continuous an pulse injections of tracer over the entire cross-section at the moel inlet as well as instantaneous point injections at several locations in the aquifer were performe n this paper, the results of the cross-sectional tracer injection tests will be escribe layer A1 layer A? -- L - - 1Sm J'f +----/ layer A3 layer B1 layer 63 layer m 125m 37(m 45m 525m 87Sm 12Sm 13i5m L : : A : = :, A,,,, >:::' i r;c f:r-};;ffcf\;ftf\:fjf,fili -AlJ%:;;; t tn "', (',1 o--x 4Sm Sm 45m 14m Fig2 Aquifer structure 23

3 3 XPRMNTAL RSULTS The ispersion experiments were performe using salt of low concentration (C <1 g/1) as a tracer labelle by a ye (uranin) The tracer of given concentration as well as the clean water was applie from a constant hea tank ach reservoir can be switche separately to the flume inlet chamber, which is equippe with valves an flushing ports for force mixing in the inlet chamber By suitable operation of the various valves an flushing ports, it was ensure that the tracer was introuce uniformly over the flume entrance cross section The experiments were conucte at a constant temperature of 2 o C The concentration measurements were performe automatically at the conuctivity cells in the aquifer an at one cell irectly at the moel outlet chamber Results of a continuous-injection tracer experiment are shown in figure 3 The normalize breakthrough curves given in the figure are measure 125 meters from the inlet at ifferent elevations (see figure 2) 1, c c: os : o,::;aaoaa- = :: tixia11wiiit!--z =,12Sm ---z;:;,25m elevation z =,17Sm -z=,7sm -,,,, -elevation z =,275m 2 4 t [hours) Fig3 Measure breakthrough curves at travel istance of 125 m at ifferent elevations Up to a travel istance of approximately 15 meters the streamlines are horizontal an hence mass transport can be stuie separately in each homogeneous layer (see figure 3): elevations z 75 m an z = 25 m (layer A2/ A3 ): The breakthrough curve at the elevation of 75 m (layer A2) shows in comparison with the measurement at elevation of 25 m (layer A3) a steeper increase of concentration The equivalent longituinal ispersivity of layer A3 grows to several times of the ispersivity of the homogeneous layer A2 The results of experimental stuies in porous meia with local heterogeneities carrie out by Herr et al, 1988, confirm this effect elevation z 125 m (layer A): The transition zone at this elevation is the largest one Due to the transverse exchange between fine layers of high an low permeability, the mass exchange causes a strong concentration tailing elevation z 175 m (layer B3): The breakthrough curve at this elevation shows that the mass transport in layer B3 is strongly a etermine by the effect of two transport regimes The steep concentration increase is similar to the breakthrough curve observe in layer B2 an hence shows the influence of the silicate san 2 The ceramic plates with a permeability less than the corresponing value of the surrouning san, however, cause a concentration tailing Such ifferences in transport behaviour in heterogeneous aquifers are also escribe in the experimental stuies of Herr et al,l988 an theoretically by Spitz, 1985 elevation z m (layer Bl): The heterogeneous silicate san 3 inclue in layer Bl has the highest permeability of all use sans This causes the shortest tracer arrival time With increasing travel istance, the influence of the vertical velocity components on the tracer spreaing becomes more an more evient This can be seen from the measurements shown in figure 4 as well as in the photographs in figure 5 X point 27---o :--- layer iscontinuity point po1nt , r--:;;;;;iiiiiiiii iiiilil r 5 - point 27 istance x =3,75 R elevation z =,175 m o , 12, t [hours) 1, , 5 u! 5 - u ' point 28 istancl! x=3,75 m l!levation z =,12 5 m o , 12, t (hoursl 1,,---;;;;;;;;; lliillii! point 38 istance x=4,5 m elevation z=,125 R o-/ , 12, t!hours) Fig4 Observe breakthrough curves at istances of 375 m an 45 m The breakthrough curve at measurement point 231

4 38, which is locate 75 m ownstream of measurement point 28 shows a markely ifferent behaviour (figure 4) The given change in the vertical sequence of moel layers at the layer iscontinuity causes a flow fiel with ownwar velocity components (see figure 5) Therefore the observe breakthrough curve at observation point 38 exhibits nearly the same shape as the breakthrough curve at observation point 27 which is locate 5 m higher than point 28 A secon type of tracer experiment using a pulse njection was performe The injection volume of the tracer pulse was equal to 1 per cent of the aquifer pore volume This correspons for the chosen hyraulic graient to a pulse injection time of one hour An illustration of the tracer spreaing at a layer iscontinuity is given in figure 5 with four photographs taken at ifferent time intervals The ominant role of the highly permeable layer (B ) is shown in the first photograph With increasing time the tracer also arrives in the neighbouring low permeable layers at this cross-section, whereas in layer Bl the tracer pulse has alreay passe Figure 6 shows breakthrough curves at a istance of 125 m at ifferent elevations (see figure 2) As iscusse before, the tracer spreaing is strongly influence by the vertical twoimensional flow fiel an hence epens on the hyraulic properties of ifferent moel layers This can also be seen by the comparison of the t = 12 min t = 15 m1n t = 165 min Fig5 Pulse injection: Tracer spreaing at a layer iscontinuity ( istance x = 45 m ) 1 r , ( travel rstance x = 1,25 m,5 Fig6 elevation z =,175m!B 1) / " : : ' ' z=225m!a3) //z=,275m!a2l 9 18 t (hours] z=,375m!a3) z=,425m!a2l Pulse injection: Observe breakthrough curves at a travel istance of 125 m 3 232

5 \ r \ ci r- -/ - :-- '\ \ J z t -+X \ 45m \ / 5m \_ LSm :-- N Fig7 Compute streamline istribution observe breakthrough curves at elevations z 225 m an z m The centre of mass arrives approximately twice as fast at elevation z 225 m (layer A3) as in the higher locate layer A3 Due to the vertical mass transport, the average pore velocities in the highly permeable layers (B, B2, B3) ecrease with travel length, while the average pore velocities in the low permeable layers (A, A2, A3) increase 4 VALDATON OF A 2D TRANSPORT MODL The availability of the etaile information about the heterogeneous structure of the artificial aquifer allows etaile transport moelling using a vertically two imensional moel The avection-ispersion equation is solve in the numerical moel using centere (Crank Nicolson) an implicit ifference formulations in time n orer to keep numerical ispersion low, a space iscretization of 1 m in length an height was chosen, which results in a total number of 728 noes n the numerical moel itself the longituinal ispersivity was set equal to zero, because the numerical ispersivity is in the same orer of magnitue as the physical ispersivity The transverse ispersivity was chosen from the results of previous stuies as (at m) The application of the Crank-Nicolson scheme requires a Courant number less than one for the time step in orer to avoi numerical instabilities This restriction, together with the large number of noes, require a powerful computer in mass storage as well as calculation spee (Cray 2) The numerical moel takes into account the etaile structure of the aquifer with all its known hyraulic properties The Darcy coefficients of the use moel layers range from 48 1-s m/s (layer Bl) to m/s (layer A2); the measure porosities are about 38 percent A etaile escription of the hyraulic ata is given in Schlifer, 1987 Figure 7 shows the calculate velocity fiel in the form of stream lines The hyraulic properties of the moel layers known from separate test series an the flow rate conition for a selecte continuous-injection tracer experiment were use as input ata The streamlines illustrate the characteristic flow pattern of the artificial aquifer Between layer iscontinuities, streamlines are essentially horizontal an the flow rate in each layer epens on the given permeability Near layer iscontinuities the flow fiel exhibits vertical velocity components which cause a spreaing an focussing, repectively, of the streamlines For constant flow conitions, mass transport was calculate for a tracer experiment with continuous injection at the inlet The comparison with experimental results is shown for several observation points in figures 8 an 9 1 c c: 5 =75m travel istance x = 175 m 6 14 t [hours) 1 r : , ( c os V elevation z = 475 m travel istc1ce x=3 75 m t [hours) Fig8 Measure (symbols) an compute (lines) breakthrough curves at a istance of x-375 m at ifferent elevations 233

6 ::-;;:::"=-"'"' c 5 1 ( 5 travel istance x =135 m elevation z=175 m t [hours) t [hours] Fig9 Measure (symbols) an compute (lines) breakthrough curves at a istance of x ljs m at ifferent elevations The calculate breakthrough curves fit well with the observe values This shows that the transport processes in the moel aquifer are well represente by the two-imensional numerical moel The goo agreement of the numerical transport moel with the experiment is unerline by figure 1, in which the calculate an measure breakthrough curves at the moel outlet chamber are compare ispersion equation The avection term, expresse by the average pore velocity, is chosen as the mean value (epth-average) of the moel layers The longituinal ispersion coefficient is escribe by the prouct of the chosen average pore velocity an the mean value of the local ispersivities; the aitional transition zone ue to the vertical velocity variation is not taken into account Results of a transport moelling with this simplifie concept are shown later (see figure 13 ) Both parameters escribe the tracer spreaing accurately only when the asymptotic regime of the transport process is reache As the tracer experiments with continous injection at the moel inlet show, the measure breakthrough curves at the outlet chamber contain a steep concentration increase an a long concentration tailing Therefore, the mass transport in the moel aquifer can not be escribe by the classical one-imensional concept A more ataile moelling approach is to use a two-layer moel, in which the aquifer is compose of two regions of ifferent mobility, each representing a characteristic part of the aquifer (figure 11 ) l 1 ( c 5 -x Figl1 Two-layer moel t (hours) FigO Comparison of calculate (line) an observe (symbols) breakthrough curves at the moel outlet chamber S SMPLFD MODLLNG APPROACHS The transport in each region is escribe by the one-imensional avection-ispersion equation, with a transfer conition along the interface coupling the two layers t is assume that complete mixing occurs in both layers an that the mass flux between the two layers is proportional to the ifference in concentrations (Skopp et al, 1981 ) The concentration in both layers can then be expresse by the transport equation as Detaile moelling of the transport process nees large amounts of computer calculation time an mass storage an requires also etaile information about the aquifer structure n orer to reuce the requirements for the calculation proceure an the ata base, two simplifie moelling concepts are consiere The simplest approach contains the classical one-imensional (epth-average) avection- 234

7 where CA an C 8 are the concentrations of a noninteractive solute (kg/m 3 ) in layer A an B, VA an V 8 are the average pore velocities (in m/), DLA an DLB are the longituinal ispersion coefficients (in m 2 /), ea an e 8 are the water contents in these zones an a is the mass transfer coefficient (in ay- 1 ) quation () an (2) are solve numerically by a finite ifference scheme The average pore velocities VA an V 8 are chosen as the mean values of layer A (mae up of A, A2, A3) an layer B (mae up of B, 82, 83) near the moel inlet As a first approach, the ispersion coefficients DLA an DLB are put equal to the respective average local values, (}A an (}B are equal to the pore volume of layer A an layer B The way how the mass transfer coefficient <i has been chosen will be escribe in the following two sections n parts of the aquifer where the streamlines are horizontal, the mass transfer normal to the streamlines is cause purely by lateral ispersion Assuming that the mixing zone at the interface between two neighbouring streamlines is small compare with the thickness of the layers, the mass flux over the interface can be calculate using an analytical solution escribe by Shamir an Harleman, 1966 A comparison of this value with the mass transfer term use in the two-layer moel gives the magnitue of the mass transfer coefficient A more significant vertical mass transfer takes place near layer iscontinuities nterrupte layers an vertical changes in hyraulic permeabilities cause an increase of vertical mixing (figure 12) Due to the layer iscontinuities, the streamlines are spreaing respectively focussing As figure 12 shows, parts of the mass concentrate in layer B are transporte into layer A Assuming that the initial concentration in layer A is zero, the mass transfer coefficient a can be estimate by a comparison of the mass flux Ms-A an the mass transfer introuce in the two-layer moel Applie to the flow fiel in the moel aquifer, the mass transfer coefficents have been calculate in such a way at istances of 45, 61 an 95 m from the moel inlet A numerical solution of equation (1) an (2) has been obtaine, which takes into account the escribe hyraulic properties as well as the estimate magnitues of the mass transfer coefficient With this simplifie moel concept, epth-average breakthrough curves were calculate at ifferent locations an compare with the numerical results of the two-imensional transport moel (figure 13) Figure 13 shows that the results of the twolayer moel escribe the main features of the given breakthrough curves (results of the 2D transport moel) much better than the epthaverage moel Yet, they still exhibit some eviations from the results of the 2D transport z l Figl2 cient 5 MB-A a(x ) 1x 1y 1z 1c stimation of the mass transfer coeffi- 2 transport mcxlel Two-layer mce! Cfle-layer mcu! t [hours) Figl3 Comparison of epth-average breakthrough curves of the 2D transport moel, the two-layer moel an the one-layer moel moel The observe tailing is fairly well escribe for both travel istances with ecreasing eviations at larger istances However the steep slope of both curves (istance xz525 m an x=l35 m) oes not fit well This shows, that the assume ispersion coefficients, ientifie as average local ispersion coefficients, o not represent the transition zone in the iniviual layers A similar result illustrates figure 14 by a comparison of calculate an measure breakthrough curves at the moel outlet chamber While the tailing in the breakthrough curves can be well escribe by the two-layer moel, significant ifferences occur in the steep slope 235

8 RFRNCS 1---Two-layer mrxx!l t hours] Fig14 Comparison of calculate (line) an measure (symbols) breakthrough curves at the moel outlet chamber of the curves n orer to get a better approximation, the ispersion coefficients of layer A an B shoul take into account the increase values cause by the averaging process This will be part of further research work 6 CONCLUSONS The experimental investigations show that vertical mixing ue to transverse ispersion is negligeably small compare with the effects of layer iscontinuities in the aquifer structure Application of a high resolution numerical moel in two imensions (vertical section) to the moel aquifer showe that a goo preiction of the transport processes is possible if all etails of the aquifer structure are known n this case, ispersion effects are small an can be ientifie with the transition zone ue to the ispersivities at the local scale Since the moel aquifer exhibits two characteristic populations of markely ifferent properties, transport processes can not be escribe aequately by one-imensional epth-average moels More promising are two-layer moels which take into account at least two ifferent velocity regimes couple with a mass transfer conition along the interface With reference to the mass flux normal to the layers, it was shown that the magnitue of the transfer coefficient introuce in this moel can be estimate from the given aquifer structure an the flow conitions However, further research work will be necessary to ientify the ispersion coefficients of the twolayer moel as a function of the chosen layer structure Gelhar, L W an Axness, C L 1983 Threeimensional Stochastic Analysis of Macroispersion in Aquifers, Water Resources Res 19 (1), pp, Kobus, H 1987 Moellierung es grobr!!umigen W!!rme- un Schastofftransports im Grunwasser, TUigkeitsbericht 1986/87, Mitteilungen es nstituts fur Wasserbau, Heft 66, Universitltt Stuttgart Herr, M, Schltfer, G an Spitz, K-H 1988 xperimental Stuies of Mass Transport in Porous Meia with Local Heterogeneities, will appear in Journal of Contaminant Hyrology Herr, M 1985 Grunlagen er hyraulischen Sanierung verunreinigter Porengrunwasserleiter, Mitteilungen es lnstituts fur Wasserbau, Universit!t Stuttgart, Heft 63 Mercao, A 1967 The Spreaing Pattern of njecte Waters in a Permeable Stratifie Aquifer, Symp of Haifa, Artificial Recharge an Management of Aquifers, AHS Pub 72, pp Pfannkuch, HO 1963 Contribution a l'etue es eplacements e fluies miscibles ans un millieu poreux, Rev nst Fr Petrol, 18(2), pp Schtifer, G 1987 xperimentelle Untersuchungen zum Stofftransport in einem inhomogenen Moellaquifer, Wiss Bericht HWV 84, nstitut fur Wasserbau, Universitltt Stuttgart Shamir, U Y an Harleman, D R F 1966 Numerical an Analytical Solutions of Dispersion Problems in Homogeneous an Layere Aquifers, Hyroynamics Laboratory Report No 89, MT Skopp, J; Garner, W R an Tyler, J 1981 Solute Movement in Structure Soils: Two Region Moel with Small nteraction, Soil Sci Soc Am J, Vol 45, pp Spitz, K-H 1985 Dispersion in porsen Meien: influb von nhomogenitlhen un Dichteunterschieen, Mitteilungen es nstituts fur Wasserbau, Heft 6, Universitllt Stuttgart ACKNOWLDGMNT This work was financially supporte by the Deutsche Forschungsgemeinschaft within the Forschergruppe Moellierung es grobr!!umigen Wlirme- un Schastofftransports im Grunwasser 236