ON THE EFFICIENCY OF STORMWATER DETENTION TANKS IN POLLUTANT REMOVAL

Transcription

1 A. amond & G. Beccu, n. J. Sus. Dev. Plann. Vol., No. (7) N THE EFFCENCY F STMWATE DETENTN TANKS N PLLUTANT EMVAL A. AMND & G. BECCU Polecnco d Mlano, aly. ABSTACT n he desgn of a sormwaer deenon ank s mporan o guaranee a suffcen reenon me for he sedmenaon of suspended solds, he bologcal upake of nurens and he de-off of bacera carred n ranwaers. Long reenon mes ncrease he capacy of polluan removal, bu also he possbly of splls n downsream recevers and he rsk of envronmenal polluon. n hs paper, an analycal probablsc approach, o esmae he probably dsrbuon funcon of he average reenon me and he effcency n polluan removal of sormwaer anks has been proposed. The possbly of waer mxng from consecuve runoff evens and sorage carryover due o successve ranfall evens has been consdered. The mehod has been appled o a case sudy n Mlano, aly. Keywords: analycal probablsc approach, envronmenal polluon conrol, sormwaer deenon anks. NTDUCTN Deenon anks are ofen used n modern urban dranage sysems o acheve boh uanave and ualave conrol of sormwaer runoff. The frs goal s acheved by sorng par of runoff o reduce overflows o recevng waer bodes; he second by ensurng proper waer reenon mes. The wo goals are n conflc wh each oher snce he growh of reenon me ncreases he probably of splls from he ank. A proper desgn should consder boh hese aspecs, also ryng o lm coss [ 4]. The key pon s he defnon of an opmal reenon me. For smplcy, many governmens sugges he use of a drawdown me (me o dran a full sorage) n he range of 4 48 h. Ths assumpon has been suppored by dfferen sudes ha concluded ha shorer reenon mes could be no suffcen o allow a good sedmenaon of mos of suspended solds, whle longer reenon mes are useless because mos of parcles conaned n sormwaers sedmen n few days [5]. Moreover, long reenon mes can cause smell problems resulng from he combnaon of wasewaer ualy, emperaure and me [6]. her sudes on reenon me [7, 8], observed ha also depends on he sze of parcles and concluded ha a reenon me of 4 h can remove mos of parcles less han μm dameer and all he parcles larger han μm. Alhough reenon me s ofen regarded as a deermnsc parameer [9 ], many auhors have observed ha should be consdered a random varable [3 5]. Therefore, also ank effcency n polluon removal should be consdered as a random varable. n hs paper, an analycal probablsc approach s proposed, for he esmaon of he probably dsrbuon funcon of he average reenon me o be used for he ank effcency Ths paper s par of he Proceedngs of he 3 rd nernaonal Conference on Desgn, Consrucon, Manenance, Monorng and Conrol of Urban Waer Sysems (Urban Waer 6) 7 WT Press, SSN: (paper forma), SSN: X (onlne), hp:// D:.495/SDP-V-N-44-54

2 A. amond & G. Beccu, n. J. Sus. Dev. Plann. Vol., No. (7) 45 esmaon. The goal s, sarng from a more rgorous defnon of average reenon me consder he possbly of spll when he volume s full and he possbly of waer mxng from consecuve ranfalls due o pre-fllng of he sorage from prevous evens. Fnal expressons have been appled on a case sudy n Mlano, aly; he seres of ranfall daa recorded a Mlano-Monvso gauge saon n he perod 99 5 has been used. esuls from he proposed mehod have been compared wh hose obaned from he connuous smulaon of observed daa. TANK EFFCENCY Effcency of a deenon ank n erms of polluan removal can be defned as he fracon of nflow parcles ha are rapped nsde. A parcle s rapped when s reenon me, defned as he me passed nsde he ank before overflow or sedmenaon, s greaer han or eual o he me of sedmenaon, defned as he me needed o reach he ank boom. f sedmenaon s supposed o be manly drven by gravy and neracon among parcles s negleced, he vercal componen of velocy V s for a parcle of dameer D s expressed by he Sokes euaon: g p D Vs ( D)= ( ρ ρ) 8 µ Where ρ p and ρ are he denses of parcles and waer and µ s he cnemac vscosy of waer. Consderng he velocy expressed by en () as a mean value of a me varan physcal uany, he me reured o a parcle on he waer surface o sele on he ank boom s s smply eual o he rao: H s ( D)= () Vs ( D) where H s he waer deph. Euang s (D) o an assumed reenon me r, he lm dameer D o can be calculaed as: D o 8 m H = g ( rp r) r All he parcles wh a dameer D D o have a sedmenaon me smaller han or eual o he reenon me r and so are rapped. The fracon of hese parcles can be esmaed by feld seve analyss or from leraure daa on sedmens n sormwaer runoff. The ohers can be rapped or no accordng o her dsance from he ank boom. Assumng a unform dsrbuon along he waer deph of parcle number of each dameer, he fracon of parcles r s wh D<D o ha s rapped s eual o: / hm( D) r Vs ( D) Vs ( D) D rs ( D)= = = = H V ( D ) V ( D ) D r s o s o o where h m s he dsance from he ank boom for whch a parcle wh D<D o has a sedmenaon me eual o r. Tank effcency n parcle removal can hen be calculaed by he followng relaonshp: D E = ( Fo )+ D fd x dx D ( ) (5) o () (3) (4)

3 46 A. amond & G. Beccu, n. J. Sus. Dev. Plann. Vol., No. (7) where F o s he fracon of parcles wh a dameer smaller han D o and f D (x) s he slope of he angen of he parcle gradaon curve. From he combnaon of ens (3) and (5) resuls ha he ank effcency E s a funcon of he reenon me. f nflow and ouflow are eual and me nvaran, as n seady flow sedmenaon anks, hs me s consan and smply calculaed by he relaonshp: B H L W * o = = (6) Q Q where B and L are he ank wdh and he lengh and Q he consan flow. Sormwaer anks, however, are characerzed by varable nflow and ouflow, causng a connuous process of fllng and empyng. So, reenon me s also varable and ofen an average value s consdered, dependng on nflow and ouflow paern. Due o hydrologc processes of ranfall-runoff ransformaon acng on he upsream urban cachmen, boh hs average reenon me and he relaed ank effcency can be regarded as random varables. has o be hghlghed ha usng an average reenon me mples also ha he ank effcency gven by en (5) should be consdered as an average oo. n he nex paragraph, he probably dsrbuon of average reenon me s derved, o be used ogeher wh en (5) o acheve a probablsc esmaon of hs average ank effcency. 3 PBABLTY DSTBUTN FUNCTN F AVEAGE ETENTN TMES n he esmaon of he probably dsrbuon funcon of average reenon mes some assumpons for he smplfcaon of he analycal probablsc model have been made: n-lne sormwaer deenon ank; nflows have been consdered of consan nensy (recangular evens); Consan ouflows rae Q () = ; unoff volume for un of cachmen surface v has been assumed eual o ranfall deph h less han an nal Absracon A mulpled by he runoff coeffcen φ, ha s v=φ (h-a); anfall-runoff ransformaon has been negleced, as ypcal for small cachmens wh shor corrvaon mes. For hghly urbanzed cachmen where A ends o zero and φ ends o one, runoff volume can be consdered eual o ranfall volume, v = h and runoff duraon can be assumed eual o ranfall duraon; Use of he ner Even Tme Defnon ETD, o solae ndependen ranfall evens from he connuous chan of sorms: f he dry me beween wo consecuve ranfall evens s smaller han ETD, he wo evens have been joned ogeher no a sngle even, oherwse hey have been consdered ndependen; Exponenal dsrbuon of he hydrologcal varables nvolved n he sorage process (ranfall deph h and duraon θ, nereven me d): f d f h = ξ e f = λ e = ψ e ξ h λθ ( ) ψ d ETD (7) (8) (9)

4 A. amond & G. Beccu, n. J. Sus. Dev. Plann. Vol., No. (7) 47 where ξ =/μ h, λ = /μ θ and ψ = /(μ d -ETD), wh μ h : average ranfall deph, μ θ : average ranfall duraon, μ d : average nereven me. To esmae he probably dsrbuon funcon of average reenon mes, care mus be aken o he defnon of reenon me. f he hypohess of plug flow (flow parcels leave he basn n he same order hey enered) and compleely mxed flow are consdered, he average reenon me. can be calculaed as he dfference beween he average release me and he average npu me sha s he horzonal dsance beween cenrods of nflow and ouflow hydrographs: = () n he assumpon of ndependence of nflow and ouflow hydrograph, en () can be smplfed as follow: f d f d = = ( ) ( ) = d () V V = Q () d Q () : release me, ha concdes wh empyng me; : npu me; V : ouflow volume; V : nflow volume; Q : ouflow rae; Q : nflow rae. For consan ouflow rae, Q (τ) = = cons., he average release me resuls: = Q () d = = V () f even nflow rae s consan durng he even, Q (τ) = = cons., he average nflow me resuls: = Q () d = = V (3) Consderng he smplfyng hypohess of ens () (3) becomes: = ( )= = (4) Somemes, he ank s no compleely empy when a new runoff even occurs, ha s here s a carryover from prevous runoffs. bvously, he probably of pre-fllng ncreases when ouflow rae s low, as n he case of anks for he enhancemen of waer ualy (e.g. frs flush anks). For hs reason, n he esmaon of he probably dsrbuon funcon of average

5 48 A. amond & G. Beccu, n. J. Sus. Dev. Plann. Vol., No. (7) reenon mes he possbly of waer mxng from wo consecuve runoffs has been consdered. n he followng, specfc varable (for un of area) have been used. For a couple of consecuve runoffs and +, f w s he sorage volume and he consan ouflow rae, wo dfferen condons can occur: w/ ETD: he possbly of pre-fllng of he sorage volume from he even a he begnnng of he even + s excluded; w/>etd: he sorage volume could be no compleely empy from he even a he begnnng of he even + and pre-fllng could occur. n case here s no waer carryover from even sorage volume s compleely empy a he begnnng of even + ( <θ +d ), as shown n Fg.. f he acve volume s parally flled a he begnnng of even + (Fg. ), waer mxng from wo consecuve evens has o be consdered n he dervaon of he probably dsrbuon funcon of average reenon mes. Fgure : Couple of runoffs whou pre-fllng. Fgure : Couple of runoffs wh pre-fllng.

6 A. amond & G. Beccu, n. J. Sus. Dev. Plann. Vol., No. (7) 49 Generally nflow raes can be hgher or lower han ouflow raes; n he frs case, he possbly of splls f sorage volume s full a he end of each even has been consdered. 3. Condon w/ ETD: pre-fllng s excluded n hs case, ner-even me s always enough o have no prefllng and evens are ndependen. The nflow me concdes wh he runoff duraon θ, so ha en (4) becomes: The empyng me can be expressed by: = h / θ + w/ = ( θ ) (5) h θ < h θ < w (6) h θ w Subsung en () n en (), he average reenon me resuls: = h / θ w/ h θ < h θ < w (7) h θ w has o be observed ha he average reenon me has an upper lm, eual o (w/)/, and s probably dsrbuon funcon s runcaed n he upper al. From ens (7), he probably ha he average reenon me s greaer han a fxed value x s hen expressed as: and * = ξ /λ. w w F = P( x < )= P x < < P + = w+ = f d fh dh+ f d f = h= ( + ) = h= w+ 3. Condon w/ >ETD: possbly of pre-fllng x h xx e dh = + * (8) n case of pre-fllng from even a he begnnng of even +, he average npu me can be expressed by: = Q () d = Q d + Q V V,, + ( ) h θ / + h+ θ + d + θ+ / = h + h + + d+ + + d d = (9)

7 5 A. amond & G. Beccu, n. J. Sus. Dev. Plann. Vol., No. (7) Euaon () n hs case resuls: ( ) h θ + h θ + d + θ = = h + h+ The empyng me can be expressed by: + + case h / cases V w/ + θ casesv V = w/ + θ+ casev ( h + h+ )/ casev θ + d + θ+ + w/ casesx X θ + ( w+ h+ )/ case X () () case anfall nensy lower han ouflow rae: h ; h + + case No pre-fllng, even whou splls: < h w; h - d ; case nensy of even lower han ouflow rae, even + whou splls: h ; <h + + w; case V Pre-fllng, even whou splls, even + wh nensy lower han ouflow rae: < h w; h - d >; h - d +h + + ; case V No pre-fllng, even wh splls: h > w; w- d ; case V Even wh nensy lower han ouflow rae, even + wh splls: h ; h + + > w; case V Pre-fllng, even wh splls, even + wh nensy lower han ouflow rae: h > w; w- d > ; w- d +h + + ; case V Pre-fllng, boh even and even +whou splls: < h w; h - d > ; < h - d +h + + w; case X Pre-fllng, boh and even and even +wh splls: h > w; w- d > ; w- d +h + + > w; case X Pre-fllng, even whou splls, even +wh splls:

8 A. amond & G. Beccu, n. J. Sus. Dev. Plann. Vol., No. (7) 5 < h w; h - d > ; h - d +h + + > w; case X Pre-fllng, even wh splls and even +whou splls: h > w; w- d > ; <w- d +h + + w. For he same assumpon on he probably dsrbuon funcons of ranfall deph, duraon and nereven me consdered above, ha s f h, =f h,+ =f h, f θ, =f θ,+ =f θ and f d =f d, =f d,+, case, case V, case V, case V and case X canno occur and en () becomes: = = [ θ d] () Subsung en () n ens (5) and (), respecvely, f a sngle even or a couple of chaned evens s consdered, he average reenon me resuls: case h = 5. ( / θ ) case h/ θ d / casev w/ ( ) casesv X X Euaon (3) s vald for w/>etd and for x < w/( ). The probably dsrbuon funcon of average reenon mes resuls: w w F = P ( x < )= P < x < P + = = f d d d d h h h 4 3 d4 d d3 h4 f dd f dh + f d f dd f dh d5 d6 h6 h5 8 7 d8 d7 h h3 f d fd dd fh dh + f d fd dd f dh θ =θ 3 =θ 5 =θ 7 =; θ =θ 4 =θ 6 =θ 8 = ; h8 h h7 d =d 8 = x ; d =d 4 =d 5 =w/; d 3 =d 7 =ETD; d 6 = ; (3) (4) h =h 5 = (θ+ x ); h =h 3 =h 8 = θ+( d+w)/; h 4 =h 6 = ; h 7 = ( x +d/+θ); whch soluon s: F y ETD x ( x)= ( ) e ( y+ x b ) + b e + * wh: β = ψ/( ξ+ ψ) and *= ξ/λ. ETD x + x (4*) 4 CASE STUDY To es he relably of derved expressons for he esmaon of he probably dsrbuons of average reenon mes, a case sudy n Mlano, aly, has been analyzed. The seres of ranfall daa recorded a Mlano-Monvso gauge saon n he perod 99 5 has been used and ETD= hours has been assumed.

9 5 A. amond & G. Beccu, n. J. Sus. Dev. Plann. Vol., No. (7) Table : Man characerscs of ranfall varables. μ h [mm] 8.49 V h [-].5 ρ h,θ [-].6 μ θ [h] 4.37 V θ [-].3 ρ θ,d [-]. μ d [h] 7.8 V d [-].3 ρ d,h [-]. Fgure 3: Probably and freuency dsrbuons of average reenon mes (w = 5 mm; = mm/h; =.5 mm/h). Fgure 4: Probably and freuency dsrbuons of average reenon mes(w = mm; = mm/h; =.5 mm/h).

10 A. amond & G. Beccu, n. J. Sus. Dev. Plann. Vol., No. (7) 53 The man characerscs (mean, varaon coeffcen and correlaon ndex) of ranfall varables nvolved n sorage process (ranfall deph h, ranfall duraon θ and nereven me d) have been shown n Table. uflow raes of =.5 mm/h and =. mm/h and a sorage volume w = 5 mm and w = mm have been consdered. Fgures 3 and 4 compare he probably dsrbuon funcons of he average reenon me, calculaed by ens (8) and (4*) wh he freuency dsrbuon of smulaed daa, respecvely, for w = 5 mm and w = mm (connuous black lne and crcles for =. mm/h and connuous grey lne and crosses for =. mm/h). Dfferences n resuls can be due o: The smplfyng assumpon on he ndependence of npu ranfall varables h, θ, d whle n parcular he correlaon ndex beween ranfall deph and ranfall duraon s no neglgble (Table ); The smplfyng assumpon on exponenal dsrbuon of npu ranfall varables h, θ, d; as can be deduced from Table, only he freuency dsrbuon of ranfall duraons perfecly fs an exponenal probably dsrbuon funcon (V θ ); The smplfyng assumpon of consderng only a couple of consecuve even a me; f he ouflow rae ends o zero, he number of chaned evens ncreases: The smplfyng assumpon of consderng he probably dsrbuon funcons of ranfall characerscs of even eual o hose of even +(f h, =f h,+ =f h, f θ, =f θ,+ =f θ and f d =f d, =f d,+ ), ha excludes cases -V-V-V-X of en () n he resulng formula (4*); 5 CNCLUSNS Proposed approach relaes he effcency of a sormwaer deenon anks n polluan removal wh he reenon me. n parcular, he probably dsrbuon funcon of he average reenon me has been esmaed. Derved formulas are easy o mplemen and can be a vald ad o engneer, when here are no long-erm regsraon of records daa and only he mean values of ranfall characerscs are avalable. Moreover, hey can be used o sze sormwaer deenon anks because allow o analyze he nfluence of ouflow raes and sorage volumes on he probably dsrbuon of he average reenon me, ha s on probably dsrbuon of he effcency of he sorage n polluan removal. EFEENCES [] Carleon, J.N., Grzzard, T.J., Godrej, A.N. & Pos, H.E., Facors affecng he performance of sormwaer reamen welands. Waer esearch, 35, pp ,. hp://dx.do.org/.6/s43-354()46-4 [] Guo, Y. & Adams, B.J., Analyss of deenon ponds for sorm waer ualy conrol. Waer esources esearch, 35, pp , 999. hp://dx.do.org/.9/999w94 [3] Beccu, G. & amond, A., Probablsc analyss of splls from sormwaer deenon facles, WT Transacons on he Bul Envronmen, 39, Urban Waer (SSN: ), WT Press, 4. hp://dx.do.org/.495/uw44

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