Fnal copy as submtted to Ground Water for publcaton as: Day-Lews, F.D., Johnson, C. D., Pallet, F.L., and Halford, K.J., 2011, A computer program for flow-log analyss of sngle holes (FLASH): Ground Water, do: 10.1111/j.1745-6584.2011.00798.x A Computer Program for Flow-Log Analyss of Sngle Holes (FLASH) Frederck D. Day-Lews 1, Carole D. Johnson 2, Frederck L. Pallet 3, and Keth J. Halford 4 Abstract A new computer program, FLASH (Flow-Log Analyss of Sngle Holes), s presented for analyss of borehole vertcal flow logs. The code s based on an analytcal soluton for steady-state mult-layer radal flow to a borehole. The code ncludes optons for (1) dscrete fractures and (2) multlayer aqufers. Gven vertcal flow profles collected under both ambent and stressed (pumpng or njecton) condtons, the user can estmate fracture (or layer) transmssvtes and far-feld hydraulc heads. FLASH s coded n Mcrosoft Excel 5 wth Vsual Basc for Applcatons routnes. The code supports manual and automated model calbraton. Introducton Flowmeters provde means to nfer the flow nto or out of boreholes connected to transmssve aqufer unts or fractures. In the past, the relatve naccuracy and dffcult operatng procedures for spnner flowmeters lmted the use of borehole flow measurements. Wth the advent of heat-pulse (e.g., Pallet et al., 1996) and electromagnetc (Molz et al, 1994) nstruments, measurements of vertcal flow as small as 0.05 lters/mnute became practcable, and borehole flowmeter loggng s becomng routne. New modelng and analyss tools are needed to acheve the full potental of these measurements. Calbraton of a borehole flow model to flowmeter data can produce estmates of transmssvty and heads for one or more flow zones (aqufer layers or fractures). Here, we brefly revew approaches for analyss of flowmeter logs and ntroduce a new computer program whch supports manual and automated calbraton of an analytcal borehole flow model. Approach Sngle-hole flowmeter data can be analyzed to estmate transmssvty profles along boreholes and characterze aqufer compartmentalzaton (e.g., Molz et al., 1989; Kabala, 1994; Pallet, 1998). Analyss of sngle-hole flowmeter data s commonly based on the Them Equaton (Them, 1906), whch wrtten for confned radal flow from a sngle flow zone (.e., aqufer layer or fracture) to a screened or open well s: 1 Correspondng Author: U.S. Geologcal Survey, Offce of Groundwater, Branch of Geophyscs, 11 Sherman Place, Unt 5015, Storrs CT 06269; daylews@usgs.gov; Phone: 860.487.7402 x21; Fax: 860.487.8802 2 U.S. Geologcal Survey, Offce of Groundwater, Branch of Geophyscs, 11 Sherman Place, Unt 5015, Storrs CT 06269 3 U.S. Geologcal Survey, Emertus, Offce of Groundwater, Branch of Geophyscs, 11 Sherman Place, Unt 5015, Storrs CT 06269 4 U.S. Geologcal Survey, Nevada Water Scence Center, 2730 N. Deer Run Rd., Carson Cty, Nevada, 89703 5 Any use of trade, product, or frm names s for descrptve purposes only and does not mply endorsement by the U.S. Government. 1
where, Q s the volumetrc flow nto the well from flow zone [L 3 T -1 ]; h w and h are, respectvely, the hydraulc head [L] at the radus of the well r w, and at radal dstance r 0, commonly taken as the radus of nfluence, where heads do not change as a result of pumpng, n whch case h s the connected far-feld head for zone ; and T s transmssvty of flow zone [L 2 T -1 ]. A number of approaches to flowmeter analyss have been proposed and demonstrated for dfferent sets of assumptons (e.g., no ambent flow n boreholes) and data requrements (e.g., flow profles collected under both ambent and stressed condtons) based ether on Equaton (1) (e.g., Molz et al., 1989) or quas-steady flow approxmatons (e.g., Pallet, 1998). We refer the nterested reader to Wllams et al. (2008) for addtonal background on flowmeter logs and focus the followng dscusson on the approach of Pallet (1998, 2001) whch s adapted here. Pallet (1998) formulated flowmeter log analyss as a model calbraton procedure nvolvng flow profles collected under both ambent and stressed (pumpng or njecton) condtons. Consderaton of the two condtons allows for estmaton of the transmssvtes and also far-feld heads of flow zones. The latter s crtcal for nterpretaton of water samples from wells that ntersect multple fractures or layers wth dfferent hydraulc head (e.g., Johnson et al., 2005). Applyng Equaton (1) to an ambent condton (condton a) and a stressed condton (condton s) gves: Q Q a s 2 T T h h ln r r total a 0 w 2 T T h h ln r r 0 w total s 0 w 0 w where, s the fracton of the borehole s transmssvty contrbuted by flow zone [-]; s the total transmssvty of the flow zones ntersected by the borehole [L 2 T -1 ];, are the ambent and stressed water levels n the well, respectvely [L]; s the far-feld head n flow zone [L]; For both ambent and stressed condtons, the water level n the borehole s assumed to be constant n tme, and the water level n the far feld of each zone s assumed to be the natural condton,.e.,. In a feld experment (Fg. 1), r w would be known, and the flow rates and water levels n the well would be measured. Radus of nfluence can be nferred expermentally based on head data at observaton wells, n whch case r 0 can be constraned durng calbraton, or else t can be approxmated (e.g., Bear, 1979, p. 306). Estmates of transmssvty are not strongly senstve to the value assumed for r 0 because t appears nsde the logarthm n Equatons (2-3). For example, a change n r 0 r w from 10 to 100 yelds a change n the estmated T of only a of 2, and order-of-magntude estmates of transmssvty are acceptable for many problems. In cases where knowledge of r 0 s unavalable, but the borehole s total transmssvty s known from specfc-capacty or slug-test results, t s possble to estmate r 0 n the calbraton procedure. We note that the forward model (Equatons 2, 3) produces twce as many ndependent equatons as there are flow zones, wth an addtonal equaton requrng values to sum to 1. The number of parameters beng estmated s twce the number of flow zones ( ) plus one parameter for ether or. Model calbraton nvolves changng the model parameters such that the flows predcted by Equatons (2-3) match the nterpreted flow profles. Followng Pallet (1998, 2001), calbraton s to the nterpreted profle and not ndvdual data. Ths formulaton allows the user to ncorporate addtonal (1) (2) (3) 2
nsght (e.g., from other logs) to dentfy the number and locatons of flow zones and elmnates the need for weghtng measurements dfferently accordng to varable measurement errors and the spatal dstrbuton of measurements along the borehole. Calbraton can be mplemented by manual tral-and-error or automated usng nonlnear regresson. Whether manual or automated, the goal for calbraton s to dentfy the set of parameters that mnmze a measure of combned data msft and model msft. Consderaton of model msft crtera, commonly referred to as regularzaton, s useful when multple models can match the data equally well or wthn measurement errors. Here, the data msft s formulated based on squared dfferences between the predcted and nterpreted flow profles, such that multple measurements may be collected n a sngle borehole nterval. The model msft could be formulated n dfferent ways, but we use crtera based on the dfferences between the water level n the borehole under ambent condtons and the far-feld heads. Thus, the objectve functon, F, conssts of two terms: (1) the mean squared error (MSE) between nterpreted and predcted flow profles, wth equal weghts for all cumulatve flows (ambent and stressed), and (2) the sum of squared dfferences ( ) between the borehole's water level and far-feld heads: subject to constrants (4) a, nt s, nt where, Q, Q are the nterpreted flow profles (.e., cumulatve flow above zones) for zone under ambent and stressed condtons, respectvely [L 3 T -1 a, sm s, sm ]; Q, Q are the smulated flow profles (.e., cumulatve flow above zones) for zone under ambent and stressed condtons, respectvely [L 3 T -1 ]; α weghts the regularzaton relatve to the data msft [L 4 T -2 ]; T s the user-specfed mnmum T for any flow zone whch can ensure non-negatve T ; s the user-specfed maxmum absolute dfference between the ambent water level and the far-feld head of any flow zone; and n s the number of flow zones. Wthout regularzaton, F reduces to the MSE between smulated and nterpreted flows. The tradeoff parameter s set by the user, wth larger values more strongly penalzng large head dfferences. Commonly, small values (<0.001) are suffcent to obtan good results. In selectng, the user should be guded by the goal of regularzaton, whch s to dentfy the "smplest" explanaton of the data whle mnmzng the data msft. Usng Flash FLASH (Flow-Log Analyss of Sngle Holes) s wrtten n Excel wth Vsual Basc for Applcatons (VBA). The spreadsheet ncludes a toggle (INPUTS worksheet cell A20) to choose between analyss for (1) fractures or fracture zones that ntersect a well at dscrete locatons, and (2) aqufer layers n porous meda. The frst s ndcated for cases where flow profles are characterzed by step ncreases/decreases, and the second for cases where flow profles show approxmately lnear change over each layer. Up to 10 fractures or layers can be modeled. The FLASH spreadsheet ncludes four worksheets: INTRODUCTION, INPUTS, FIELD_DATA, and PLOTTING. INTRODUCTION provdes nformaton about the program and nput parameters. On the INPUTS worksheet, the user enters nformaton about the flow zones, transmssvtes, and heads. Note that the user must nterpret flow profles from the flowmeter data, for mn 3
both the ambent and stressed condtons. The flow measurements are entered n FIELD_DATA, and the nterpreted profles are entered n INPUTS. The nterpreted profles plot as dashed lnes, the data as ponts, and the smulated profles as sold lnes (Fgure 2). Lne and marker styles can be modfed usng standard Excel tools. Flows are postve upward and negatve downward. PLOTTING s used by the program and does not requre the user's attenton. In the INPUTS worksheet, nput parameters are entered n the cells wth lght blue and brght aquamarne backgrounds. The former nclude specfcatons of the experment setup (e.g., borehole dameter and water level), and the latter nclude calbraton parameters. Manual calbraton s performed by adjustng the values of the cells TFactor and h, whch are, respectvely, T, and the dfference between the flow zone s far-feld head and the ambent water level n the borehole. As parameters are adjusted, the smulated flow profles update automatcally, thus gudng the user toward best-ft parameters. The MSE between smulated and observed flows s calculated n cell B36 on the INPUTS worksheet. Although the prncple calbraton parameters are T and h, the radus of nfluence, r 0, and total transmssvty, T total, also are possble calbraton parameters as explaned above and ndcated by aquamarne hghlghtng. By nspecton of Equatons (2-3), t s not possble to estmate unque values for both radus of nfluence and total transmssvty, but only the rato of total transmssvty dvded by ln(r 0 /r w ). In general, the user wll have more nformaton about total transmssvty than radus of nfluence. Total transmssvty s estmated readly usng an open-hole slug test or specfc capacty test. Indeed, the drawdown and pumpng rate under stressed condtons could serve as data to estmate a total transmssvty for the borehole. In rare cases, however, the estmated total transmssvty may be consdered unrelable, e.g., n the presence of ambguous slug-test data or dscrepancy between the volumes over whch the slug test and flowmeter analyss measure. In such cases t may be useful to allow thet values to sum to a value other than 1. FLASH assumes a unform radus of nfluence for all flow zones. In realty the effectve radus of nfluence may vary between zones accordng to ther transmssvtes and dstances to boundares. Data to support varable radus of nfluence, however, s commonly unavalable; furthermore, transmssvty estmates are not a strong functon of the assumed radus of nfluence, as explaned prevously. Automated model calbraton s mplemented usng the Excel Solver, an optmzaton tool based on a Generalzed Reduced Gradent algorthm (Lasdon and Smth, 1992). The Solver s nvoked usng VBA control buttons on the INPUTS worksheet. Rado buttons allow for selectons of (1) the parameters to be estmated (Estmate ROI (radus of nfluence) or Estmate Transmssvty), and (2) regularzaton (Solve wthout Regularzaton or Solve wth Regularzaton). Under the opton Estmate ROI, the Solver estmates the values of T for all, and the sngle radus of nfluence. Under the opton Estmate Transmssvty, radus of nfluence s assumed known, the parameters for estmaton are T for all, such that total transmssvty s allowed to vary. Users are encouraged to perform manual calbraton before attemptng automated calbraton. Manual calbraton provdes nsght nto the senstvty of flows to parameters, and helps to dentfy a good startng model for automated calbraton. As for any non-lnear optmzaton, the algorthm may get stuck n local mnma and fal to dentfy the globally optmal parameter values. Consderaton of multple startng models s advsed. Addtonal nformaton and the FLASH spreadsheet are avalable onlne, as noted under 'Supportng Informaton' at the end of ths artcle. 4
Example FLASH s demonstrated for a smple dataset from a fractured-rock aqufer (Fgure 2). Johnson et al. (2005) provde addtonal detals for ths dataset, for whch addtonal borehole logs were used to dentfy fractures and select locatons for flow measurements. Under ambent condtons, the deeper fractures #1 and #2 experence nflow to the borehole, whch ndcates the far-feld heads for each of these fractures s greater than the head n the borehole thus producng upward flow (Fgure 1). Under ambent condtons, upflowng water exts the borehole at fracture #3, ndcatng the far-feld head s lower than the head n the borehole. Under low-rate pumpng condtons, water contnues to enter the borehole at fracture #1, addtonal water enters at fracture #2, ndcatng the far-feld heads for fractures #1 and #2 are hgher than the quas-steady state, open-hole water level under pumpng condtons. The uppermost fracture (#3) no longer shows outflow, ndcatng the far-feld head s equal to the pumpng water level. In ths example, fracture #2 has a farfeld head smlar to the ambent water level n the well and therefore does not result n a substantal change n borehole flow under ambent condtons. Smlarly, fracture #3 has a far-feld head smlar to the stressed water level n the well and does not produce a measurable change n borehole flow under stressed condtons. Ths feld example underscores the mportance of collectng both ambent and stressed flow profles wth only ambent data, fracture #2 could not be dentfed, and wth only stressed data fracture #3 could not be dentfed. To nduce flow from a gven fracture to enter the borehole, the for that fracture must be postve. Conversely, to nduce flow from the borehole to the fracture, the must be negatve. The rate of flow s determned by the magntude of a gven flow zone s and transmssvty. Thus, manual calbraton entals for each zone (1) adjustment of a (cells F21:F30) to control whether flow enters or exts the borehole from that zone, and (2) adjustment of a T to control the rate of flow. A fnal soluton can be obtaned wth the manual ft, or after a startng model s generated manually, the Solver can be appled. For the example here, automated calbraton produces an excellent match to the data (Fgure 2) usng optons "Estmate ROI" and "Estmate wth Regularzaton." Dscusson And Conclusons We present a new tool to ad n flowmeter log analyss, a computer code named FLASH. We follow a model-calbraton strategy smlar to that of Pallet (1998), wth a smple analytcal model for borehole flow based on the Them Equaton (Them, 1906), whch has been used extensvely n prevous analyses of flowmeter logs. It s mportant to note that FLASH assumes a borehole flow model that neglects head losses n the borehole or across the well screen, and these losses are mportant n some datasets (Zlotnck and Zurbuchen, 2003). We also note the lmtatons nherent to flowmeter methods, prmarly that they not as senstve as straddle-packer hydraulc testng. Flowmeter methods consstently dentfy transmssvtes wthn 1.5-2 orders of magntude of the most transmssve zone n a borehole, dependng on the resoluton of the flowmeter tself (Wllams et al., 2008), but straddle-packer tests can see features 6 orders of magntude less transsmve than s possble wth flowmeter (Pallet, 1998; Day- Lews et al., 2000; Shapro, 2001). Despte the lmted resoluton of flowmeter measurements, flowmeter modelng results can reproduce packer-test estmates to wthn an order of magntude, and far-feld head values determned wth flowmeter methods commonly compare well wth packer-test results and dscrete-nterval water-level montorng (Johnson et al., 2005; Wllams et al., 2008). FLASH provdes a graphcal user nterface for calbraton of an analytcal borehole flow model and estmaton of flow-zone transmssvtes and far-feld heads. The program supports manual and automated calbraton, wth and wthout regularzaton. FLASH s hghly customzable. Experenced 5
Excel users may prefer to nvoke the Solver outsde of FLASH's VBA routnes, or to use alternatve objectve functons or regularzaton crtera, or varable weghtng for ambent vs. stressed flows. Future extensons may nclude tools for analyss of crosshole flowmeter data and evaluaton of estmaton uncertanty. Acknowledgments Ths work was supported by the U.S. Envronmental Protecton Agency, Regon 1, the U.S. Geologcal Survey Groundwater Resources Program and Toxc Substances Hydrology Program. The authors are grateful for revew comments from Tom Relly, Allen Shapro, Tom Burbey, John Wllams, Roger Morn, Lands West, and Mary Anderson. Supportng Informaton Supplemental materal avalable onlne nclude: (1) the FLASH spreadsheet, whch also can be downloaded from http://water.usgs.gov/ogw/flash/ ; and (2) a README fle wth nformaton for nstallaton and troubleshootng. References Bear, Jacob, Hydraulcs of Groundwater, McGraw-Hll, Inc., New York, 1979. Day-Lews, F.D., Hseh, P.A., and Gorelck, S.M., Identfyng fracture-zone geometry usng smulated annealng and hydraulc-connecton data, Water Resources Research, 36 (7), 1707-1721, 2000. Johnson, C.D., Kochss, C.K., and Dawson, C.B., Use of dscrete-zone montorng systems for hydraulc characterzaton of a fractured-rock aqufer at the Unversty of Connectcut landfll, Storrs, Connectcut, 1999 to 2002: U.S. Geologcal Survey Water-Resources Investgatons Report 03-4338, 105 p, 2005. Kabala, Z. J., Measurng dstrbutons of hydraulc conductvty and storatvty by the double flowmeter test, Water Resources Research, 3, 685 690, 1994. Lasdon, L.S. and Smth, S. Solvng large sparse nonlnear programs usng GRG, ORSA Journal on Computng, 4(1), pp. 2-15, 1992. Molz, F. J., G. K. Bowman, S. C. Young, and W. R. Waldrop, Borehole flowmeters feld applcaton and data analyss, J. Hydrology, 163(3-4), p. 347 371, 1994. Molz, F.J., R.H. Morn, A.E. Hess, J.G. Melvlle, and O. Guven, The mpeller meter for measurng aqufer permeablty varatons: evaluatons and comparson wth other tests, Water Resources Research, 25(7), p. 1677-1683, 1989. Pallet, F.L., Flow modelng and permeablty estmaton usng borehole flow logs n heterogeneous fractured formatons, Water Resources Research, 34(5), 997-1010, 1998. Pallet, F. L., R. E. Crowder, and A. E. Hess, Hgh-resoluton flowmeter loggng applcatons wth the heat-pulse flowmeter, J. Envronmental and Engneerng Geophyscs, 1(1), 1 14, 1996. Pallet, F.L., Hydraulc head applcatons of flow logs n the study of heterogeneous aqufers, Ground Water, 39(5), p. 667-675, 2001. Shapro, A.M., Effectve matrx dffuson n klometer-scale transport n fractured crystallne rock, Water Resources Research, 37(3), 507-522, 2001. Them, Gunther, Hydologsche methoden: Lepzg, J. M. Gebhardt, 56 p, 1906. Wllams, J. H., 2008, Flow-log analyss for hydraulc characterzaton of selected test wells at the Indan Pont Energy Center, Buchanan, New York: U.S. Geologcal Survey Open-Fle Report 2008-1123, 31 p. 6
Zlotnk, V.A. and B.R. Zurbuchen, 2003. Estmaton of hydraulc conductvty from borehole flowmeter tests consderng head losses, Journal of Hydrology, 281(1-2): 115-128. Fgures Fgure 1. Schematc of flowmeter experment n a fractured-rock aqufer, wth (a) flow-log profles for ambent (blue) and stressed (dashed red) condtons; and conceptual cross sectons of flow system for (b) ambent condton and (c) stressed condton. In ths example, two flow zones (fractures) ntersect a well. Under ambent condtons, flow enters the well from fracture 1 and exts from fracture 3. Under pumpng condtons, flow enters the well from fractures 1 and 2. The far-feld head of zone 2 s equal to the ambent water level; thus there s no flow to/from zone 2 under ambent condtons. The far-feld head of zone 3 s equal to the stressed water level; thus there s no flow to/from zone 3 under pumpng condtons. 7
Fgure 2. The INPUTS worksheet, after executon of the Solver wth optons "Estmate ROI" and "Solve wth regularzaton," for the example. On ths worksheet, the user enters the well and flow-log specfcatons and performs model calbraton. Data (ponts) and nterpreted profles (dashed lnes). Smulated profles (sold lnes) are for an arbtrarly selected startng model. 8