Selected Analytical Methods for Well and Aquifer Evaluation

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model. Each block in figure 18 may represent either anindividual instruction to the computer or many individualinstructions.Figure 18. Abbreviated flow diagram for digital computeranalysis of a mathematical modelThe first step after starting the Illiac, block 1 of figure18, involves arrangement of the complete program of instructionsin designated locations in the memory. Block 2inserts values of T and S as input data and blocks 3 and 4insert values of r and tables of Q and t, respectively. Instructionblocks 3 and 4 are used several times during an analysis,with block 4 functioning more frequently than block 3.Increments of drawdown and buildup for given values ofQ and t and particular real and image wells are givenidentification numbers (ID numbers). Instructions given inblocks 5, 9, 17, and 18 insure proper identification of themany drawdowns and buildups. Block 5 functions moretimes than the other input blocks in providing sets of identificationnumbers for use during analysis. The printing of T,block 7, also provides identification and segregates groupsof values in the output format.The first five blocks of figure 18 provide the Illiac witha complete program of instructions and one set of datawith identification numbers, which are required before the26machine can proceed to obey arithmetic-type instructions.During the computational phase, the programmer mustarrange for arithmetic instructions to function in harmonywith instructions involving movement of data in the computer,subsequent insertion of other sets of data from theinput tape, and the output of results. The algebraic sign ofa number is frequently used as a basis for synchronizing theoperation of the different types of instructions. For example,quantities conveniently referred to as —T, —Q, and IDare punched at the end of their respective tables (see figure17) to enable the Illiac to make pertinent decisions in flowdiagram blocks 6, 8, 19, and 24. An alternate cycle fromblock 12, when u is greater than 10, was also arranged becausedrawdowns associated with these values of u are toosmall to be of practical significance. The alternative savescomputer time and omits several insignificant entries in theoutput record.A table of values for W(u) and u has been published andcould be stored in the Illiac. However, a table would usevaluable memory space and it is quicker and easier for theIlliac to compute the required values of W(u ) when neededthan to locate them in a table stored in the computermemory. Instructions represented by block 14 are concernedwith the solution of the exponential integral W(u ) that ishandled as a convergent series by accumulating pairs ofterms enclosed by parentheses in the nonleaky artesianformula. The summation process continues until the incrementbecomes less than a preassigned value ∆. Subsequently,the value of W(u) is printed and the computation for drawdownis completed in blocks 15 and 16, respectively.At this point in the instruction program, the Illiac hascompleted a cycle for one drawdown or buildup. Themachine will continue to operate as shown diagrammaticallyin figure 18 until all sets of input data have been read fromthe tape and used in computations.A teletypewriter reads the output tape and prints valuesof T, identification numbers, values of u and W ( u), anddrawdown or buildup. Data in the output format and a fewcomputations made by conventional methods are used tospot check the performance of the Illiac.Well CharacteristicsThe drawdown s in a production well has all or someof the following components, depending upon geohydrologicand well conditions: the drawdown s a (aquifer loss) due tolaminar flow of water through the aquifer towards the well;plus the drawdown s w (well loss) due to the turbulent flowof water through the screen or well face and inside thecasing to the pump intake; plus the drawdown S p due to thepartial penetration of the pumped well; plus the drawdowns d due to dewatering a portion of an aquifer; plus the drawdowns b due to barrier boundaries of the aquifer; minus thebuildup s r due to recharge boundaries of the aquifer. Statedas an equation:S = S a + S w + S p + S a + S b — S r(66)
Well LossThe components of drawdown and buildup, except wellloss and partial penetration loss, can be computed with thenonleaky artesian or leaky artesian formula. Well loss maybe represented approximately by the following equation(Jacob, 1946b):s w =CQ² (67)where:s w = well loss, in ftc = well-loss constant, in sec² /ft 5Q = discharge, in cubic feet per second (cfs)Rorabaugh (1953) derived a similar equation and presentsa more exact method for evaluation of well loss whena large range of pumping rates is encountered. In practice,however, equation 67 has been found to be adequate inmost cases.The value of C in equation 67 may be computed fromthe data collected during a “step-drawdown” test, in whichthe well is operated during successive periods at constantfractions of full capacity, by using the following equation(Jacob, 1946b):(∆ s i i -1/ ∆ Q i ) — (∆s / ∆ Q i -1 )C =(68)∆Q i -1 + ∆ Q iThe ∆ s terms in equation 68 represent increments ofdrawdown produced by each increase (∆Q) in the rate ofpumping. The dimensions of ∆s and ∆ Q are feet and cubicfeet per second, respectively. Increments of drawdown aredetermined by taking in each case the difference betweenthe observed water level and the extension of the precedingwater-level curve. Steps of any length of time may be usedproviding the ∆s values chosen are for the same length oftime in each step. For steps 1 and 2 equation 68 may berewritten as:(∆s 2 /∆Q2 ) — (∆s 1 /∆Q 1 )C =(69)∆ Q1 + ∆Q 2For steps 2 and 3, equation 68 may be written as:C = (∆ s 3 / ∆ Q 3 )—( ∆ s 2 ∆ Q 2)∆ Q 2 + ∆ Q 3(70)Equation 68 assumes that the well is stable and that Cdoes not change during the step-drawdown test. However,newly completed wells and old wells are sometimes unstableand the value of C is affected by changes in pumping rates.The value of C computed for steps 1 and 2 may be greateror less than that computed for steps 2 and 3 if the well isunstable. Sand and gravel often shift outside a well duringstep 3 under the influence of a high rate of pumping, resultingin either the development or clogging of the pores ofthe aquifer immediately behind the well screen. If the valueof C for steps 2 and 3 is considerably less than that for steps1 and 2, it is probable that development has occurred duringthe step-drawdown test. A large increase in C with higherpumping rates indicates clogging < of the well screen or wellwall. If development during the pumping period is large∆ s 2 /∆ Q 2 will be greater than ∆S3 / ∆Q 3 and solution of equation70 will be impossible. Thus, it is possible to appraisethe stability of a well with step-drawdown test data andequations 69 and 70.Drilling processes often clog the voids or fracture openingsof the well face and well wall or the openings of thewell screen. Maximum yield per foot of drawdown cannotbe obtained unless development is sufficient to remove thesefine materials. The effectiveness of development can beappraised from the results of a step-drawdown test. Thevalue of C of a properly developed and designed well isgenerally less than 5 sec 2 /ft 5 .The capacities of wells often diminish with heavy pumpingas screen slots or perforations and the voids of theaquifer in the immediate vicinity of the well bore becomeclogged. The step-drawdown test also can be used to appraisethe degree of well deterioration. Values of C between5 and 10 sec 2 /ft 5 indicate mild deterioration, and cloggingis severe when C is greater than 10 sec 2 /ft 5 . It is difficultand sometimes impossible to restore the original capacityif the well-loss constant is greater than 40 sec 2 /ft 5 . Wells ofdiminished capacity can often be returned to near originalcapacity by one of several rehabilitation methods. The successof rehabilitation work can be appraised from the resultsof step-drawdown tests made prior to and after treatment.Collector WellsThe problem of estimating the sustained yields of collectorwells is often encountered. The complex constructionfeatures of collector wells cannot be directly considered withexisting ground-water formulas. However, drawdown incollector wells can be estimated by simulating the collectorwell with a vertical well having the same specific capacityas the collector well. The effective radius of a vertical wellthat simulates the collector well can often be determinedwith aquifer-test data.Several Ranney collector wells have been constructed inIllinois. The Ranney collector well consists of a large diameterreinforced concrete caisson from which horizontalscreen laterals are projected radially near the bottom. Thestandard caisson is generally 13 feet in diameter. The horizontalscreen laterals are fabricated from heavy steel plate,perforated with longitudinal slots, and may be 8 to 24inches in diameter and 100 to 450 feet in length dependingupon geologic conditions and design of unit (Mikels andKlaer, 1956).Because the flow pattern within the horizontal lateralsystem is complex, the sustained yield of the collector isusually determined by simulating the collector with a verticalwell having the same specific capacity as the collectorwell. The effective radius of a vertical well that simulates acollector well in the case of a radial lateral pattern coveringthe entire circumference and having equal length laterals, isequal to 75 to 85 per cent of the individual lateral lengths27
Page 1: BULLETIN 49STATE OF ILLINOISDEPARTM
Page 4 and 5: PAGEModel aquifer and mathematical
Page 6: ivFIGURE65 Model aquifers and mathe
Page 9 and 10: Part 1. Analysis of Geohydrologic P
Page 11 and 12: aquifers” (Hantush, 1956) and is
Page 13 and 14: S y =P =m =application of the nonle
Page 15 and 16: yond ln u becomes insignificant. Wh
Page 18 and 19: point D(u) q , l/u², s, and t are
Page 20 and 21: it is required to estimate the rang
Page 22 and 23: emain as it was because it would ca
Page 25 and 26: The computed value of T and other k
Page 27 and 28: part of 90°.” Under the foregoin
Page 29 and 30: however, ground-water runoff under
Page 31: the hydraulic properties of the aqu
Page 35 and 36: a screen and an optimum screen entr
Page 37 and 38: Part 3. Illustrative Examples of An
Page 39 and 40: properties of the aquifer and confi
Page 41 and 42: downs in the observation wells were
Page 43 and 44: Figure 33.Thickness of dolomite of
Page 45 and 46: constructed with figure 34 by the p
Page 47 and 48: increases in the yields of newly co
Page 49 and 50: Effects of Acid TreatmentAcid treat
Page 51 and 52: Coefficient of TransmissibilityThe
Page 53 and 54: Formation, probably the least perme
Page 55 and 56: of water levels after 53 hours of p
Page 57 and 58: 45 and 46 were used to determine th
Page 59 and 60: cross sections A—A' and B—B' is
Page 61 and 62: water storage during 1951, 1952, an
Page 63 and 64: and the coefficient of transmissibi
Page 65 and 66: 200,000 gpd (Walker and Walton, 196
Page 67 and 68: and the source of recharge is preci
Page 69 and 70: gpd/ft and 410 gpd/sq ft, respectiv
Page 71 and 72: The test was started at 11:20 a.m.
Page 73 and 74: projects from the caisson at a dept
Page 75 and 76: ConclusionsIt is often possible to
Page 77 and 78: Hantush, M. S. 1957b. Preliminary q
Page 79 and 80: APPENDIX AVALUES OF W (u, r/B)r / B
Page 81 and 82: APPENDIX A (CONTINUED)VALUES OF W(u
Page 83 and 84:
NAPPENDIX B (CONTINUED)VALUES OF Ko
Page 85 and 86:
λr w/BAPPENDIX DVALUES OF G(λ, r
Page 87:
APPENDIX FSelected Conversion Facto
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Selected Analytical Methods for Well and Aquifer Evaluation

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