Factors Influencing the Iterative Accuracy of Ground Water Level in Forecasting the Water Burst of D

Jun.2002Journal of China University of Mining &. TechnologyVol. 12 No. 1Factors Influencing the IterativeAccuracy of Ground Water Level inForecasting the Water Burstof Deep Drawdown MinesLI Duo (李铎)12, YANG Xiao-hui (杨小荟)*,WU Qiang (武强)'， ZHANG Zhi-zhong (张志忠)'( 1. Department of Resource Exploitation Engineering, CUMT，Beiing 100083，P. R. China ;2. Department of Resource and Environment Engineering , ShijazhuangUniversity of Economics , Shijiazhuang 050031，P. R. China )Abstract: The purpose of this paper is to discuss the influential factors of iteration accuracy when we use itera-tion to determine the numerical model for predicting water yield of deep drawdown mines and calculating thegroundwater level. The relationship among the calculation error of groundwater level, the pumping rate, thelimit of iteration convergence error, the calculation time, and the aquifer parameters were discussed by using anideal model. Finally, the water yield of Dianzi iron mine was predicted using the testified numerical model. It isindicated that the calculation error of groundwater level is related to the limit of iteration convergence error, thecalculation time and the aquifer parameters, but not to the pumping rate and the variation of groundwater level. .Key words: deep drawdown; water yield ;groundwater level; iteration ;error limitCLC number: P 64 Document code: AArticle ID: 1006- 1266(2002)01 -0081-051IntroductionTwo commonly used numerical methods forThe numerical method is widely used in solv-estimating the water yield of mines are finite ele-ing groundwater flow problems for evaluating andment method and finite difference method. Bothpredicting the water yield of mines. The numeri-methods convert the equation solving from mathe-cal simulation of groundwater flow is a necessarymatical equation to linear algebraic equation sys-process for designing the groundwater resourcetem although they have different principles. Themanagementmodel imines[1.Therefore,solving methods of linear algebraic equation sys-whether or not to correctly predict water yield oftem are direct and iterative processes. The directmines and to design management model ofmethod is a single solving process which has lessgroundwater resource in mines depends essential-calculations, but its error accumulation increasesly on the numerical simulation of groundwaterwith the increase of calculation cells and time in-flow. The accuracy of the numerical simulationtervals. The iterative procedures could graduallyfor groundwater flow calculation also depends onapproach the true solution of the equation systemthe solving method of mathematical model， be-中国煤化工teps[3]. Iterative preci-sides the groundwater flow equation, precision ofYHC NM H G factors, especially bythe aquifer parameters and the summarization ofselecting the limit of iterative convergence error.hydrogeological conception model2.The larger the limit is, the larger the calculationReccived date:. 2001 -11-21Biographb万数据( 1963 ), male, from Shanxi Province, associate professor, engaged in water resource and hydrogeology.8:Journal of China University of Mining &. TechnologyVol. 12 No. 1error is, vice versa. But the progress of calcula-groundwater level is the exact solution of thetion will become slowed with the increase of itera-problem，otherwise, it is not an exact solution.tive times. In this paper, the influence factors ofOQ = μ,SOH，(1)the iterative precision are analyzed in allusion towhere△Q is the storage capacity; Hsis the storagegroundwater flow calculation, especially, to thecoefficient; S is the area of calculation region; andlimit of iterative convergence error.△H is the variation of groundwater level withinA square model with an area of 100 km2 iscalculation period.designed for calculation by using head boundaryBased on this principle, the calculated abso-and flux boundary in this discussion. When thelute error of the amount of groundwater is shownhead boundary is used， it is converged rapidlyin Table 1 on distinct condition of pumping rateseven with a small limit of iterative convergenceif we keep a 40000 m*/d of recharge rate througherror, the small drawdown results in a small iter-the flux boundary and the error limit is onlyation error. When we use flux boundary and neg-0.00001. The absolute error of the groundwaterative equipoise to calculate， the successive de-amount is shown in Table 2 on different condi-scending will result in a large drawdown, the con-tions of pumping rate and the limit of iterativevergence velocity is quite slow if the limit of itera-convergence error.tion convergence error is small. Therefore, weTable 1 and 2 show that the variation ofwill discuss only numerical model with fluxpumping rate has only a little influence on the cal-boundary. The groundwater flow is a two-dimen-culation result of the amount, but the limit of it-sional flow in confined aquifer. The mathematicalerative convergence error has an obvious influencemodel is solved using finite difference method ofon it. The absolute error of the amount is 1~1.5triangular grid1. The calculation area is dividedm*/d if the limit of iterative convergence error isinto 200 triangle elements with 121 nodes. The0.00001，therefore，, the calculated groundwaterpumping well is located in center node (Fig. 1).level in the condition of 0.00001 error limit is theexact solution of the problem.Table 1 Calculation error for 0. 00001error limiV /(m3●d-')RealCalculatedAbsolute\ WellPumping ratedifferencereserveerror48000-8000- 7998.661.3444800- 4800一, 4798.591.4141600一1600- 1598. 921.08Table 2 Calculated water error fordifferent error limitV /(m3●d -1)Fig.1 Divided diagram of analysis modelPumping rat0. 000010. 000050. 00012 Exact Solution of the Problem1.34 .8.1216.5444800 .8.1716.63It is required to determine the solution o41 6001.08.7. 8316.33groundwater level accurately in order to comparecalculation errors under different conditions in an-Relationship Between Calculation Erroralyzing calculation result. The principle of the中国煤化Iroundwater Level ascalculation method is as follows: the dynamicMYHCNMHGateamount of groundwater in the area is the differ-ence between recharge and discharge. If the im-This relationship is discussed first to find outposed difference between recharge and dischargethe influence factors on the calculation error ofwithin ther数据very close to the result which isthe groundwater level. Because the variation ocalculated by equation ( 1 )，this calculatedthe groundwater level can be realized by changingLI Duoet al.Factors Influencing the Iterative Accuracy of Ground water Level ...the pumping rate， the relationship between thethe limit of iterative convergence error is， the .calculation error and the variation of the ground-larger the calculation error of groundwater levelwater level can be demonstrated by the relation-is，vice versa.ship between the calculation error and pumping5Relationship Between Calculation Errorrate. The calculated results for the nodes ofof Groundwater Level and Calculationpumping wells are shown in Table 3 if we use 0Time00005 error limit, the constant T and μ。，5 timeintervals with 20 days time step (in all 100 days).The groundwater levels are calculated in dif-It indicates that the pumping rate and groundwa-ferent time intervals and constant pumping rateter level variation have no obvious influences onand error limit (48000 m8/d and 0. 00005，respec-the calculation error of groundwater level. .tively). If 10 days and 50 days are taken as timeTable 3 Calculation error of groundwater levelintervals，the calculation error of groundwaterfor different pumping ratelevelatthe100thdayis0.034m;If50daysandPumping rateWater level/m100 days are taken， the calculation error of/(m3●d-1)VariationError4160015. 290. 034groundwater level at the 200th day is 0. 068m. It23. 510.034indicates that the calculation error of groundwater44800 .31. 72.level is not related to the time interval, but to the4800048. 15total calculation time. The calculation result of4 Calculation Error of Groundwater Lev-center node shows in Table 4 and Fig. 3 on dis-el and Iterative Convergence Errortinct error limits and calculation time.Table 4 Calculation errors under different conditionsLimitError limit10d20d50d 100d 200 dBecause the calculation error of groundwater0. 000050.0030.0070.0160.0340.0680. 00010. 007 0.014 0. 0360. 076 0. 152level is not related to the pumping rate and the0. 00050.039 0.077 0.193 0.413 0. 827variation of the groundwater level， we only take0. 001).078 0. 156 0.390 0. 834 1. 66848000 m*/d pumping rate to discuss this problem0.0050.391 0. 7830. 010. 779 1.561 3. 905 8. 426 16. 852in the above mentioned testing conditions withconstant T and μ。，5 time intervals with 20 days10.0step (in all 100 days). The calculation results are●0.0058.shown in Fig. 2 on the node of pumping well.6.010.00占4.2.0e 1.0- 0.000I0 80 120 160 200t/d0.10 .Fig.3 Relationship between errorsand calculation time0.01Table 4 and Fig. 3 show that the calculation .0.00001 0.0001 0.001Iterative convergence ernor中国煤化工el are positively corre-time when the limit ofFig.2Relationship between errors and the:TCHCNMHGlimit of iterative convergence erroriterative' convergence error is in constant. I he .Table 4 and Fig. 2 show that the calculationslope of the line is also variable if the limit of iter-error of groundwater level is related to the limit .ative convergence errors is variable， i. e.，theof iterativ99数gence error by logarithmic rela-greater the limit of iterative convergence error is,tionship for constant calculation time. The largerthe steeper the slope of the line is.8Journal of China University of Mining &. TechnologyVol. 12 No. 16 Relationship Between Calculation Errorboundary between Zihe and Mihe rivers, and itsnorth is Fanjialin fault which is a flux boundary.of Groundwater Level and ParametersThe south boundary is Juziyu fault and Shentoux-of Aquiferihe fault that both are flux boundary. The west ofThe errors of groundwater level are calculat-the north boundary is the axial plane of Hutianed in the conditions of constant pumping rate andsyncline, and its east is Wangjiazhuang-Liuyingerror limit (48000 m'/d and 0.0001, respectively)fault that is an impermeable boundary. The verti-with some variable coefficients of transmissibilitycal exchange of groundwater involves rainfall in-and storage. Table 5 lists the calculation errors offiltration, river percolation, and groundwater ex-groundwater level in different transmissibility co-ploitation. .efficients ( T ) whens = 2x10- ‘and the pump-The mathematical model of groundwatering time is 10 days. Table 6 lists the calculationseepage that describes hydrogeological conceptionerrors of groundwater level in different storagemodel iscoefficients ( μ。) when T = 1000 m2/d and the2( KM?H+三KM?H+W=μXaHax)x |pumping time is 10 days.(x,y)∈G,t>0Table 5 and 6 show that the aquifer parame-H(x,y,t) = Ho(x,y)(x,y)∈G,t= 0ters have some influences on the calculation errorH(x,y,t) = H,(x,y,t) (xr,y) ∈I,t> 0of groundwater level， i. e.，the calculation errorof groundwater level has a positive correlationKM = 92(x,y,l)(x,y)∈T2,l> 0with transmissibility coefficient and a negativewhere H is the groundwater level of the aquifer;correlation with storage coefficient.H。is the initial groundwater level; M is theTable 5 Relationship between errors and Taquifer thickness; K is the aquifer permeabilityT /(m2●d-1)Error/m1000. 000.coefficient; μis the aquifer specific yield; H is5000. 003.the groundwater level of head boundary; qzis the1 0000. 007unit width flux on flux boundary; W is the verti-1 5000.011 .2 0000.014cal exchange of groundwater; Gis the research re-gion; I is head boundary; T2 is flux boundary;Table 6 Relationship between errors and μand n is the direction of normal line of flux bound-Water level error/mary.1.0X10-0. 005.0X10-30.03The research region is divided into 314 ele-1.0X10-80.15ments with 178 nodes. The mathematical model5.0X10-+0.31of groundwater seepage is changed into the sys-1.0X10- 40.76 _tem of equations by using finite difference7 Case Applicationmethod. The system of equations is solved usingDianzi iron mine is located in the north of Zi-iteration with error limit of 0. 00001.In order to objectively reflect the hydrogeo-he faulted zone in Zihe river basin of Zibo city inShandong provincesl. Its main oreboby is buriedlogical condition of the research region, the nu-eded by using dynamicein the range of 70~ 420m depth. Its country rock中国煤化工E 24 observation wellsis limestone of Ordovician in which the karst andTH. CNM HGm 2 years (1993.10the groundwater are abundant. The groundwateris phreatic water. The west boundary of the re-1995.9)，24 time intervals with monthly timesearch region is the groundwater- dividing bound-step (in all 24 months). The parameter regionsary betweg-t数gand Xiaofuhe rivers. The southare shows in Fig. 4, and the parameters of all re-of the east boundary is the groundwater-dividinggions are shown in Table 7.LI Duo et al.Factors Influencing the Iterative Accuracy of Ground water Level ...1) The calculation error of groundwater level18-17is closely related to the limit of iterative conver-116]gence error. The larger the limit of iterative con -(5vergence error is, the larger the calculation error3|of groundwater level will be. .2) The calculation error of groundwater level7 12is not related to the pumping rate and the varia-(1tion of groundwater level in some restrictions.Fig.4 Parameter zones of the case model3) The calculation error of groundwater levelis related to total calculation time but it is not re-Table 7 Parameters in different regionsRegions T /(m2.d-1) μ I Regions T /(m2●d-1) μlated to time intervals， the longer total calcula-100. 0012000. 005tion time is，the larger the calculation error of15000. 0120. 006groundwater level is.5000.004!34004) Transmissibility coefficient T and storage100004400000.005150. 002coefficient μ have some influence on the calcula-15000i61000 .0. 0049000 .800000. 0001tion error of groundwater level, but the influence7000018is relatively small and can be neglected.30000.001 .!91500000. 007.1 300200, 007In short, influence factors of the calculation .error of groundwater level include the limit of it-The water yield of Dianzi iron mine is pre-erative convergence error，total calculation timedicted by using proofreaded numerical model.and aquifer parameters， and their influenceThe results of different exploitation level arecreases with the decrease of limit of iterative con-showed in Table 8.vergence error. The most effective method for re-Table 8 Mine outflow rate on distinct levelducing the calculation error of groundwater levelLevel/m- 50一150一200is to control the limit of iterative convergence er-Outlow/425497005977659ror. In general, it is required to take a small limit(m3. d-1)of iterative convergence error when the total cal-8 Conclusionsculation time is longer, transmissibility coefficientSome knowledge is obtained through discus-is larger, and storage coefficient is smaller, vicesions.versa.References[1]武强,金玉洁.华北型煤田矿井防治水决策系统[M].北京:煤炭工业出版社,1995:162-164.[2]万力.浅议地下水数值模型的误差[J].水文地质工程地质,1992,19(4):8-9.[3]李铎,万力.多层网格法在地下水水流计算中的应用[J].水文地质工程地质,1995,22(2):1-4.[4]李俊亭. 地下水流数值模拟[M].北京:地质出版社,1989:44-55.[5] 李铎.淄河断裂岩溶发育规律探讨[J].河北地质学院学报,1995,18(2):123- 128.中国煤化工MHCNM HG