Inverse analysis for transmissivity and the Red river bed's leakage factor for Pleistocene aquifer in Sen Chieu, Hanoi by pumping test under the river water level fluctuation

Vietnam Journal of Earth Sciences, 40(1), 26-38, Doi: 10.15625/0866-7187/40/1/10876 26  (VAST) Vietnam Academy of Science and Technology Vietnam Journal of Earth Sciences Inverse analysis for transmissivity and the Red river bed's leakage factor for Pleistocene aquifer in Sen Chieu, Hanoi by pumping test under the river water level fluctuation Trieu Duc Huy1, Tong Ngoc Thanh1, Nguyen Van Lam2, Nguyen Van Hoang*3 1Vietnam National Center for Water Resources Planning and Investigation 2Hanoi University of Geology and Mining 3Institute of Geological Sciences, Vietnam Academy of Science and Technology Received 20 April 2017; Received in revised form 26 October 2017; Accepted 15 November 2017 ABSTRACT Aquifer parameters and riverbed hydraulic resistance to an aquifer have an important role in the quantitative assess- ment of groundwater sources, especially the aquifer recharge from river. The analytical determination of aquifer parame- ters and riverbed hydraulic resistance to the aquifer is rather complicated in case if the water level in the river fluctuates before and during the pumping test time. This is especially true for Pleistocene aquifer along the Red River in Hanoi city, where the riverbed has been changed very much during the recent decades. A trial-error inverse analysis in the parame- ters' determination by a group pumping test data obtained with a test located close to the Red river bank in Sen Chieu area, Phuc Tho district, Hanoi city was carried out. Before and during the pumping test time the water level in the river changed five times. The results have shown that the Pleistocene aquifer has a relatively high hydraulic conductivity of 55.5 m/day, which provides a good role in the transport of a large volume of water recharged by the river to the abstrac- tion wells located near the river. The aquifer storage coefficient had lightly decreased with the pumping time, which is corresponding to the physical nature of that the aquifer stativity is a function of the aquifer pressure. A special point is worthwhile to be noted that the Red river bed resistance to the Pleistocene is very low, about 0.537 days, which is corre- sponding to the increase of the distance from the river bank further from the well in 28.4 m to have the river as a speci- fied water level boundary of the aquifer. In contrast, the 1990's investigations had found that the Red river bed resistance to the Pleistocene aquifer to be about 130 days (Tran Minh, 1984), which is corresponding to the increase of the distance from the river bank further from the well in a thousand of meters to have the river as a specified water level boundary for the aquifer. Keywords: Group-well pumping test; pleistocene aquifer; riverbed resistance; leakage factor. ©2018 Vietnam Academy of Science and Technology 1. Introduction1 The interaction between surface water and groundwater has a great attention of water *Corresponding author, Email: N_V_Hoang_VDC@yahoo.com resources workers, both managers and re- searchers thanks to its important role in both long-term studies for determining the effects of hydrologic and climatic conditions on the groundwater resources and in short-term tests Vietnam Journal of Earth Sciences, 40(1), 26-38 27 to determine local-scale effects of pumping on the exchange of surface water bodies and groundwater aquifers (John H. Cushman and Daniel M. Tartakovsky, 2017). That chal- lenging problem attracted many researchers to deep into the study, although still leaving an open door for new researches in that direction. Christensen (2000) studied experimental and hydrogeological conditions which draw- down analysis can be expected to produce aquifer parameters and leakage factor, and then proposed some recommendations for the design of pumping test near a stream in order to achieve the determination of the parame- ters, especially a methodology used to esti- mate the duration of the pumping test in which the desired accuracy of either the pa- rameters or the stream flow predicted from these estimates. Hunt et al. (2001) had car- ried a field experiment to measure draw- downs in observation wells and stream deple- tion flows that occurred when water was ab- stracted from a well beside a stream. The analysis used early time drawdowns with a match point method to determine aquifer transmissivity and storage coefficient, and stream depletion measurements at later times used to determine leakage factor. Sopho- cleous (2001) had presented that a great re- quirement for an advanced conceptual and another modeling of groundwater and surface water systems, for a broader perspective of such interactions across and between surface water bodies, interface hydraulic characteri- zation and spatial variability. Fox (2004) had carried out a pumping test next to the backwater stream channel at the Tamarack State Wildlife Area in eastern Colo- rado, analyzed the drawdown measured in ob- servation wells and predicted drawdown by an- alytical solutions to derive simultaneously es- timates of aquifer parameters and streambed resistance to the aquifer. The author had come to the conclusion that the analytical solutions are capable of estimating reasonable values of both aquifer and streambed parameters. How- ever, the changes in the water level in the stream during the test time and a varying water level profile at the beginning of the pumping test influence the application of the analytical solutions. Lough and Hunt (2006) had carried out a complicated group-well pumping test besides a stream to estimate aquifer and streambed re- sistance parameters and a sensitivity analysis to determine the relative importance of each pa- rameter in the stream depletion calculations. Therefore, the analysis of aquifer parame- ters based on the field pumping test data is a rather complicated work for the cases of a mul- tiple or single aquifer (with leakage) with a boundary of a specified fluctuating water level, or head-dependent boundary with fluctuating water levels at the boundary, or boundary of a varying inflow. For aquifers with head- dependent boundary (leakage) boundary, the accurate determination of leakage factor would provide an accurate assessment of the recharge from the river to the aquifer, which is very im- portant for both sustainable groundwater and river water management. The Red river plays an important role in re- charging the Pleistocene aquifer since the aqui- fer groundwater level had been decreased to a level lower than the river's water level. This is especially true for the present conditions when an extensive sand and gravel excavation in the river (Vu Tat Uyen and Le Manh Hung, 2013; Pham Dinh, 2016) has remarkably changed the hydraulic interaction between the river and the Pleistocene aquifer. Therefore, the determina- tion of the most accurate leakage factor of the Red river to the Pleistocene aquifer has a valu- able scientific and practical importance. Within the implementation of the project "Groundwater of Urban are of Hanoi" (Trieu Duc Huy, 2015), several group-well pumping tests had been carried out for determination of Trieu Duc Huy, et al./Vietnam Journal of Earth Sciences 40 (2018) 28 aquifer parameters. Some the group-well pumping tests are located along the Red river for the purpose of determination of the riv- erbed's hydraulic resistance to the Pleistocene aquifer. Under the river water level fluctua- tions, the aquifer parameter determination is much more complicated than the case of a con- stant river water level. The inverse analysis of the aquifer parame- ters including the leakage factor for the Pleisto- cene aquifer becomes more complicated due to the Red river water level fluctuation before and during the group-well pumping test. 2. Background The main productive groundwater aquifer in Hanoi area is the Pleistocene aquifer. Gen- eral hydrogeological conditions of the area may be referred to many publications, for ex- ample, Nguyen Minh Lan, 2014; Tong Ngoc Thanh et al., 2017; Nguyen The Chuyen et al., 2017. This work is dealing with a particular site in Sen Chieu commune, Phuc Tho district, Hanoi city where a group-well pumping test was carried. The testing wells in the direction perpendicular to the river bank is shown in Figure 1: central pumping well CHN1, obser- vation well CHN1-1B and CHN1-2B. The Pleistocene aquifer consists of upper Pleistocene sub-aquifer (qp2) and of lower Pleistocene sub-aquifer (qp1). There is no aq- uitard between qp2 and qp1 in the testing site. Water level drawdown during the pumping and recovery after pumping stop were meas- ured in all wells (Figure 1). The following are the arguments for selec- tion of the conceptual aquifer scheme used in the inverse analysis: - The Pleistocene aquifer (with two sub- aquifer qp2 and qp1) is a confined aquifer with an impermeable layer on the top and in the bottom. The top of the aquifer can be con- sidered as impermeable thanks to the presence of Vinh Phuc clay and silty clay layer of a thickness of about 10 m. The uderneath Neo- gene formation consists of sandstone, grit- stone, and siltstone with the thickness of 50 m to 350 m and transmissivity of 55 m2/day to 840 m2/day. The Neogene formation in the South-East of Hanoi from Nhat Tan, Xuan La has a better transmissivity (Nguyen Minh Lan, 2014). If the average thickness of Neogene in the testing site of about 100 m then the per- meability is about 0.55 m/day. Therefore, the leakage from the Neogene formation into the Pleistocene aquifer during the pumping test would be negligible in the aquifer parameter inverse analysis. - The Pleistocene aquifer has hydraulic connectivity with the Red river: Two possible boundary conditions of the Pleistocene aquifer can be used for the Red river: (1) The first kind of boundary condition (Dirichlet bounda- ry: specified water level) by increasing the distance from the well to the river edge in a distance of L, which is a function of the aq- uifer parameters and the river's bed layer above the aquifer (this is described in para- graph 2); (2) Third kind of boundary condi- tion (mixed boundary: water level depend- ence): the recharge from the river to the aqui- fer is a function of the river water level and aquifer water level and the river bottom leak- age factor). In this work, the first kind of boundary condition is used in the analysis. The Red riv- er water level fluctuations in the river before and during the pumping test time had caused groundwater level changes in the group-well pumping test wells. Those groundwater level changes need to be taken into account in the parameter analysis. Figure 2 showing a river water level fluc- tuations in the area of groundwater pumping test in an aquifer having hydraulic interaction  with the river for used for illustrating their ef- fect on the groundwater level fluctuations in the following formulation. Vietnam Journal of Earth Sciences, 40(1), 26-38 29 Figure 1. Cross section though the testing wells perpendicular to the Red river bank Figure 2. River water level fluctuations which cause the groundwater level fluctuations The river water level changes illustrated in the Figure 2 can lead to the change h of groundwater level at a distance x in accordance with (Mironhenko V.A. and Shestakov V.M., 1974; Nguyen Quoc Thanh and Nguyen Van Hoang, 2007) by the follow- ing formula:     n i iiii RttVVtRVΔh 1 10 )())(()(  (1) In which h - magnitude of groundwater level change (m) (up/down) from time t=0 to t, V0 - river water level change speed (m/day) from time t=0 to t1, t - time counted from the moment the river water level started to change (day) to the time moment of calculation. at LxeerfcR 2; 2)()21()( 22     (2) In which: erfc() - complementary error function; x - distance from the river edge to the considered point (m), L - an increased distance equivalent to the riverbed resistance to the aquifer (m); a=Km/S* (m2/day); K- hy- draulic conductivity (m/day); m-aquifer thick- ness (m); S*- aquifer storage coefficient; Vi - Trieu Duc Huy, et al./Vietnam Journal of Earth Sciences 40 (2018) 30 river water level change speed from time ti-1 to ti (m/day) (with sign “+” if the river water level increases and with sign “-” if the river water level decreases). The increased distance equivalent to the river bed resistance to the aquifer L is deter- mined in order to apply the First kind bounda- ry condition. L is determined by the follow- ing formula (Mironhenko V.A. and Shestakov V.M., 1974): 0 0 0 0 00 0.5 ; ; ( )mB e eL A Km cth A cth K e eA Km                  (3) In which: B0 - the river width (distance be- tween the two river edges) (m); A0 - hydraulic resistance (day); 1/A0 - leakage factor (1/day). Groundwater flow analytical analyses re- quire prototype aquifer distribution such as infinite or semi-infinite. For semi-infinite aq- uifer with the First kind of boundary condition a principle of super-imposition of flow with the introduction of so called imaginary wells is used to have an infinite aquifer distribution (Figure 3), where the river bed's resistance- equivalent length is implicitly in the L value. - The groundwater level drawdown in the pumping well having 100% of well complete- ness is determined by the following formula (refer to Fetter, 2001; Nguyen Van Hoang, 2016): LKLK r L T Qs 2lg366.0 (4) - The groundwater level drawdown in the pumping well: (2 )0.366 lg QSQS QS L rQs T r  (5) Figure 3. Analysis scheme for semi-infinite aquifer with boundary of the first kind In which: s is drawdown (m); Q is pump- ing rate (m3/day); T is aquifer transmissivity; LK stands for pumping well; QS stands for observation well; rlk is pumping well's radius (m); rQS is distance from pumping well to ob- servation well (m); L is distance from pump- ing well to the river edge plus equivalent river bed's resistance (m) (Figure 3). For the case when there are two wells in a line which is perpendicular to the river edge and the water level in the specified head boundary is a constant, the aquifer transmis- sivity and the L value are determined by a sys- tem of two equation (4) and (5). Therefore the river bed's resistance-equivalent length is equal to the calculated L minus the field dis- tance L. Vietnam Journal of Earth Sciences, 40(1), 26-38 31 Since there are groundwater level changes thanks to the river water level fluctuations, in order to determine T and L it requires to intro- duce the value of groundwater change (h) due to the river water level fluctuation. The value of (h) is the groundwater level change h at any time minus the groundwater level change h0 at the moment just before pumping started. Putting (h)=h-h0 into (4) and (5) for observation well QS1 and QS1 results in:     1 1 2 1 2 2 2 2 (2 )0.366 lg (2 )0.366 lg QSH QS QS QS QSH QS QS QS L rQs h T r L rQs h T r         3. Data and Method 3.1. Data Within the implementation of the project "Groundwater of Urban are of Hanoi" (Trieu Duc Huy, 2015), one of several group-well pumping tests was carried out in Sen Chieu commune, Phuc Tho district, Hanoi city in a short distance from the Red river edge. The testing wells in the direction perpendicular to the river bank is shown in Figure 1: central pumping well CHN1 is 24.6 m from the river edge with a constant pumping rate of 9.37 l/s=809.57 m3/day, the pumping time was about 3000 minutes); observation well CHN1- 1B (like QS1) is 8.7 m from the pumping well (15.9 m from the river edge) and observation well CHN1-2B (like QS1) is 21.1 m from the pumping well (3.5 m from the river edge). The Pleistocene aquifer thickness is 27 m, which consists of 7.4 m of Upper Pleistocene sub-aquifer (qp2) and 19.7 m of lower Pleis- tocene sub-aquifer (qp1). There is no aquitard between qp2 and qp1 in the testing site. The pumping from Pleistocene aquifer lasted from 15h50 the 10th of Dec. 2015 to 9h00 the 12th of Dec. 2015. Water level drawdown during the pumping and recovery after pumping stop were measured in all wells. The Red river water level was monitored and recorded at Son Tay hydrological station every 6 hours and is presented in Figure 4: for 60 hours before pumping started and for 70 hours after pumping started. 3.2. Method The Red river water level fluctuations and four speeds of the river water level rising or declining have been determined and presented for the time expressed relatively to pumping start (t=0) is presented in Figure 5. By Eq. (1) with Eq. (2) and (3) and the Red river water level changes in Figure 4 the change of groundwater level at any borehole of the testing group CHN1 of wells can be de- termined upon given values of T, S* and A0. First of all, an initial assessment of groundwater water level change (increase or decrease) caused by the Red river water level fluctuations at the testing site. Among the pa- rameters T, S*and A0, parameter A0 is the most concerned parameter in this work and is a most variable parameter since the hydraulic conductivity K0 of the river bed's silty layer is in a large range from 0.001 m/day to 0.01 m/day (Fletcher, 1987), which corresponding- ly gives A0 a value from 20 days to 200 days for the thickness of the river bed of 0.2 m. For the extensive sand and gravel excavation in from the river (Vu Tat Uyen and Le Manh Hung, 2013; Pham Dinh, 2016), the river bed's silty layer may not be existing, A0 would be a very small value, even close to zero. It is worthwhile to note that several decades ago in accordance to Tran Minh (1984), A0 is about 130 days (mostly because the sand and gravel excavation was not too extensive as present). The initial assessment of groundwater level change at the testing site caused by the Red river water level fluctuations, T=1300 m2/day, S*=0.0001 and A0=5 days are used with the river water level data from the 60 days before pumping started. The initial pre- Trieu Duc Huy, et al./Vietnam Journal of Earth Sciences 40 (2018) 32 dicted groundwater level decrease or increase relatively to the groundwater level at the moment of 60 hours before pumping started is presented in Figure 6 for the central well CHN1. From that initial predicted groundwater level decrease or increase, predicted groundwater level change relatively to the groundwater level at the moment of pumping start can be determined and presented in Figure 7 for the central well CHN1, which is needed to be abstracted from the measured groundwater level in the central well CHN1 during the pumping test in parameter analysis. Similarly, the groundwater level change relatively to the groundwater level at the moment of pumping start need to be determined for other wells CHN1-1B and CHN1-2B. Figure 4. The Red river water level before and during the pumping test Figure 5. The Red river water level and its increase/decrease speed before and during the pumping test 3.1.1. Inverse analysis for aquifer parameters from group-well pumping test data CHN1 If a model structure is determined, the parameter identification based on the observed states and other available information is called inverse analysis (Ne-Zheng Sun, 1994). In a certain sense, parameter identification is an inverse of a forward problem. If the output of the forward problems (in this case, groundwater level) are the input and the aquifer parameters 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 7/12/2015 8/12/2015 9/12/2015 10/12/2015T he Re d r ive r w ate r le vel at So n Ta y h yd rol og ica l st ati on (M SL ) Day/Month/Year (2hour grid) The Red river water level at Son Tay hydrological station Pu mp ing sta rt 3.0 3.5 4.0 4.5 5.0 5.5 ‐60‐54‐48‐42‐36‐30‐24‐18‐12 ‐6 0 6 12 18 24 30 36 42 48 54 60 66 Th e R ed riv er wa ter lev el at So n Ta y h yd rol og ica l st ati on (M SL ) Time from the pumping start ‐ t (hour) Red river water level change speed at Son Tay hydrological station(m) t2 t3t1 t0 V1 = 0m/h Vietnam Journal of Earth Sciences, 40(1), 26-38 33 are the output then parameter identification are often called inverse problem (Ne-Zheng Sun, 1994), regardless, the model is numerical or analytical. Figure 6. Initial predicted groundwater level decrease/increase at well CHN1 caused by the Red river water level fluctuations before and during pumping test Figure 7. Initial predicted groundwater level change relatively to the groundwater level at the beginning of pumping at well CHN First, the aquifer storage coefficient S* determined by Cooper-Jacob method to deter- mined aquifer storage coefficient with determination of so-called zero drawdown- distance (refer to Fletcher, 1987) as follows: 2 20 0 2.25 2.251 ** Tt TtS S r r    (6) In which: t is the time after pumping started (days) and r0 is the distance (m) at which the drawdown is zero (the groundwater ‐0.6 ‐0.4 ‐0.2 0.0 0.2 0.4 0.6 0.8 1.0 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 ‐60‐54‐48‐42‐36‐30‐24‐18‐12 ‐6 0 6 12 18 24 30 36 42 48 54 Gro und wa ter  lev el I ncr eas e (+ ) De cre ase  (‐)   (m ) The  Re d r ive r w ate r le vel  at  Son  Ta y  hyd rol ogi cal  sta tio n ( MS L) Time from pumping start ‐ t (hour) Co rre spo nd ing to gr ou nd wa ter lev el a t th e m om en t of pu mp ing sta rt ‐0.6 ‐0.5 ‐0.4 ‐0.3 ‐0.2 ‐0.1 0.0 0 5 10 15 20 25 30 35 40 45 50 55 60 Tot al g rou nd wa ter  lev el c ha nge fro m  pu mp ing  sta rt Time from pumping start ‐ t (hour) Trieu Duc Huy, et al./Vietnam Journal of Earth Sciences 40 (2018) 34 level just stars to decline) at that time t. The distance drawdown lines at different yearly pumping time area used for the purpose. This obtained storage coefficient can be considered as "real value" since the method used is considered as the most reliable when time drawdown in observation wells are used. Therefore, the inverse analysis in this paragraph is using that storage coefficient value for determination of T and A0 and also L. The inverse analysis is using trial-and- error approach as follows. 3.1.2. Interpretation of the groundwater drawdown in the testing wells The groundwater level drawdown in the testing wells are presented in Figure 8-10 have shown that the groundwater level in the wells started to be stabilized with small fluctuations at the 120 minutes of pumping in the pumping well CHN1, ~1600 minutes in the well CHN1-1B and ~1800 minutes in the well CHN2B. It can be thought that from the 120 minutes the pumping rate is relatively balanced with the groundwater flow from the aquifer its own and from the Red river upon a negligible influence of the river water level fluctuations on the groundwater level during this pumping time; after that ~1000 minutes of pumping, the groundwater level drawdown started to increase again until about the 2400th minute. Figure 8. Time drawdown in pumping well CHN1 Therefore, utilization of water level drawdown data during the time between 120 minutes and 1600 minutes would give the most reliable value of parameter L. Figure 9. Time drawdown in observation well CHN1-1B Figure 10. Time drawdown in observation well CHN1-2B 4. Results 4.1. At time after pumping started t=180 minutes With  h  =-0.059 m (Figure 7), substituting the measured drawdowns in well CHN1-1B and CHN1-2B into Eq. (4) and (5) results in the following: 0.366 (2 8.7)0.218 lg 8.7 0.366 (2 21.1)0.121 lg 21.1 Q L T Q L T     The solutions are L=49.2 m; L=25.6 m; T = 1380.9 m2/day; A0=0.475 days. 4.2. At time after pumping started t=360 minutes With  h  =-0.118 m (Figure 7), substituting the measured drawdowns in well 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1 10 100 1000 Dr aw do wn s (m ) Time after pumping started t (minutes) Pumping well CHN1 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 1 10 100 1000 Dr aw do wn s (m ) Time after pumping started t (minutes) Observation well CHN1-1B 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 1 10 100 1000 Dr aw do wn s (m ) Time after pumping started t (minutes) Observation well CHN1-2B Vietnam Journal of Earth Sciences, 40(1), 26-38 35 CHN1-1B and CHN1-2B into Eq. (4) and (5) results in the following: 0.366 (2 8.7)0.192 lg 8.7 0.366 (2 21.1)0.112 lg 21.1 H H Q L T Q L T     The solutions are L=54.6 m; L=30.0 m; T = 1642.1 m2/day; A0=0.503 days. For that two times of analysis, average values of the parameters are T = 1511.5 m2/day; A0 = 0.503 days; L = 27.8 m. 4.3. Determination of aquifer storage coefficient S* With average transmissivity of T=1511.5 m2/day, it gave: - t= 10-15 minutes: ro = 24.0 m (Figure 11); S*=0.0042; - t= 36-40 minutes: ro = 23.4 m (Figure 12); S*=0.00129; - t= 70-100 minutes: ro = 30.9 m (Figure 13); S*=0.00167; Average aquifer storage coefficient is S*=0.00113. Figure 11. Distance drawdown (well CHN1-B and CHN1-2B) at pumping time: 15 minutes Figure 12. Distance drawdown (well CHN1-B and CHN1- 2B) at pumping time: 16-40 minutes Figure 13. Distance drawdown (well CHN1-B and CHN1-2B) at pumping time: 50-220 minutes (an yearly time of 50 minutes is used) 4.4. Inverse analysis procedure and final result The initially selected values of T=1300 m2/day, S*=0.0001 and A0=5 days had resulted in T = 1511.5 m2/day, A0 =0.5115 days. Using those obtained values to determine the groundwater level change h  caused by the Red river water level fluctuations and then determine new values of T and A0. This procedure repeats until an insignificant difference between the parameter values is achieved. At time after pumping started t=180 minutes: With  h  =-0.057 m (Figure 14), substituting the measured drawdowns in well CHN1-1B and CHN1-2B into Eq. (4) and (5) results in the following: 0.366 (2 8.7)0.220 lg 8.7 0.366 (2 21.1)0.123 lg 21.1 Q L T Q L T     The solutions are L=49.6 m; L=25.0 m; T = 1369.2 m2/day and A0=0.457 days. 0.00 0.05 0.10 0.15 0.20 0.25 0.8 1 1.2 1.4 Dr aw do wn (m ) 10-base logarithm of distance from CN1 (m) 3 4 5 6 7 8 9 10 11 12 13 14 15 Time (min) t=10‐15min lg(ro)=1.38 0.00 0.05 0.10 0.15 0.20 0.25 0.8 1 1.2 1.4 Dr aw do wn (m ) 10-base logarithm of distance from CHN1 (m) 16 17 18 19 20 22 24 26 28 30 32 34 36 38 40 Time (min) t=36‐40min lg(ro)=1.37 0.00 0.05 0.10 0.15 0.20 0.25 0.8 1 1.2 1.4 1.6 1.8 Dr aw do wn (m ) 10-base logarithm of distance from CHN1 (m) 50 55 60 70 80 90 100 110 120 140 160 180 200 220 Time (min) t=70‐100min lg(ro)=1.49 Trieu Duc Huy, et al./Vietnam Journal of Earth Sciences 40 (2018) 36 Figure 14. Total groundwater level change relatively to the groundwater level at the beginning of pumping at well CHN1: A0=0.5115 days, T=1511.5 m2/day, S*=0.00113 At time after pumping started t=360 minutes: With  h  =-0.114 m (Figure 14), substituting the measured drawdowns in well CHN1-1B and CHN1-2B into Eq. (4) and (5) results in the following: 0.366 (2 8.7)0.196 lg 8.7 0.366 (2 21.1)0.116 lg 21.1 H H Q L T Q L T     The solutions are L=56.3 m; L=31.7 m; T = 1627.5 m2/day; A0=0.617 days. For the that two analysis times, averages values of the parameters are T = 1498.4 m2/day; A0 = 0.537 days; L = 28.4 m Table 1 summaries the results of the inverse analysis of just two steps of the trial and error of parameter determination. The results have shown that the values of the parameters converged very fast with the relative differences of 0.9% for transmissivity T, 6.4% for A0 and 2.1% for L. Table 1. Summary of inverse analysis results Input of step 1 Output of step 1 Relative difference in step 1 (%) Input of step 2 Output of step 2 Relative difference in step 2 (%) T=1300 m2/day T=1511.5 m2/day T: 14.0% T=1511.5 m2/day T=1498.4 m2/day T: 0.9% S*=0.0001 S*=0.00113 A0: 9.9% S*=0.00113 S*=0.00113 A0: 6.4% A0=5.0 days A0=0.503 days L: 65% A0=0.503 days A0=0.537 days L: 2.1%  L=80.6 m  L=27.8 m  T=1511.5 m2/day L= 28.4 m K=55.5 m/day 5. Discussion and Concluding remarks The the real values of aquifer parameters and riverbed layer's resistance are unique combination which scientifically and practically need to be determined. The estimated values of the parameters may be of very high errors if the boundary conditions and boundary conditions' values and one or some parameters' values are far from the real values. Tong Ngoc Thanh et al. (2017) and Nguyen The Chuyen (2017) have presented some arguments of wrong utilization of of a single Pleistocene confined aquifer without leakage from underlying Neogene aquifer in Thuong Tin district and Mo Lao-Ha Dong areas in determination of the Pleistocene aquifer transmissivity. Besides, the study of true hydrogeological aquifer structure is very important including the determination of the ‐0.6 ‐0.5 ‐0.4 ‐0.3 ‐0.2 ‐0.1 0.0 0 5 10 15 20 25 30 35 40 45 50 55 60 Tot al g rou nd wa ter  lev el c ha ng e  fro m  pu mp ing  sta rt Time from pumping start ‐ t (hour) Groundwater level change during pumping test relatively to the groundwater level at the pumping started (at t=0): A0=0.503 days; T=1511.5m2/day; S*=0.00113 Vietnam Journal of Earth Sciences, 40(1), 26-38 37 nature of the over-lying and lower-lying for- formations in regards to the leakage to the main aquifer in the setting up the conceptual aquifer scheme, for which geophysical prospecting would be very helpful and effective (Nguyen Van Giang et al., 2014). The determination of the exact boundary condition kinds, boundary values and aquifer parameters values for the areas along the Red river as well as for the areas of boundary of the Pleistocene aquifer with the bed rock in the West and South-West areas of the Red river plain have a very important role in the of the natural groundwater resources and groundwater abstraction potential along with the recharge components, which would also have a significant role in the soil hydrodynamic mechanics in the engineering geological problems, including land subsidence due to groundwater abstraction. The analysis results have shown that the Pleistocene aquifer has relatively high hydraulic conductivity up to 55.5 m/day so the aquifer has very high capacity of water conduction and transmission water from the Red river to the abstraction facilities. The phenomenon of that the Pleistocene aquifer storage has a declining tendency with the pumping time is well corresponding with the physical nature that the compressibility of the aquifer little decreases with the aquifer pressure removal. This needs to be accounted in future actual groundwater modelling. A special feature is that the Red river bed layer has very insignificant resistance to the Pleistocene aquifer (0.537 days) which is corresponding to the increase of the distance of only 28.4 m to the river edge for utilization of the boundary as the first kind condition. Meanwhile the investigation during the 1990's years had shown that the leakage factor of about 130 days, which is corresponding to the increase of the river edge tin a distance of thousands of meters. This would be an argument to support the thought that the extensive sand and gravel excavation in the river has cause the removal of the fine bed materials of the river bed. This factor needs to be taken into consideration and into account in the design and assessment of groundwater abstraction of the abstraction facilities to be built along the Red river bank. More studies and field experiments need to be carried out in the process of groundwater resources assessment and evaluation for the areas having surface streams which have a more or less interaction with groundwater aquifers, for which both the surface water and groundwater have significant role in water supply due to the spatial and temporal variations in order to have a real picture of the physical surface water and groundwater interaction through the est mates of leakage characteristics of the streambed to the aquifer, especially due to the nature of that the leakage parameter is a site specific. 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