Van Hoang Nguyen

Institute of Geological Sciences-Vietnam Academy of Science and Technology, Hanoi, Vietnam.

Abstract: The groundwater tracer injection and withdrawal tests are often carried out for the determination of aquifer solute transport parameters. However, the parameter analyses encounter a great difficulty due to the radial flow nature and the variability of the temporal boundary conditions. An adaptive methodology for the determination of groundwater solute transport parameters using tracer injection and withdrawal test data had been developed and illustrated through an actual case. The methodology includes the treatment of the tracer boundary condition at the tracer injection well, the normalization of tracer concentration, the groundwater solute transport finite element modelling and the method of least squares to optimize the parameters. An application of this methodology was carried out in a field test in the South of Hanoi city.The tested aquifer is Pleistocene aquifer, which is a main aquifer and has been providing domestic water supply to the city since the French time. Effective porosity of 0.31, longitudinal dispersivity of 2.2 m, and hydrodynamic dispersion coefficients from D = 220 m2/d right outside the pumping well screen to D =15.8 m2/d right outside the tracer injection well screen have been obtained for the aquifer at the test site. The minimal sum of squares of the differences between the observed and model normalized tracer concentration is 0.001 19, which is corresponding to the average absolute difference between observed and model normalized concentrations of 0.035 5 (while 1 is the worst and 0 is the best fit).

Keywords: Groundwater solute transport; Tracer injection; Effective porosity; Longitudinal dispersivity;Flow distortion coefficient; Normalized concentration

Introduction

Solute transport parameters of aquifer formations are important for many environmental applications and modelling processes such as transport of chemicals and fertilizers in agricultural soils, salt water intrusion into fresh aquifers, desalinization of salinized aquifers, groundwater (GW) contamination,remediation of contaminated aquifers etc. Therefore, GW solute transport parameter identification is very essential in soil and GW environmental science and engineering. The success of the GW solute transport parameter identification in terms of both financial constraints and reliable analysis certainty is a high expectation and wish of the GW hydrologists.

There are two groups of experiments for determining these parameters such as laboratory and field tracer experiments. The laboratory tracer experiments usually used the prototype configurations which provide essential one-dimensional or twodimensional flow with uniform flow velocity and determined boundary conditions which allow analytical analyses in case of uniform soil column, or numerical analyses in case of multi-layer soil column (Zhou, 2002; Sharma et al. 2014). In more general situations, the field tracer experiments can be conducted in a variety of flow conditions,including steady-state flow (either induced or ambient) and transient flow. Analytical solutions could be available only under steady flow and in homogeneous aquifer in terms of hydraulic properties (aquifer thickness, hydraulic conductivity,porosity, etc.) and dispersion properties. Otherwise, numerical methods need to be used to interpret test results for the determination of dis-persivity and effective porosity. The most popular method of conducting tracer experiments involves one or more tracer injection wells and multiple withdrawal wells (Shook et al. 2004).

There are numerous studies both on laboratory and field tracer experiments and analyses, of which some are shortly described in chronological sequence as follows. Klotz et al. (1980) carried out laboratory and field tracer tests to determine longitudinal dispersion, the results of which are compared and correlated to translate the laboratory results to the field conditions based on the sediment properties. Barone et al. (1992) conducted a series of laboratory tracer column tests with undisturbed clayey soils and found that diffusion coefficient is significantly influenced by adsorption of the tracer, however the tests may provide estimates on the upper and lower bounds of soil diffusion coefficient. Welty and Gelhar (1994) considered non-uniform flow effects in determination of fieldscale values of longitudinal dispersivity from tracer tests in aquifers in convergent radial flow, divergent radial flow, and doublet ( a test using tracer injection well and withdrawal well ) with pulse and step tracer inputs. Glen et al. (1999) carried out three doublet tracer tests at spacings of 30.5, 91.4 and 183.0 meters in approximately 40-meter-long open boreholes using a pulsed bromide injection and both analytical and numerical simulations were used to determine the longitudinal dispersivity and effective porosity of fractured aquifer in Newark basin, New Jersey, USA. Yan et al. (2019) carried out a series of laboratory tracer column experiments for the determination of hydrodynamic dispersion coefficient in the form of a power of 1-2 of the seepage velocity, as the studies of Rifai et al.(1956) and others showed that the hydrodynamic dispersion coefficient is a power of slightly greater than one of the seepage velocity.

The preference of laboratory or field tracer tests,besides various study constraints such as budget and time, depends upon the scale of the study area.The mean travel distance of 2-4 m for a tracer solute or a contaminant is defined as a local scale by Fried (1975), for which the laboratory tracer tests are appropriate. The mean travel distances 4-20 m, 20-100 m and greater than 100 m are defined as global scale 1, scale 2 and scale 3, respectively(Fried, 1975), for which field tracer tests are preferable. According to Gelhar et al. (1992), highreliability dispersivity data obtained from field tracer tests should meet the following criteria: 1)carried out in ambient flow, diverging radial flow or injection-withdrawal wells; 2) well defined tracer input; 3) conservative tracer; 4) appropriate measurements of tracer concentration; 5) appropriate parameter analysis (breakthrough curve analysis in case of ambient flow and radial flow; method of spatial moments in case of ambient flow;numerical method). Therefore, the tracer test using injection-withdrawal wells along with the four remaining criteria is considered in this study. Analytical analyses of the tracer injection-withdrawal testing data can only be done for specific conditions, including steady state flow and certain injection schemes (slug injection or constant continuous injection) and are approximate solutions using average pore water velocity with three parametervariables: Longitudinal dispersivity, average hydrodynamic dispersion coefficient and effective porosity (Shook et al. 2004; Gutierrez et al. 2013).Numerical models have become standard methods of interpreting tracer tests (Shook et al. 2004).

The parameter analysis used in this study is the Galerkin finite element (FE) method which is applied to the advection-dispersion equation describing the solute transport by GW. Considering a two-dimensional plane view, since the groundwater flow and solute transport have a radial divergingconverging flow nature, two-dimensional numerical model would not be able to cope with this advanced radial nature. However, the one-dimensional model domain along the line connecting the tracer injection and withdrawal wells would represent the main solute transport from tracer injection well to withdrawal well properly. Besides,from the practical point of view in applications of numerical modelling, the best available models do not have to be more sophisticated models for solving a specific problem as they do not necessarily give more accurate results (Dong, 1998). Therefore, an adaptive methodology of determining GW solute transport parameters using tracer injectionwithdrawal test data is worthwhile to be developed.The paper presents the development of a methodology which includes the treatment of the tracer boundary condition at the tracer injection well, the normalization of tracer concentration, the GW solute transport FE modelling and the optimization of parameters using the method of least squares. The application of the developed methodology is illustrated through sodium chloride injection-withdrawal test in Pleistocene aquifer in the northern area of Hanoi city.

1 Local hydrogeological units, testing wells’ scheme and testing data

1.1 Hydrogeological units

Groundwater from Pleistocene aquifer in Hanoi city has been exploited for different purposes since the late of 19th century and is still a predominant source of domestic water for Hanoi city(Honjo et al. 1997; Keisuke et al. 2017). As a result, the cone of GW level depression is getting larger and approaching the boundary of brackish groundwater in the south of Hanoi city (Trieu Duc Huy, 2015)①Trieu Duc Huy (Project head). 2015. Groundwater protection in large cities (city: Hanoi). Vietnam National Center for Water Resources Planning and Investigation-MoNRE.. The salt solution (hereafter called a tracer or solute in concrete context) injection testing at the experimental well system CHN5 had been conducted to determine the solute transport parameters of the lower Pleistocene aquifer,namely the effective porosity neffand longitudinal dispersivity aL. These parameters are needed for the predictive modeling of the contaminant transport in the aquifer, including the brackish groundwater intrusion from Southern Hanoi (Fig.1) towards the center of Hanoi city where the GW pumping fields are located. Besides the salt intrusion, the aquifer is also vulnerable to arsenic as the concentration is high in some parts of the Pleistocene aquifer and the above Holocene aquifer(Do Van Binh, 2013; Martyna et al. 2021). Fig.2 shows the boundary between the fresh and brackish GW in the Pleistocene aquifer in Southern Hanoi.

Fig.1 Location map of the study area

The following hydrogeological units are present in the study area from top to bottom:

-Holocene aquifer (qh): covering the whole area.The aquifer is between the depths of 4-5 m and 40-44 m, mainly consisting of sands and silty sands.Overlying the aquifer is a low-permeability layer with clay and silty clay of 2.8-5.0 m in thickness.

-Vinh Phuc formation (Q13vp): With low permeability and thickness of 2-8 m. This layer is present throughout the study area.

-Pleistocene aquifer (qp): occurring between the depths of 43-52 m and 64-69 m. This aquifer is usually divided into two sub-aquifers: The upper Pleistocene aquifer (qp2) and the lower Pleistocene aquifer (qp1), separated by an impermeable layer of clay. The aquifer consists of pebbles and gravels with sands. The wells in the aquifer have pumping rates from 6.06 L/s to 12.33 L/s. The estimated transmissivity is from 80 m2/d to 630 m2/d.

-Fractured Neogene aquifer (n2): underlying the sub-aquifer qp1, this aquifer consists of sandstone and conglomerate.

1.2 Scheme of testing wells and testing data

Based on the average thickness and effective porosity of the aquifer (qp) in the testing area (Table1)and the approved testing time in the project proposal, the distances between the testing wells have been determined as 8 m as shown in Fig.2 and Fig.3. The wells include the central pumping well CHN5, the tracer solution injection well QS-5, and the observation well QS-5B for monitoring the possible intrusion of the brackish GW. The hydrogeological section through the wells has been constructed from the drilling data (Fig.3) and well log(Fig.4) of the central well CHN5. The central well has a diameter of 0.168 m and both observation wells have a diameter of 0.09 m.

Fig.2 Testing wells' scheme, location and Pleistocene aquifer on fresh-brackish boundary

Fig.3 Hydrogeological section through the testing wells

Fig.4 Well log of central well CHN5

Table1 Estimated hydraulic parameters of the Pleistocene aquifer and well information in the testing area

The aquifer under testing is the sub-aquifer qp1in the depth from 55.05 m to 67.75 m, i.e. the aquifer thickness is 12.7 m (Fig.4). The testing time is 60 hours. The pumping out and tracer solution injection started at the same time. Pumping rate is 2 592 m3/d (30 L/s) and injection rate is 60.48 m3/d (0.7 L/s), which is equivalent to 2.33% of the pumping rate. With these pumping and injection rates, the possible maximal total dissolved solids (TDS) of the pumped out water would be 1.675 g/L, which has a TDS increased 228% since the natural GW of the sub-aquifer qp1at the testing site has TDS of 0.51 g/L and the injection salt solution is prepared by adding 5 g of salt in a litter of the natural GW. If the flow distortion coefficient αwis very high, for example 20, then the TDS of the pumped out water would be 0.568 g/L which is equivalent to TDS increase of 11.4%, which is big enough to analyze the TDS breakthrough curve. The TDS of the water is always referred to water at the temperature of 25℃. The salt solution in the injection well is constantly well mixed with the well water.

1.3 Obtained testing data

The testing started at the 8 AM the 11th Oct. 2015.The TDS of the water inside the injection well is plotted against the full testing time in Fig.5 and that of the pumped out water is plotted in Fig.6.

Fig.5 GW TDS in the injection well

Fig.6 TDS of the pumped out GW

1.4 Boundary condition at the outside injection well

Boundary condition of solute transport at the injection well can be interpretated differentially by diff-erent researchers in order to solve the problem.

According to Novakowski (1992), the flow rate of the solute mass in GW around the injection well can be considered as a specified value equal to the dispersion term and advection term. However, in the case of injection borehole with filter pack, both the dispersion and advection terms are unknown.This type of boundary condition can’t be directly used in this case.

According to Drost et al (1968), the solute concentration of GW around the injection well depends upon the flow rate through the well towards the pumping well and the solute solution injection regime, and can be considered as a specified solute concentration. The specified solute concentration outside the screen of the injection well may be determined as follows.

For the case of the injection well does not cause any disturbance of the GW flow as that there is no well, the GW flow through the entire injection well section (Qnat) (Fig.7) is determined by the following equation:

Where: Q is the pumping rate from the central pumping well (M3/T); Qnatis the flow through the injection well section (M3/T); rIis the radius of the injection well (L); rLis the distance between the central pumping well and injection well (L); m is the aquifer thickness (L); neffis the effective porosity of the aquifer.

Fig.7 GW flow through the injection well section

With the pumping rate of 2 592 m3/day and other relevant data as given above, the natural flow rate through the injection well section is Qnat= 0.193 5 m3/h. Due to the additional hydraulic resistance from the injection well, the actual flow rate through the well is always smaller than the natural flow rate given in Equation (1) and Fig.7 (Drost et al. 1968). The distortion flow coefficient αWis defined as the ratio between the flow rates through the injection well section with and without its presence (αw= Qnat/Qwell) (Drost et al. 1968; Hall,1996). As the TDS of the GW inside the injection well is measured during the testing, the GW flow rate Qwellinto and out the injection well can be determined by the following balance of the mixing of two volumes of water with two known TDS values: known volume of water inside the injection well with known TDS equal to C1wellat time t1,TDS equal to C2wellat time t2= t1+Δt and TDS of the natural GW equal to Cnat:

Then the flow distortion coefficient αwis the ration between Qwelland Qnat.

By Equation (2) using the obtained measured TDS inside the injection well, the following results have been obtained (Fig.5):

-From the 3.5th hour to the 15.5th hour: Qwell=0.010 4 m3/h (αw= 18.66);

-From the 17.5th hour to the 45th hour: Qwell=0.013 0 m3/h (αw= 14.88);

-From the 49th hour to the end of the testing:Qwell= 0.017 8 m3/h (αw= 10.76).

It is worthwhile to note that Brouyère (2003)had obtained αw=11.50 for a well of radius 0.025 m in the study, which is close to the value (αw=10.76) in the last stage of the testing in this study.

2 Proposed methodology for determining effective porosity and longitudinal dispersivity

2.1 Interpretation of the obtained tracer injection testing data

The TDS breakthrough curves for injection well and pumped out water are combined into one plot in Fig.8. The TDS of the GW in the pumping well started to increase very early since the 2ndhour and almost linearly increased until the 13thhour. The curve shows a stabilization trend at the 18thhour,which may indicate that the advection time of the solute from the injection well to the pumping well is around 18 hours. After 18 hours the solute concentration is fluctuated till the 36thhour due to the most probable reason that the solute injection rate was not stable all the time. The solute concentration then decreases from the 36thhour to 55thhour.

Fig.8 Breakthrough curves of TDS in injection and pumping wells

In the injection well, the solute concentration has an increasing trend from the 16thhour, which is corresponding to the maximal solute concentration in the pumping well at the 34thhour and the advection time from the injection well to the pumping well of 18 hours. The advection time of 18 hours is used in the identification of effective porosity and the longitudinal dispersivity in the following part of the paper.

2.2 FE modeling for determination of effective porosity and longitudinal dispersivity

The Galerkin FEM with linear shape functions and central time scheme with time step Δtn(Zienkiewicz and Morgan, 1983) has been applied to the partial differential equation describing the solute transport by advection-dispersion in one dimensional space between the injection well and pumping well. The time step and element size have been selected based on the criteria on Peclet and Courant numbers (Huyakorn and Pinder, 1983). The GW flow and solute transport FE modeling software was developed within the NOFOSTED research project headed by Nguyen Van Hoang (2018).The GW solute transport FEM program had been embedded with the algorithm of the method of least squares for parameter identification.

The main mechanism of solute transport by GW in the zones between the injection and pumping wells have been identified and described by Zlotnik and Logan (1996). The width W between the capture zone in the upstream of the injection well and the supply zone to the pumping well by Drost et al (1968) has a value not greater than two times of injection well’s diameter if the permeability of the disturbed aquifer around the injection well is smaller than that of the natural aquifer. This always happens in the practice of drilling and construction of GW monitoring wells. Therefore, for the testing scheme in this study, the maximal width of the solute transport zone is about 0.2 m, which is significantly smaller than the distance between the injection and pumping wells. Therefore, one-dimensional modelling of the solute transport may be applied for the purpose of transport parameter identification.

In the testing, the solute concentration of the pumped-out GW is measured, however, the modelling can provide the GW concentration only at the edge of the pumping well screen. As a rule, the concentration in the pumped out GW is exactly linearly proportional to the solute concentration right outside the pumping well. Therefore, normalized solute concentrations shown in Fig.9 for the pumped out GW and GW right outside the pumping well may be used for the purpose of parameter identification. Theoretically, the two normalized solute concentrations are identical. Taking notations of the solute concentration of pumped out GW as Cpumwith the maximal value Cpummaxand minimal Cpummin(Fig.9a), and correspondingly those for the solute concentration at the edge of the pumping well in the model as C1Dmaxand C1Dmin, the normalized solute concentrations in the pumped out GW and GW in the edge of the pumping well are as follows:

The transformation of absolute solute concentration (Fig.9a) into normalized solute concentration is illustrated in Fig.9b.

Fig.9 The transformation of absolute solute concentration into normalized solute concentration

2.3 Parameter identification results

Since the Pleistocene aquifer consists of coarse sands, gravels and pebbles, the adsorption or desorption of salt may be negligible, i.e. the retardation coefficient is assumed as 1.0 in the identification of effective porosity and dispersivity.

In accordance with the results of pumping test of the sub-aquifer qp1(Tong Thanh Tung, 2015)①Tong Thanh Tung. 2015. Specialized report: Interpretation and analysis of aquifer parameters for pumping test at group-well test CHN5 in Nghiem Xuyen-Thuong Tin-Hanoi. Project “Groundwater protection in large cities (city: Hanoi)”. Vietnam National Center for Water Resources Planning and Investigation-MoNRE.the sub-aquifer qp1is a leaky confined aquifer thanks to the contact with the Neogene (n2) fractured sandstone and conglomerate aquifer below. For a leaky confined aquifer, the early pumping data are entirely representing the confined aquifer without leakage effect (Fetter, 2001). As the data in Fig.10 shows, during the first 60 minutes of pumping, the slope of the drawdown curve is equal to 0.36 which is two times greater than the average slope over the whole pumping time. It means that the leakage from the Neogene aquifer provides around 50% of the pumping rate during the later pumping time. Therefore, the pumping rate Q should be decreased to the half value in the calculation of the sub-aquifer qp1, which would result in an effective porosity of 0.390 2. The effective porosity shall be further refined together with the longitudinal dispersivity identification by the FE modeling.

Fig.10 Drawdown curve of the pumping well QS-5A 13 (Tong Thanh Tung, 2015)

Effective porosity and longitudinal dispersivity have been identified and refined by the algorithm of least squares between the observed and modelled concentrations. The FE modeling of the advection-dispersion solute transport by GW was provided by the Governmental project supported by NAFOSTED-MOST (Nguyen Van Hoang, 2018).The input ranges of the effective porosity and longitudinal dispersivity are 0.20-0.40 and 1.0-3.4 m, respectively. The identification analysis yielded the effective porosity of 0.31 and longitudinal dispersivity of 2.20 m which are corresponding to the least squares of 0.001 19. The detailed results of the identification modeling are presented in Table2 and Fig.11.

Fig.11 The average least squares and corresponding effective porosity and longitudinal dispersivity

Table2 The average least squares and corresponding effective porosity and longitudinal dispersivity

The absolute and normalized solute concentrations in the pumped GW and at the pumping well screen corresponding to the identified effective porosity and longitudinal dispersivity which had the minimal least squares are presented in Fig.12 and Fig.13, respectively. With the identified effective porosity and longitudinal dispersivity the hydrodynamic dispersion is estimated as from D = 220 m2/d at the pumping well screen to D = 15.8 m2/d at the injection well screen with the minimal average least squares of 0.001 19, which is corresponding to average difference between the observed and model normalized concentration of 0.035 5 while the normalized concentration range is 0-1.The model result shows that the maximal solute concentration outside the pumping well screen is 6.1 times greater than the solute concentration of the pumped water (Fig.12).

Fig.12 Absolute solute concentration in the pumped GW and outside the pumping well screen corresponding to the minimal least squares

Fig.13 Normalized solute concentration in the pumped GW and outside the pumping well screen corresponding to the minimal least squares

2.4 Parameter identification uncertainty

The model used in the parameter identification is a lumped-parameter model in which spatial variations of parameters are ignored and the aquifer is described by fitted parameter values (effective porosity and dispersivity). Therefore, the estimated parameters’ uncertainty is due to the possible variation of the parameters in space and even in directional orientation.

The second possible factor affecting the parameters' uncertainty is the assumption of no adsorptiondesorption in the aquifer as the formation mainly consists of coarse sands, gravels and pebbles. However, the formation would not be completely free of organic maters and clay minerals.

The third possible factor affecting the parameters' uncertainty is that the GW velocity in the solute transport was calculated for a non-leaky confined aquifer. The tested aquifer qp1is overlain by a layer of clay and silty clay and underlain by the Neogene sandstone and conglomerate which may provide some leakage to the tested aquifer, and therefore may change the GW velocity.

The hydrodynamic dispersion coefficient used in the parameter analysis is a linear function of seepage velocity. However, the hydrodynamic dispersion coefficient may be in the form of a power function of seepage velocity as addressed early (Rifai et al. 1956; Yan et al. 2019).

Other factor of the parameters' uncertainty is the so-called scale-dependence of longitudinal dispersivity, i.e. dispersivity increases with the scale of test (the distance between the tracer injection and observation wells) as Gelhar et al. (1992) have found based on the analysis of 59 different field sites.

The parameters uncertainty may be also from the error of the numerical modelling due to the temporal and spatial discretization. Meanwhile, the parameter identification deals with two unknown parameter variables, i.e. effective porosity and dispersivity, in one advection-dispersion differential equation, in which a dispersion term contains a ratio of dispersivity to effective porosity, and an advection term contains effective porosity. The sensitivity of the two terms in the resulted tracer transport and possible numerical modelling error would provide an identified ratio of dispersivity to effective porosity and a set of the two parameters.This phenomenon would be seen from Fig.11 the sets of porosity and dispersivity would be from 0.30 m and 2.0 m to 3.4 m and 3.1 m with the squared errors of from 0.001 190 to 0.001 239.

3 Discussions

Through the interpretation of the GW tracer injection testing data and analysis of the solute transport parameters of the sub-aquifer qp1in the southern part of Hanoi city, the following discussions can be addressed:

-In accordance with Fetter (2001), the total porosity of well sorted gravels is in the range 0.25-0.50 and that of the gravels is 0.20-0.35. For the sands, gravels and pebbles, the effective porosity is almost the same as the total porosity (Fetter, 2001)since there are almost no dead-end pores in such loose formation (Bear and Verruijt, 1987). Therefore, the identified effective porosity equal to 0.31 obtained in this work is within the possible porosity range for sands, gravels and pebbles of the subaquifer qp1, without any contradiction. This value is well comparative with the value presented by Zhu et al. (2018) for sandy soil northwest of Laixi in Shandong Province, China.

-During the tracer injection, some instabilities of the injection (variable injection rates or even with some discontinuity of injection) did occur. The effective porosity may be calculated through such discontinuity points along with other relevant parameters (pumping rate, aquifer thickness and distance between the pumping and injection wells).However, for incompletely single confined aquifer(for example, for leaky confined aquifer), such application definitely produces errors and inaccuracies. A careful pumping data interpretation and analysis need to be carried out in order to apply the effective porosity determination in an appropriate way.

-The identified longitudinal dispersivity value of 2.20 m for the sub-aquifer qp1is a rather high value compared to the characteristic grain size of the aquifer (Bear and Verruijt, 1987), i.e. the longitudinal dispersivity is an order of the characteristic grain size. However, in the practice, there are lots of experimental data showing this large value trend of the longitudinal dispersivity. This obtained longitudinal dispersivity value is even smaller than 10-15 m which were used by Zhu et al. (2018) for sandy soil northwest of Laixi in Shandong Province, China.

-The flow distortion coefficient αwis an important parameter in the data interpretation and analysis of GW solute transport parameters and plays an important role in the efficiency of the tracer injection testing. Therefore, appropriate drilling and GW well construction technique should be used to ensure the maximal well efficiency.

4 Conclusions

The study has proposed an adaptive way to analyze tracer injection-withdrawal testing data to identify both effective porosity and longitudinal dispersivity of non-adsorptive aquifers. The proposed methodology uses only one-dimensional numerical modelling and had been shown to be successful in the application to a real field testing data. The methodology may overcome some required strict constraints in injection-withdrawal models, such as the steady state flow condition and constant continuous tracer injection, and also in more sophisticated two- or three-dimensional models which would require more parameter-variables such as transverse dispersivity in vertical and horizontal perpendicular to the radial direction. The methodology may cope with some convenient issues such as only solute concentration of pumped GW is measured, the injection rate and tracer concentration of injected fluid would accidentally be changed (but need to be recorded) etc.

To ensure the accuracy of parameter identification, reliable testing data during a tracer injectionwithdrawal testing and to deal with the parameter identification uncertainty, the following is recommended: 1) A stable solute injection in term of solute concentration and injection rate to ensure a smooth temporal concentration without any further data processing which may bring some inaccuracy;2) Some solute monitoring wells along the section line connecting the pumping and injection wells are recommended to be installed to monitor the solute concentration outside the well's screen; 3)Exact estimates of the aquifer thickness and leakage parameters of the aquifer are required in order to be able to analytically determine the effective porosity; 4) Constant pumping and injection rates to ensure a stable velocity field over the entire testing time; 5) Maximal well efficiency of the tracer injection well should be achieved to ensure an efficient use of tracer and an accuracy of tracer analysis.