Drawdown Curve Research Articles

Simulation of Complex Groundwater Flow Processes in Low‐Fidelity Radial Flow Model Using a Mathematical Representation of the Variation of Vertical Hydraulic Conductivity With Depth

ABSTRACTNumerical groundwater models are key tools to calculate the deployable output from pumped boreholes. Their calibration requires undertaking multiple runs to optimise the parameter values. To maintain computational efficiency, the hydrogeological complexity of fractured and weathered aquifers is often represented in numerical models using a simplified approach consisting of a mathematical equation that describes the vertical variation of horizontal hydraulic conductivity () value with depth. In this article, we present the inclusion of the variation of the vertical hydraulic conductivity () with depth to a radial flow model. We derive the mathematical equation controlling the flow vertically between the numerical nodes. We show that the inclusion of variation with depth have a limited impact on the shape of the time drawdown curve at the early times of a pumping test but its significance is higher at later times. This also has a measurable impact on the water level inside the pumped borehole especially when the variations of both and are accounted for. We use a simple linear variation of with depth but the method is also applicable to complex profile of aquifer heterogeneity if this complexity can be represented using polynomial approximation. This illustrates the applicability of the proposed method to a wide range of weathered aquifer settings.

Unveiling subsurface heterogeneity in porous aquifers: Insights from hydrogeophysics and derivative analysis

Groundwater is a crucial resource, particularly in urban areas where the need for alternative water sources is rising. Securing groundwater resources is paramount, requiring a concentrated effort to assess these resources and mitigate the increasing water shortages in urban regions. Despite its significance, the application of hydrogeophysics and derivative analysis in understanding aquifer dynamics is often overlooked and underused. Consequently, this study argues that neglecting the integration of hydrogeophysics dataset and derivative analysis in aquifer characterization leads to developing models that lack solution-oriented approaches, hindering effective groundwater management. This study aimed to enhance understanding of aquifer dynamics for solution-based modeling while emphasizing the importance of integrating hydrogeophysics dataset and derivative analysis to highlight aquifer system heterogeneities. The electrical resistivity tomography and derivative analysis of pumping test were used in this study to image the subsurface and amplify aquifer flow regimes respectively. The results of the electrical resistivity survey revealed a distinct layer of fine to medium-grain sand at depths of approximately 60 m in certain areas intercalated with medium-to-coarse-grain sand and thin layers of peat. Derivative analysis plots indicated that the predominant flow regime is linear and bilinear, with evidence of fracture dewatering during pumping cycles suggesting an unconfined aquifer. Additionally, aquifer heterogeneity and a no-flow boundary were evident during the pumping cycle. This study underscores the efficacy of combining hydrogeophysics and derivative analysis of pumping tests as a robust approach for imaging and validating subsurface conditions. The implications of these findings extend beyond the specific case study, offering valuable insights for groundwater utilization, monitoring, and management on a broader scale. By elucidating effective methodologies, this research enhances groundwater security and meets the escalating demand for sustainable water sources in urban areas. In conclusion, electrical resistivity tomography is an effective tool for characterizing subsurface aquifer systems, while derivative analysis of pumping tests is crucial for highlighting aquifer system heterogeneities. These methods offer a more practical interpretation compared to traditional drawdown versus time curve approaches, making the results invaluable for groundwater usage monitoring and management.

АНАЛИЗ РЕЗУЛЬТАТОВ ИССЛЕДОВАНИЙ МЕТОДОМ КРИВОЙ ПАДЕНИЯ ДАВЛЕНИЯ ПОСЛЕ ГИДРОРАЗРЫВА ПЛАСТА

The study presents an analysis of well testing using the pressure draw-down curve method after hydraulic fracturing in 2018‒2019. According to the analysis, that 67 % of studies are not data-supported, whereas 33 % are credible. Some study parameters were not employed due to the reasons described in the article. A scrutinized analysis of possible deviations in the results of the studies from the design concept for hydraulic fracturing is conducted. It is noted that fracture half-length and formation pressure determined by well testing differ from those determined by planning. Based on the results of the pressure draw-down curve, the author determines the dependence of the time required for the diagnosis of radial filtration mode on the range of reservoir permeability and the value of the half-length of a fracture. Based on the Nolte‒Smith plot, an approach to determining the nature of fracture development is proposed in order to obtain parameters sig-nificant for planning, control, and analysis of field development and geological and engineering activities and are used for detecting well deliverability and inflow area created due to hydraulic fracturing.

A simple method for correcting the effects of initial soil moisture on Modified Philip-Dunne Infiltrometer drawdown curves

The effect of varying initial soil moisture (θin) of a given soil on the drawdown curve measured using the Modified Philip-Dunne Infiltrometer (MPDI) and consequently on the estimated saturated hydraulic conductivity (Κs) value, was investigated. The laboratory tests completed using three different types of soil show that the drawdown curve was sensitive to θin for all three soils. This resulted in yielding Κs values that are sensitive to the values of θin. The lowest value of Κs was observed when the MPDI was used under wet conditions. To obtain a consistent estimate of Κs, a new correction factor was developed. This factor can be multiplied with the geometrical coefficient used in the governing equations of the MPDI to make appropriate corrections. After employing the correction factor, the variations in Κs values for all three tested soils decreased from 66%, 61% and 59%, to 26%, 16% and 26%, respectively. In situ experimental tests also show similar results and the coefficient of variation decreased from 81% to 61% after applying the correction factor. The performance was further validated by testing the relative performance of the MPDI against the results obtained using Minidisk Infiltrometer (MDI) under varying θin values. Results from the MDI show that the coefficient of variation for the Κs values of the three soils were 20%, 28%, and 32%, which are similar to the variations obtained after applying the correction factor in the MPDI model calculations. The aforementioned results indicate that the correction method proposed in this study is a useful method for improving the overall performance of MPDI.

An alternative approach to designing hydrogeological conceptual models in cases of scarce field data

The sensitivity of the derivative analysis to the variation of flow rates allows it to solve ambiguities, provide diagnostics of the flow dimension, and identify the boundary conditions of the tested aquifer. Based on the results of a derivative analysis, it was hypothesized that the set of assumptions for the fitted solution to the drawdown curve are valid for the tested aquifer. Thus, combining the derivative analysis results and the detailed geological characterization, a new approach was developed to build preliminary conceptual hydrogeological models in cases where field data are scarce. Applying this approach, it was concluded that basaltic aquifers in the Serra Geral Aquifer System (SGAS) are comprised of leaky confined aquifers, which the alternation of basalt floods that have permeable horizons at the top and with low permeability of interior flow. The simulated drawdown curve in a transient flow model perfectly matched with the drawdown curve recorded in the field, thus supporting the suitability of the built conceptual model. This statement challenges the prevailing theory that conceptualizes SGAS as a fractured aquifer. Conclusively, the current approach is capable of producing suitable conceptual models in cases of field data scarcity. Future investigations in other complex geological contexts may validate the present approach.

Identification of non-Darcian flow effect in double-porosity fractured aquifer based on multi-well pumping test

Well testing in double-porosity fractured aquifers or oil and gas reservoirs is one of the long-lasting research problems in subsurface hydrology and petroleum engineering, where the double-porosity implies that the media of concern can be approximated as a two interrelated continuums (fracture network and rock matrix) with two distinctively different porosities. However, most of those studies in double-porosity fractured aquifers only concern Darcian flow in the fractured continuum. In this study, we will expand such studies from Darcian flow regime to non-Darcian flow regime, which is most likely to be the case for the field well testing site reported in this investigation. New solutions based on power law and a linearization approximation are obtained for hydraulic heads in Laplace domain and subsequently inverted to give spatiotemporal distributions in real-time domain. The non-Darcian flow model in single porosity media is obtained by setting the leakage coefficient (C) to 0 or the storage coefficient of the matrix (Sm) to 0, where C is the rate of fluid transfer between the fracture and rock matrix. Parameter analysis is conducted using dimensionless formats. A larger dimensionless quasi conductivity coefficient KqD, a larger drawdown in the early stage, and a smaller drawdown in the late stage. The dimensionless parameters CD and ϕ influence the drawdown in transitional state, and the values get larger, the drawdown in transitional state drop smaller. A pumping test conducted in Huangtun, Anhui province of China has been applied to test the non-Darcian flow effect in a double-porosity aquifer, in which a particle swarm optimization (PSO) algorithm will be applied here to seek the optimal hydraulic parameters. As the result shows, the observed drawdown data fit well with the new model in the pumping stage. The predicted recovery drawdown curve with the calculated parameters of the new model also performs well with the field drawdown data, which supports the applicability of the new model to interpret the field data.

Semi-analytical model for pumping tests in discretely fractured aquifers

In this paper, a novel semi-analytical model for pumping tests in discretely fractured aquifers with randomly distributed and finitely conductive fractures is presented to investigate the wellbore drawdown transient behaviour. An aquifer model and discrete fracture model are established. The flux and drawdown equivalent conditions in the Laplace space are applied in the fracture wall to couple the fluid flow in both systems. The advantage of the proposed semi-analytical model is that only fractures must be separated into segments, not the entire domain. Then, a matrix of the fracture segment in Laplace space can be built and solved by using Gauss's elimination method. A final solution for wellbore drawdown can be easily evaluated using the numerical Laplace inversion algorithm of Stehfest. The model is compared with a previous result of an extended well. The proposed model allows us to consider the problems of pumping tests in complex fracture networks, including parallel uncrossed fracture networks, arbitrary distribution non-intersected fracture networks, and intersected fracture networks with isolated fractures. In the past studies, some scholars have found that the drawdown or pressure derivative curve will present only one dip valley which looks like a V-shaped curve for the naturally fractured confined aquifer or reservoirs, and number of dip valleys are only related to porous media type. However, this study illustrates that the drawdown transient behaviour and the number of dip valleys are closely related to fracture density, fracture conductivity, fracture length, fracture orientation, fracture distribution, position of a pumping well, and the distance between the pumping well and fracture.

Experimental Study on the Effective Utilization of Reserves in Tight Sandstone Gas Reservoirs and Their Applications

The effective utilization of reserves in tight sandstone reservoirs is one of the major concerns in terms of the development of tight sandstone gas reservoirs. However, the characteristics of reserve utilization are not fully understood, and many uncertainties still exist in the process. For this purpose, long cores on the Su 6 block of Sulige tight sandstone gas field in China were selected, and a multipoint embedded measurement system was established to study the characteristics of effective reserve utilization. Then, the effects of the related reservoir properties and production parameters were investigated. Based on the similarity theory, the effective conversion relationship between the physical experiment and the actual field production was established. The results showed that the pressure distribution in the exploitation of tight gas reservoir is nonlinear, and water cut in the reservoir will hinder the effective utilization of reserves. The lower the reservoir permeability, the larger the negative effect of water on reservoir utilization. Lower gas production rate and higher original pressure are associated with a smoother drawdown curve, which results in larger reserve utilization. The moving boundary expands with time, and its initial propagation velocity increase and then decrease. Additionally, the water cut in the reservoir can delay the spread of moving boundary propagation. The experimental results are consistent with the actual results of the field production by the similarity criterion, which can reflect and predict the production performance in tight gas reservoirs effectively. These results can provide a better understanding of reservoir pressure distribution and effective utilization of reserves to optimize the gas recovery and development benefit in tight sandstone gas reservoirs.

Unlined trench as a falling head permeameter: Analytic and HYDRUS2D modeling versus sandbox experiment

An isosceles triangle in a vertical cross-section of a trench is considered as a boundary from which free water in the trench seeps into a porous bed. A finite, initially impounded water volume vanishes from the channel and soil moisture moves in conjugation with surface water in a transient 2-D saturated-unsaturated regime. If capillarity is ignored and the subjacent soil is assumed to be dry before filling the channel, then a wetting front propagates as a sharp interface mated with drawdown of the channel free water. A Lembke method of consecutive steady states is used to model the interface as a rotating straight-line. A zone of Darcian seepage is a triangle, three sides of which (at each time instance) are a streamline, a constant piezometric head line and isobar. The instantaneous hinge point of the interface demarcates a zone of imbibition from a zone of drainage of this saturated triangle. Mathematically, a Green-Ampt type nonlinear first order ODE is obtained and explicitly integrated by separation of variables and the drawdown time t is explicitly expressed through the water depth H in the trench. In a sandbox with a dune sand, an experimental H(t) is measured in a trench having mild and steep bank slopes. When H(t) > 0 the drawdown rate increases that is attributed to an increase of the effect of capillarity. For this stage, Riesenkampf’s analytical solution for steady 2D tension-saturated flow with a capillary fringe is used. The analytical and experimental results are compared with those obtained by HYDRUS-2D (numerical modeling), involving a reservoir boundary condition introduced for furrow irrigation applications. Model performance parameters including the root mean squared error (RMSE), mean absolute error (MAE), coefficient of determination (r2) and Nash-Sutcliffe efficiency (E) showed a good agreement between the measured and simulated values of drawdown time. Results of the t-test between the measured and simulated drawdown time showed insignificant differences at a 5% confidence interval for all the trenches (p > 0.05). HYDRUS simulations quantified the dynamics of a “sinking” saturated “bubble” under the trench: isobars, isotachs, streamlines and loci of the stagnation points are plotted. We illustrate how to use a drawdown curve H(t) for determination of saturated hydraulic conductivity and air-entrance pressure in the Vedernikov-Bouwer model.

Research and Application of the Novel Deep Plugging Method in the Oilfield

In long-term water drive reservoir, small dose and short radius profile control cannot meet the needs, so deep profile control and flooding are needed. During the placement and processing of conventional deep profile control and flooding agent, the zone classification formed by the changes of pressure field and fluid field are not taken into account. In order to better develop these reservoirs, we proposed a novel deep profile control method, that is, the iso-pressure drop gradient progressive deep profile control method. The key features of the method include: 1) the method took into account the reservoir pressure distribution; 2) it proposed a novel standard to divide the orders of zone; 3) the method has been successfully applied in 4 wells in China Oilfield. The method divided the formation into near wellbore zone, well-far zone and deep zone according to the drawdown curve. As each zone of the pressure gradient is different and therefore require different intensity of slug. Then design the agent slugs according to iso-pressure drop gradient rule, and the breakthrough pressure gradient of agent is equal to the formation pressure gradient, and it achieved the fluid diversion of whole course by combining the different intensity of blocking agent. The method was applied successfully in 2 wells in China Oilfield from May to November in 2008. The method can smartly improve the sweep efficiency, and field test shows that it can play a very good efficiency of reducing water and increasing oil production. This method is becoming more of a concern in the oilfield develop.

Generalizing Agarwal's Method for the Interpretation of Recovery Tests Under Non‐Ideal Conditions

AbstractPumping tests are performed during aquifer characterization to gain conceptual understanding about the system through diagnostic plots and to estimate hydraulic properties. Recovery tests consist of measuring head response in observation and/or pumping wells after pumping termination. They are especially useful when the pumping rate cannot be accurately controlled. They have been traditionally interpreted using Theis' recovery method, which yields robust estimates of effective transmissivity but does not provide information about the conceptual model. Agarwal proposed a method that has become standard in the oil industry, to obtain both early and late time reservoir responses to pumping from recovery data. However, the validity of the method has only been tested to a limited extent. In this work, we analyze Agarwal's method in terms of both drawdowns and log derivatives for non‐ideal conditions: leaky aquifer, presence of boundaries, and one‐dimensional flow. Our results show that Agarwal's method provides excellent recovery plots (i.e., the drawdown curve that would be obtained during pumping) and parameter estimates for nearly all aquifer conditions, provided that a constant pumping rate is used and the log derivative at the end of pumping is constant, which is too limiting for groundwater hydrology practice, where observation wells are usually monitored. We generalize Agarwal's method by (1) deriving an improved equivalent time for time‐dependent pumping rate and (2) proposing to recover drawdown curves by extrapolating the pumping phase drawdowns. These yield excellent diagnostic plots, thus facilitating the conceptual model analysis for a broad range of conditions.

A generalized model for pumping well hydraulics in confined aquifers

AbstractA generalized model for well hydraulics in confined aquifers is presented. The lattice Boltzmann method (LBM)-based altered-velocity model is used to simulate well hydraulics in homogeneous and heterogeneous confined aquifers for different pumping conditions. LBM is applied to simulate well hydraulics in two different configurations of heterogeneous aquifer, where (1) a circular disk of material or (2) an infinite linear strip of material is embedded in a matrix of differing hydraulic properties. The effect of hydrogeologic boundaries on drawdown curve in confined aquifers is simulated using LBM. The LBM is further applied to simulate drawdown during harmonic pumping well test. The LBM data in lattice units are scaled to physical units using non-dimensional discharge rate and diffusion length. The results from LBM were found to be sensitive to the relaxation parameter and the RMS error for drawdown was found to be less than 1% for later time. This work will verify the potential of LBM to simulate well hydraulics in homogeneous and heterogeneous confined aquifers for constant, step, and harmonic pumping.

Characteristics of dewatering induced drawdown curve under blocking effect of retaining wall in aquifer

Summary For deep excavation pits that require the pumping of confined groundwater, a combination of a retaining wall and dewatering with large-diameter wells is usually adopted during excavation to improve safety. Since a retaining wall has a much lower hydraulic conductivity than the surrounding material in the aquifer, blocking of seepage to prolong the seepage path of the groundwater outside of the pit is effective. The retaining walls used during excavation dewatering cause hydraulic head drawdown inside the pit much faster than outside the pit. Thus, difference in hydraulic head between inside and outside of the pit increases. To investigate the mechanism of the blocking effect, numerical simulation using the finite difference method (FDM) was conducted to analyze the effects of pumping in the pit. The FDM results show that drawdown varies along the depth of the confined aquifer. The influence factors of drawdown inside and outside the pit include insertion depth of retaining walls, anisotropy of a confined aquifer and screen length of pumping wells. In addition, FDM results also show that the drawdown-time curve can be divided into four stages: in Stage I, drawdown inside the pit is very small and outside the pit it is almost zero; in Stage II, drawdown increases quickly with time; in Stage III, the drawdown curve is parallel to the Cooper–Jacob curve on semi-log axes; and in Stage IV, the drawdown becomes constant. These characteristics of the drawdown curve under the blocking effect of a retaining wall in an aquifer provide a way of estimating hydrogeological parameters according to pumping test results.

A simple data reduction method for pumping tests with tidal, partial penetration, and storage effects

Single-well and group-well pumping tests were undertaken in a deep gravel formation of the Taipei basin to determine the hydraulic parameters and better understand the drawdown characteristics across the basin. The periodic drawdown fluctuation due to tidal loading from the overlying river resulted in a difficulty in determining the hydraulic parameters by those conventionally used graphic techniques. In addition, many other site-specific influencing factors, such as the partial penetration effect and the large diameter of the wells, had to be considered. In this paper, a simple data reduction method was presented to resolve the above-mentioned complications. It was demonstrated that the drawdown data induced by group-well pumping were well predicted using the shifted drawdown curve deduced by the proposed method.

Study on the Methods of Layer Adjustment in Gas Dynamic Reserve Measurement

To get the accurate gas pool dynamic measurement is the one of the basic work of oil field development. The geologic conditions, one of the aspects, limited the gas pool. It often appears reshooting another layer to commingled production or block off the seriously water producer in layer adjustment, calculation of reserves depends on the alteration of the model condition. Through the material balance and its further work, set the gas pool reserves calculation methods under the layer adjustment condition. The closed constant volume gas pool, its drawdown curve becomes the transition with the adjustment of the layer. Through the original formation pressure with two different slope straight lines before and after adjustment, Using linear extrapolation can get the reserves before and after adjusted.

Influence of Groundwater Seepage during Foundation Pit Dewatering on Soil’s Effective Stress

Engineering dewatering not only makes soil release gravity water, increasing soil self-weight stress, but also lead to seepage occur along the two sides of waterproof curtain driven by water head difference inside and outside the pit, forming a hydrodynamic pressure, which are the main reasons causing ground settlement. In this paper, the equation of groundwater level drawdown funnel curve firstly is deduced, then we investigate the total effective stress increments of foundation pit soil with seepage works alone as well as both gravity drainage and seepage effect work together, and obtained the formulas for soil effective stress increment calculation. Studies show that the shape of soil settlement cross-section is closely related to the characters of water drawdown funnel curve.

Improved predictions of saturated and unsaturated zone drawdowns in a heterogeneous unconfined aquifer via transient hydraulic tomography: Laboratory sandbox experiments

► Uniform parameters lead to biased drawdown predictions in the (un)saturated zones. ► Accounting for aquifer heterogeneity yields significant improvements in predictions. ► Considering unsaturated zone (UZ) heterogeneity produced a minor improvement. ► UZ heterogeneity plays a minor role in forming the S shape drawdown curve. ► Hydraulic tomography can be used to characterize unconfined aquifers. Interpretation of pumping tests in unconfined aquifers has largely been based on analytical solutions that disregard aquifer heterogeneity. In this study, we investigate whether the prediction of drawdown responses in a heterogeneous unconfined aquifer and the unsaturated zone above it with a variably saturated groundwater flow model can be improved by including information on hydraulic conductivity ( K ) and specific storage ( S s ) from transient hydraulic tomography (THT). We also investigate whether these predictions are affected by the use of unsaturated flow parameters estimated through laboratory hanging column experiments or calibration of in situ drainage curves. To investigate these issues, we designed and conducted laboratory sandbox experiments to characterize the saturated and unsaturated properties of a heterogeneous unconfined aquifer. Specifically, we conducted pumping tests under fully saturated conditions and interpreted the drawdown responses by treating the medium to be either homogeneous or heterogeneous. We then conducted another pumping test and allowed the water table to drop, similar to a pumping test in an unconfined aquifer. Simulations conducted using a variably saturated flow model revealed: (1) homogeneous parameters in the saturated and unsaturated zones have a difficult time predicting the responses of the heterogeneous unconfined aquifer; (2) heterogeneous saturated hydraulic parameter distributions obtained via THT yielded significantly improved drawdown predictions in the saturated zone of the unconfined aquifer; and (3) considering heterogeneity of unsaturated zone parameters produced a minor improvement in predictions in the unsaturated zone, but not the saturated zone. These results seem to support the finding by Mao et al. (2011) that spatial variability in the unsaturated zone plays a minor role in the formation of the S-shape drawdown-time curve observed during pumping in an unconfined aquifer.

Measuring Soil Hydraulic Properties Using a Cased Borehole Permeameter: Falling‐Head Analysis

The falling‐head cased borehole analysis of Philip for determining the field‐saturated hydraulic conductivity (Kfs) and sorptive number (α*) in the vadose zone was extended and assessed. The extension allows several water discharge configurations (vertical, radial, combined vertical and radial), variable length (L) and radius (a) of outflow screen, variable reservoir radius, and use of Excel Solver to calculate Kfs and α* via numerical optimization. The assessment used simulated borehole drawdown curves from HYDRUS‐2D to determine the accuracy with which the Philip and extended solutions determined Kfs and α*. Using the Philip “flow efficiency correction,” CP = π2/8, and “gravity factor,” GP = equivalent sphere radius r0 (maximum gravity effect), caused the Philip and extended solutions to overestimate Kfs or α* by amounts ranging from a few percent in strong‐capillarity soils to several orders of magnitude in weak‐capillarity soils. Replacing CP with CE = 1 (no flow efficiency correction) and GP with GE = 0 (negligible gravity effect) in the extended solution resulted in accurate Kfs determinations (≤20% error) regardless of discharge geometry, screen configuration, drawdown range, or soil capillarity. Consistently accurate determination of α* required use of the CE and GE coefficients, 1 ≤ L/a ≤ 4, and avoidance of small borehole drawdowns. Solver‐based determination of Kfs and α* using several heads distributed along the drawdown curve was less sensitive to measurement error and lack of data‐model fit than the two‐head approaches of Philip and others. The extended analysis improves the accuracy and utility of the falling‐head cased borehole permeameter.

A revisit of drawdown behavior during pumping in unconfined aquifers

In this study, the S‐shaped log‐log drawdown‐time curve typical of pumping tests in unconfined aquifers is reinvestigated via numerical experiments. Like previous investigations, this study attributes the departure of the S shape from the drawdown‐time behavior of the confined aquifer to the presence of an “additional” source of water. Unlike previous studies, this source of water is reinvestigated by examining the temporal and spatial evolution of the rate of change in storage in an unconfined aquifer during pumping. This evolution is then related to the transition of water release mechanisms from the expansion of water and compaction of the porous medium to the drainage of water from the unsaturated zone above the initial water table and initially saturated pores as the water table falls during the pumping of the aquifer. Afterward, the 1‐D vertical drainage process in a soil column is simulated. Results of the simulation show that the transition of the water release mechanisms in the 1‐D vertical flow without an initial unsaturated zone can also yield the S‐shaped drawdown‐time curve as in an unconfined aquifer. We therefore conclude that the transition of the water release mechanisms and vertical flow in the aquifer are the cause of the S‐shaped drawdown‐time curve observed during pumping in an unconfined aquifer. We also find that the moisture retention characteristics of the aquifer material have greater impact than its relative permeability characteristics on the drawdown‐time curve. Furthermore, influences of the spatial variability of saturated hydraulic conductivity, specific storage, and saturated moisture content on the drawdown curve in the saturated zone are found to be more significant than those of other unsaturated properties. Finally, a cross‐correlation analysis reveals that the drawdown at a location in a heterogeneous unconfined aquifer is mainly affected by local heterogeneity near the pumping and observation wells. Applications of a model assuming homogeneity to the estimation of aquifer parameters as such may require a large number of observation wells to obtain representative parameter values. In conclusion, we advocate that the governing equation for variably saturated flow through heterogeneous media is a more appropriate and realistic model that explains the S‐shaped drawdown‐time curves observed in the field.

A case history of field pumping tests in a deep gravel formation in the Taipei Basin, Taiwan

33 large-diameter wells embedded in 2-m thick, 63-m deep diaphragm walls were constructed to reduce both the uplift pressures and the groundwater inflow during the excavations. As the actual thickness of the pumped aquifer is unknown, the installed wells are regarded as partial penetration wells. Single-well and multi-well pumping tests were conducted in the deep gravel formation of Taipei Basin to derive the hydraulic parameters and to investigate the drawdown characteristics at both the construction and remote sites. However, the tidal effect on the drawdown of both the pumping well and nearby observation wells was found significant. Additionally, wellbore storage, skin, and leakage need to be taken into account for deriving the hydraulic parameters. Hence, a method to remove these five factors influencing the drawdown curve is developed, which takes advantage from the late-time characteristics of drawdown data and the early-time behavior of drawdown. Some currently available semi-log graphic techniques are therefore proven applicable for parameter determination. Validity of the proposed method is verified by the good agreement between the calculated and the measured drawdown of both the pumping well and observation well.