The use of MRS in the determination of hydraulic transmissivity: The case of alluvial aquifers

Magnetic Resonance Sounding (MRS) is nowadays accepted as a new geophysical method that can be used for a reliable determination of the ground water content distribution in the top 150 m. A great effort has also been made in MRS development to deduce the hydraulic transmissivity, based on empiric relationships of the permeability with a factor F which is calculated with NMR parameters measured at laboratory scale. To use this relationship under field conditions a calibration coefficient C_T = T_pt / F has to be previously established, which demands the knowledge of the transmissivity T_pt evaluated in the pumping test. The transmissivity can then be calculated at any other site of the same aquifer using the relation T_mrs = C_TF. The C_T values reported suggest a certain relationship with the lithology, but with a great dispersion and contradictory results. MRS surveys carried out in alluvial aquifers in Spain have shown that the value of C_T evaluated at one site may not be valid at another place of the same aquifer, because of the great heterogeneity of this kind of geological environment. The demand of a pumping test at each site where a MRS is measured invalidates the method actually used for MRS transmissivity evaluation. More than 50 MRS have been used to propose a new methodology. The aquifers visited cover a great range of transmissivities (from 2 × 10^− 6 to 9 × 10^− 3 m²/s). The MRS signal amplitude varies between 20 and 1400 nV, the signal/noise ratio is in the range from 0.6 to 42, and the value of the decay time constant varies from 200 to 800 ms. It has been demonstrated that when the transmissivity increases, the value of F decreases, and C_T increases, except for certain groups of MRS taken at the same aquifer or part of one aquifer, for which F increases with T_pt, keeping C_T constant. A function C_T(F) of the type C_T = mF^− n has been obtained that allows the transmissivity evaluation without the need of T_pt. Considering that both values of transmissivity, T_pt and T_mrs, are subjected to deviations due to the experimental errors as well as due to evaluation errors, the prediction achieved by the proposed equation is rather good. To perform a better evaluation of the values of the coefficients m and n it is necessary to have a greater number of MR soundings of good quality and with a trustworthy inversion at locations where a really comparable and good performed pumping test is available, covering a sufficient range of transmissivities. Though the data we have used do not always fulfil these conditions, the result is promising. Once a trustable function is available, the forecast of the transmissivity using MRS will not need the existence of any pumping test in the area. The general extension of this methodology demands the availability of MRS taken at all kinds of geological and hydrogeological environments, which is impossible without the existence of a universal MRS data base.     

Contribution of magnetic resonance sounding to aquifer characterization and recharge estimate in semiarid Niger

To improve the knowledge of the regionally important Continental Terminal 3 (CT3) aquifer in south-western Niger, fifteen magnetic resonance soundings (MRS) were carried out in December 2005 in the vicinity of wells and boreholes. The output MRS geophysical parameters, i.e. water content and decay constants versus depth, were compared to hydrogeological characteristics, i.e. water table depth, total porosity, specific yield and transmissivity estimated from direct measurements, pumping tests and transient groundwater modelling. The MRS-determined parameters were then used to estimate the rates of groundwater recharge.Contained in poorly consolidated Tertiary sandstones, the CT3 aquifer's water table has continuously risen by 4 m in total over the past four decades. Additionally, a significant portion of this increase has occurred in the past decade alone, with an annual rise now ranging between 0.1 and 0.3 m depending on the monitored well. Increase in groundwater recharge due to land clearance and deforestation explains this situation. According to previous estimations, the pre-clearing recharge ranged from 1 to 5 mm per year in 1950–60 s, while more recent recharge rates (1990s–2000s) range from 20 to 50 mm per year. These recharge values are directly affected by estimated aquifer specific yield value, while the spatial variation of rates of water table rise can be attributed to large scale hydrodynamic heterogeneities in the aquifer. However, few field measurements were available to confirm these assumptions.The main results of this study are: (1) The water table depth and aquifer transmissivity are estimated from MRS output parameters with an average accuracy of ± 10% and ± 9% respectively. (2) The MRS-determined water content is linked to both the total porosity and the specific yield of the aquifer, but no quantitative formulation can be proposed as yet. (3) Using the average MRS-determined water content over the investigated area, i.e. 13%, the groundwater recharge rates can be estimated to be ~ 2 mm per year in the 1950–1960s (pre-clearing period), and ~ 23 mm per year for the last decade. (4) The variations in specific yield and transmissivity cannot explain by themselves the spatial variability of the rise of the water table. (5) The ranges in transmissivity and water content obtained from MRS are more realistic than the groundwater modelling outputs. Therefore, MRS could be used to better constrain the aquifer parameters in groundwater modelling with a dense site network.Finally, this work illustrates how MRS can successfully improve characterisation and transient multi-year groundwater balance of commonly found sedimentary aquifers, particularly when integrated with well observations and pumping tests.     

Mixing at the interface between fresh and salt waters in 3D steady flow with application to a pumping well in a coastal aquifer

We consider 3D steady flow of fresh water over a salt water body in a confined aquifer of constant thickness D, with application to a pumping well in a coastal aquifer. With neglect of mixing, a sharp interface separates the two fluid bodies and an existing analytical solution, based on the Dupuit assumption, is adopted. The aim is to solve for the mixing between the fresh and salt waters for α_T/D  1 (α_T transverse dispersivity), as field studies indicate that α_T = O(10⁻³ − 10⁻² m). The mixing zone around the interface is narrow and solutions by existing codes experience numerical difficulties. The problem is solved by the boundary layer (BL) approximation, extending a method, applied previously to two-dimensional flows. The BL equations of variable-density flow are solved by using the Von Karman integral method, to determine the BL thickness and the rate of entrainment of salt water along the interface. Application to the pumping well problem yields the salinity of the pumped water, as function of the parameters of the problem (well discharge, seaward discharge, well distance from the coast and density difference).     

Efficiency of joint use of MRS and VES to characterize coastal aquifer in Myanmar

The productivity and the water quality of coastal aquifers can be highly heterogeneous in a complex environment. The characterization of these aquifers can be improved by hydrogeological and complementary geophysical surveys. Such an integrated approach is developed in a non-consolidated coastal aquifer in Myanmar (previously named Burma).A preliminary hydrogeological survey is conducted to know better the targeted aquifers. Then, 25 sites are selected to characterize aquifers through borehole drillings and pumping tests implementation. In the same sites, magnetic resonance soundings (MRS) and vertical electrical soundings (VES) are carried out. Geophysical results are compared to hydrogeological data, and geophysical parameters are used to characterize aquifers using conversion equations. Finally, combining the analysis of technical and economical impacts of geophysics, a methodology is proposed to characterize non-consolidated coastal aquifers.Depth and thickness of saturated zone is determined by means of MRS in 68% of the sites (evaluated with 34 soundings). The average accuracy of confined storativity estimated with MRS is ± 6% (evaluated over 7 pumping tests) whereas the average accuracy of transmissivity estimation with MRS is ± 45% (evaluated using 15 pumping tests). To reduce uncertainty in VES interpretation, the aquifer geometry estimated with MRS is used as a fixed parameter in VES inversion. The accuracy of groundwater electrical conductivity evaluation from 15 VES is enough to estimate the risk of water salinity. In addition, the maximum depth of penetration of the MRS depends on the rocks' electrical resistivity and is between 20 and 80 m at the study area.     

Quaternary aquifer transmissivity derived from vertical electrical sounding measurements in the semi-arid Khanasser Valley Region,Syria

Vertical electrical sounding technique (VES) is used as an alternative approach to pumping test for computing the Quaternary aquifer transmissivity in the Khanasser Valley, Northern Syria. The method is inexpensive, easy and gives faster results with higher special resolution than the traditional pumping technique. The hydraulic conductivity values obtained using VES agree with the pumping test results, which in the Khanasser Valley vary between the order of 0.864 and 8.64 m/day (10⁻⁵ and 10⁻⁴ m/s). The probable location of the Quaternary aquifer in the Khanasser Valley is obtained through the transmissivity map derived from VES. The knowledge of transmissivity is fundamental for modeling and management processes in the Khanasser Valley. Other similar semiarid regions can benefit from the approach successfully applied in the study area.     

Characterization of aquifers in the Vientiane Basin,Laos, using Magnetic Resonance Sounding and Vertical Electrical Sounding

The aim of this study is to define and characterize water bearing geological formation and to test the possibility of using geophysical techniques to determine the hydrogeological parameters in three areas in the Vientiane basin, Laos. The investigated areas are part of the Khorat Plateau where halite is naturally occurring at depths as shallow as 50 m in the Thangon Formation. Magnetic Resonance Sounding (MRS) has been used in combination with Vertical Electrical Sounding (VES) in different geological environments. In total, 46 sites have been investigated and the MRS and VES recognized the stratigraphic unit N₂Q_1–3, consisting of alluvial unconsolidated sediments, as the main water bearing unit. The aquifer thickness varies usually between 10 and 40 m and the depth to the main aquifer range from 5 to 15 m. The free water content is here up to 30%, and the decay times vary between 100 and 400 ms, suggesting a mean pore size equivalent to fine sand to gravel. The resistivity is highly variable, but usually around 10–1500 Ω-m, except for some sites in areas 1 and 2, where the aquifer is of low resistivity, probably related to salt water. Hydraulic and storage-related parameters such as transmissivity, hydraulic column, have been estimated from the MRS. The MRS together with VES has been shown to be a useful and important tool for identifying and distinguishing freshwater from possible salt-affected water as well as the salt-related clay layer of the Thangon Formation. This clay layer is characterized by very low free water content and a resistivity lower than 5 Ω-m and can be found in all 3 areas at depths from 15 to 50 m.     

Interpretation of a Pumping Test with Interference from a Neighboring Well

In confined aquifers, the influence of neighboring active wells is often neglected when interpreting a pumping test. This can, however, lead to an erroneous interpretation of the pumping test data. This paper presents simple methods to evaluate the transmissivity (T) and storativity (S) of a confined aquifer under Theis conditions, when an interfering well starts pumping in the neighborhood of the tested well before the beginning of the test. These new methods yield better estimates of the T and especially S values than when the interfering well influence is neglected. They also permit to distinguish between interfering wells and other deviations from the Cooper‐Jacob straight line, such as impermeable boundaries. The new methods were then applied on data obtained from a numerical model. The new methods require knowing the pumping rate of the interfering well and the time elapsed since the pumping started in each well, but contrary to previous methods, they do not require the aquifer natural level at the beginning of the test, which is often unknown if the interfering well has started pumping before the tested well.     

Groundwater investigation on sand dunes area in southern part of Vietnam by magnetic resonance sounding

In the last five years, magnetic resonance sounding (MRS), as a non-invasive geophysical method, has emerged as a new technique for ground water investigation in Vietnam. In this paper, we present the general theoretical basis of this method together with acquisition, processing, and interpretation of the MRS data. We show a case study of MRS surveys in sand dunes area in order to characterize aquifers situated in the southern part of Vietnam. From the interpretation of MRS soundings we delimited an aquifer layer in the subsurface with strong lateral variations for which we determined the depth at 44 m and water content between 3% and 9.5%. The longitudinal relaxation constant T*₁ is about 250 m s, while the transverse relaxation T*₂ is between 150–200 m s. That indicates fine to medium grain size and thus low to medium hydraulic permeability. These results are confirmed by the observations from the well LK1 between 45 to 70 m. The results of other MRS measurements showed the presence of a low water bearing aquifer and were confirmed by the observations in two other wells.     

Assessing radial transmissivity variation in heterogeneous aquifers using analytical techniques

Pumping tests are one of the most commonly used in situ testing techniques for assessing aquifer hydraulic properties. Numerous researches have been conducted to predict the effects of aquifer heterogeneity on the groundwater levels during pumping tests. The objectives of the present work were as follows: (1) to predict drawdown conditions and to estimate aquifer properties during pumping tests undertaken in radially symmetric heterogeneous aquifers, and (2) to identify a method for assessing the transmissivity field along the radial coordinate in radially symmetric and fully heterogeneous transmissivity fields. The first objective was achieved by expanding an existing analytical drawdown formulation that was valid for a radially symmetric confined aquifer with two concentric zones around the pumping well to an N concentric zone confined aquifer having a constant transmissivity value within each zone. The formulation was evaluated for aquifers with three and four concentric zones to assess the effects of the transmissivity field on the drawdown conditions. The specific conditions under which aquifer properties could be identified using traditional methods of analysis were also evaluated. The second objective was achieved by implementing the inverse solution algorithm (ISA), which was developed for petroleum reservoirs to groundwater aquifer settings. The results showed that the drawdown values are influenced by a volumetric integral of a weighting function and the transmissivity field within the cone of depression. The weighting function migrates in tandem with the expanding cone of depression. The ability of the ISA to predict radially symmetric and log‐normally distributed transmissivity fields was assessed against analytical and numerical benchmarks. The results of this investigation indicated that the ISA method is a viable technique for evaluating the radial transmissivity variations of heterogeneous aquifer settings. Copyright © 2013 John Wiley & Sons, Ltd.     

Conservative identification of nodal transmissivities: theory,computational experiments and application to the Rharb coastal aquifer (Morocco)

Abstract

In order to calculate the transmissivity from the inverse problem corresponding to the groundwater flow in an isotropic horizontal aquifer, a numerical conservative approach is tested. The method deals with triangulation of the domain and applies the conservation of mass to elements of the mesh using the harmonic mean for internodal transmissivities. An optimal sweeping algorithm is used to evaluate nodal transmissivities from one element to another with a minimal relative error accumulation. The practical importance of the method is demonstrated through two synthetic examples representing those experienced in the field, then through application to a Moroccan aquifer. The computed hydraulic head is well fitted to the reference one, which confirms the validity of the identified transmissivity model.     

Inverse modelling using PS‐InSAR data for improved land subsidence simulation in Las Vegas Valley,Nevada

Las Vegas Valley has had a long history of groundwater development and subsequent surface deformation. InSAR interferograms have revealed detailed and complex spatial patterns of subsidence in the Las Vegas Valley area that do not coincide with major pumping regions. This research represents the first effort to use high spatial and temporal resolution subsidence observations from InSAR and hydraulic head data to inversely calibrate transmissivities (T), elastic and inelastic skeletal storage coefficients (S_ke and S_kv) of the developed‐zone aquifer and conductance (CR) of the basin‐fill faults for the entire Las Vegas basin. The results indicate that the subsidence observations from InSAR are extremely beneficial for accurately quantifying hydraulic parameters, and the model calibration results are far more accurate than when using only groundwater levels as observations, and just a limited number of subsidence observations. The discrepancy between distributions of pumping and greatest levels of subsidence is found to be attributed to spatial variations in clay thickness. The Eglington fault separates thicker interbeds to the northwest from thinner interbeds to the southeast and the fault may act as a groundwater‐flow barrier and/or subsidence boundary, although the influence of the groundwater barrier to this area is found to be insignificant. Copyright © 2016 John Wiley & Sons, Ltd.     

Correlation of Geoelectric Data with Aquifer Parameters to Delineate the Groundwater Potential of Hard rock Terrain in Central Uganda

Knowledge of aquifer parameters is essential for management of groundwater resources. Conventionally, these parameters are estimated through pumping tests carried out on water wells. This paper presents a study that was conducted in three villages (Tumba, Kabazi, and Ndaiga) of Nakasongola District, central Uganda to investigate the hydrogeological characteristics of the basement aquifers. Our objective was to correlate surface resistivity data with aquifer properties in order to reveal the groundwater potential in the district. Existing electrical resistivity and borehole data from 20 villages in Nakasongola District were used to correlate the aquifer apparent resistivity (ρ _e) with its hydraulic conductivity (K _e), and aquifer transverse resistance (TR) with its transmissivity (T _e). K _e was found to be related to ρ _e by; $ {\text{Log }}(K_{\text{e}} ) = - 0.002\rho_{\text{e}} + 2.692 $ . Similarly, TR was found to be related to T by; $ {\text{TR}} = - 0.07T_{\text{e}} + 2260 $ . Using these expressions, aquifer parameters (T _c and K _c) were extrapolated from measurements obtained from surface resistivity surveys. Our results show very low resistivities for the presumed water-bearing aquifer zones, possibly because of deteriorating quality of the groundwater and their packing and grain size. Drilling at the preferred VES spots was conducted before the pumping tests to reveal the aquifer characteristics. Aquifer parameters (T _o and K _o) as obtained from pumping tests gave values (29,424.7 m²/day, 374.3 m/day), (9,801.1 m²/day, 437.0 m/day), (31,852.4 m²/day, 392.9 m/day). The estimated aquifer parameter (T _c and K _c) when extrapolated from surface geoelectrical data gave (7,142.9 m²/day, 381.9 m/day), (28,200.0 m²/day, 463.4 m/day), (19,428.6 m²/day, 459.2 m/day) for Tumba, Kabazi, and Ndaiga villages, respectively. Interestingly, the similarity between the K _c and K _o pairs was not significantly different. We observed no significant relationships between the T _c and T _o pairs_. The root mean square errors were estimated to be 18,159 m²/day and 41.4 m/day.     

Comparison of Two Computational Methods for Estimating Transmissivity Based on the Picking Equation

A comparison is presented of two computational methods, PICKINGmodel and PPC-Recovery, to estimate transmissivities based on the Picking equation using water-level recovery data from brief pumping tests of relatively low-yielding domestic wells. The tests were performed by the United States Geological Survey (USGS) in 50 domestic bedrock wells in south-central New York State, and USGS staff performed the analysis using PICKINGmodel based on the Picking equation. The results indicated that the estimated transmissivities ranged from 0.86 to 2900 ft²/d (0.080 to 270 m²/d) with a median of 41 ft²/d (3.8 m²/d). The same data were later analyzed using PPC-Recovery also based on the Picking equation. The two sets of estimated transmissivities were compared and statistically had the same median value at a probability of 95%. In another analysis, the PPC-Recovery method was applied to the same data that had been truncated at the point when the slope of the recovery data curve began to deviate from a straight line aligned with the middle portion of the recovery data. Comparing these resulting estimates of transmissivity with values originally obtained using the PICKINGmodel, the two had statistically the same median value for transmissivity at a probability of 95%. It was concluded that using PPC-Recovery in this manner to estimate transmissivity in low-yielding domestic wells will yield transmissivity values sufficiently close to the results had PICKINGmodel been used, and with less time and effort.     

Reservoir lifetime and heat recovery factor in geothermal aquifers used for urban heating

Simple models are discussed to evaluate reservoir lifetime and heat recovery factor in geothermal aquifers used for urban heating. By comparing various single well and doublet production schemes, it is shown that reinjection of heat depleted water greatly enhances heat recovery and reservoir lifetime, and can be optimized for maximum heat production. It is concluded that geothermal aquifer production should be unitized, as is already done in oil and gas reservoirs.Nomenclature a distance between doublets in multi-doublet patterns, meters - A area of aquifer at base temperature, m² drainage area of individual doublets in multidoublet patterns, m² - D distance between doublet wells, meters - h aquifer thickness, meters - H water head, meters - Q production rate, m³/sec. - r _e aquifer radius, meters - r _w well radius, meters - R _g heat recovery factor, fraction - S water level drawdown, meters - t producing time, sec. - T aquifer transmissivity, m²/sec. - v stream-channel water velocity, m/sec. - actual temperature change, °C - theoretical temperature change, °C - water temperature, °C - heat conductivity, W/m/°C - _r rock heat conductivity, W/m/°C - _aC_a aquifer heat capacity, J/m³/°C - _aC_r rock heat capacity, J/m³/°C - _WC_W water heat capacity, J/m³/°C - aquifer porosity, fraction     

Anisotropy in the Ironton and Galesville Sandstones Near a Thermal-Energy-Storage Well, St. Paul, Minnesota

The U.S. Geological Survey is studying the potential for storage of heated water in a sandstone aquifer in St. Paul, Minnesota. The efficiency of the aquifer to store thermal energy is related, in part, to the hydrogeologic characteristics of the aquifer. The movement of heat away from the injection well is directly related to the anisotropy. Aquifer tests were conducted to determine the anisotropy near the heated-water injection well. The maximum and minimum values of transmissivity along the principal directions of the hydraulic conductivity tensors of the Ironton and Galesville Sandstones in St. Paul, Minnesota are approximately 1,090 and 480 feet squared per day. The storage coefficient is 4.5 × 10⁻⁵. These values represent the average of four determinations of nonsteady flow to a well in an idealized infinite anisotropic aquifer. Analysis of the values of transmissivity and storage coefficient for hypothetical changes in location of two of the monitoring wells where depth-deviation surveys were not available indicates that computed transmissivities vary less than 5 percent and storage coefficients vary less than ±6 percent.     

The response of water level in the YuZ-5 well, Kamchatka to the magnitude 9.3, Sumatra-Andaman earthquake of December 26, 2004

Forced and free oscillations of water level were recorded in the YuZ-5 well, Kamchatka due to the passage of seismic waves from the Sumatra-Andaman earthquake of December 26, 2004, M _w = 9.3, hypocentral distance 8250 km. The greatest amplitude of water level oscillations, at least 5 cm, was observed during the onset of seismic surface waves with a typical period of 20–50 s. The total duration of the forced and free water level oscillations was about ten hours. The available theoretical models that describe oscillations of water level in a well due to seismic waves and rapid injection of water were used to estimate the transmissivity of the aquifer. The values obtained exceed by at least two orders of magnitude the transmissivity derived from pumping test measurements. A hypothesis was proposed to explain the temporary increase in aquifer transmissivity during the passage of seismic waves by invoking disturbances in the structure of the crack-pore space and a sharp increase in aquifer rock permeability.     

Groundwater flow through a Miliolite limestone aquifer

Abstract

This paper describes a study of groundwater flow in a coastal Miliolite limestone aquifer in western India. An examination of field information suggested that the transmissivity of the aquifer varies significantly between high and low groundwater heads. Pumping tests indicate that this is due to the development of major fissures in the upper part of the aquifer. A regional groundwater model with varying transmissivities is used to represent the field behaviour. The model is also used to examine the effect of artificial recharge on the alleviation of saline intrusion problems in the coastal area.     

Compositional effect on the pressure derivatives of bulk modulus of silicate melts

Although the bulk moduli (K_T0) of silicate melts have a relatively narrow range of values, the pressure derivatives of the isothermal bulk modulus (K_T0^′) can assume a broad range of values and have an important influence on the compositional dependence of the melt compressibility at high pressure. Based on the melt density data from sink/float experiments at high pressures in the literature, we calculate K_T0^′ using an isothermal equation of state (EOS) (e.g., Birch–Murnaghan EOS and Vinet EOS) with the previously determined values of room-pressure density (ρ₀) and room-pressure bulk modulus (K_T0). The results show that best estimates of K_T0^′ vary considerably from ~ 3 to ~ 7 for different compositions. K_T0^′ is nearly independent of Mg # (molar Mg/(Mg + Fe)), but decreases with SiO₂ content. Hydrous melts have anomalously small K_T0^′ leading to a high degree of compression at high pressures. For anhydrous melts, K_T0^′ is ~ 7 for peridotitic melts, ~ 6 for picritic melts, ~ 5 for komatiitic melts, and ~ 4 for basaltic melts.     

Radial groundwater flow to a finite diameter well in a leaky confined aquifer with a finite‐thickness skin

A mathematical model that describes the drawdown due to constant pumpage from a finite radius well in a two‐zone leaky confined aquifer system is presented. The aquifer system is overlain by an aquitard and underlain by an impermeable formation. A skin zone of constant thickness exists around the wellbore. A general solution to a two‐zone leaky confined aquifer system in Laplace domain is developed and inverted numerically to the time‐domain solution using the modified Crump (1976) algorithm. The results show that the drawdown distribution is significantly influenced by the properties and thickness of the skin zone and aquitard. The sensitivity analyses of parameters of the aquifer and aquitard are performed to illustrate their effects on drawdowns in a two‐zone leaky confined aquifer system. For the negative‐skin case, the drawdown is very sensitive to the relative change in the formation transmissivity. For the positive‐skin case, the drawdown is also sensitive to the relative changes in the skin thickness, and both the skin and formation transmissivities over the entire pumping period and the well radius and formation storage coefficient at early pumping time. Copyright © 2009 John Wiley & Sons, Ltd.     

The Effect of Undetected Barriers on Groundwater Drawdown and Recovery

In large-scale pumping projects, such as mine dewatering, predictions are often made about the rate of groundwater level recovery after pumping has ceased. However, these predictions may be impacted by geological uncertainty—including the presence of undetected impermeable barriers. During pumping, an impermeable barrier may be undetected if it is located beyond the maximum extent of the cone of depression; yet it may still control drawdown during the recovery phase. This has implications for regional-scale modeling and monitoring of groundwater level recovery. In this article, non-dimensional solutions are developed to show the conditions under which a barrier may be undetected during pumping but still significantly impact groundwater level recovery. The magnitude of the impact from an undetected barrier will increase as the ratio of pumping rate to aquifer transmissivity increases. The results are exemplified for a hypothetical aquifer with an unknown barrier 3 km from a pumping well. The difference in drawdown between a model with and without a barrier may be <1 m in the 10 years while pumping is occurring, but up to 50 m after pumping has ceased.