Evaluation of groundwater withdrawal from a mountain watershed, Colorado, USA

The purpose of this study is to evaluate the groundwater-withdrawal potential of the Fraser River watershed, a mountainous drainage system in north-central Colorado. Laboratory tests, field investigations, and numerical modeling are conducted to present a quantitative understanding of the watershed’s groundwater-flow system. Aquifer hydraulic conductivity values obtained from aquifer tests range from 1E?5 to 1E?3 m/s. Groundwater withdrawal is concentrated in channel-fill deposits of the Troublesome Formation within the Fraser basin. A steady state groundwater-flow model of the Fraser River watershed is developed and calibrated using 24 observation wells in the Fraser River valley and estimated baseflow of the Fraser River. Modeling results suggest that surface recharge is the major source of groundwater in the watershed. Groundwater exits the watershed through evapotranspiration and discharge to rivers. Transient groundwater-flow modeling evaluates future withdrawal scenarios using the hydraulic head distribution from the steady state model as the initial condition. Drawdown within Troublesome Formation aquifers from the current pumping schedule approaches 2 m. When the daily pumping rate is doubled, drawdown approaches 4 m. The radius of influence is hundreds of meters to 1 km. Pumping wells withdraw approximately 2 and 15 % of groundwater flowing through the well field for hydraulic conductivity of 1E?3 and 1E?5 m/s, respectively. This study suggests that the groundwater system at the Fraser Valley could sustain current and future withdrawals, given that the current recharge condition is maintained.     

Impact of spate irrigation of flood waters on agricultural drought and groundwater recharge: case of Sidi Bouzid plain,Central Tunisia

In Sidi Bouzid plain, rainfall alone is insufficient to satisfy crop water requirements. Within this framework, and in order to improve water resources in the region, the Tunisian State adopted non-conventional water mobilization techniques, among which artificial spate irrigation. The objective of the study is to evaluate the impact of spate irrigation of flood water on the mitigation of agricultural drought and the enhancement of groundwater recharge. Annual and monthly rainfall data as well as flood water volumes were monitored. The study focused on the groundwater drawdown monitoring. Results showed a high flood water contribution to crop water requirements that exceeded rainfall. This water prevented drought in the spate perimeters. The groundwater drawdown was found to fluctuate over time, with an average decreasing rate of 0.4 to 0.5 m/year. Groundwater recharge was found to be highly correlated with flood water contribution through spate irrigation (R ² = 84 %). Out of the spate zone, a high decrease in the groundwater level was noted. The lowest rate of 1 m/year was that of the farthest piezometer from the spate perimeters. This is influenced by the excessive pumping out of the spate zone. In 1980, groundwater flew from the west to the east. In 2015, the flow movement from the east to the center of the plain did not change due to the presence of the spate perimeters. Nevertheless, excessive pumping around sabkhas changed the flow directions at the outlet zone. A variation in groundwater salinity was observed in both space and time. In 1975, salinity was very low. The outlet zone was the most affected where the drawdown reached several meters, causing saltwater intrusion from the surrounding sabkhas.     

冲洪积平原渗流和管流耦合的辐射井结构

利用新疆阿克苏台兰河流域冲洪积平原区非稳定流抽水试验资料,以辐射井为研究对象,结合辐射管内的水头损失及流态,建立粗颗粒潜水含水层渗流和水平管流耦合的地下水流数值模型。利用数值模型,分析在粗颗粒含水层中辐射管不同根数、不同长度、等效渗透系数、辐射井的井径以及不同含水层的渗透系数、不同降深对辐射井出水量的影响,并且根据各参数的相互关系,提出冲洪积平原辐射井的出水量的经验公式。为优化设计辐射井结构及辐射井布置提供依据,对台兰河地下水库的建设及后期运行管理提供了技术支撑。     

Hydraulic analysis of a radial collector well for riverbank filtration near Nakdong River, South Korea

A radial collector well is used for the extraction of a large amount of groundwater without causing a deep drawdown at the well??s center, and it is appropriate for the supply of municipal water through riverbank filtration (RBF). Flow path changes caused by water extraction through a radial collector well were simulated to estimate the amount of river water induction at a RBF site associated with Nakdong River in South Korea. The structure of the screened horizontal arms of a radial collector well was examined with respect to effective riverbank filtration. The relative ratio of the river water induced to the radial collector well compared to the total groundwater extraction was estimated to be 27?C52%. The amount of induced river water varies with the distance of a horizontal arm from the river, indicating that the location and structure of the collector well is significant for RBF. In all simulation cases, the maximum drawdown of the groundwater level near the collector well was 2.1?m, which is not significant considering the substantial pumping rate at the study site. It was concluded that RBF radial collector wells can be used at the study site for a sustainable water supply.     

Stochastic groundwater modeling of a sedimentary aquifer: evaluation of the impacts of abstraction scenarios under conditions of reduced recharge

A transient finite difference groundwater flow model has been calibrated for the Nasia sub-catchment of the White Volta Basin. This model has been validated through a stochastic parameter randomization process and used to evaluate the impacts of groundwater abstraction scenarios on resource sustainability in the basin. A total of 1500 equally likely model realizations of the same terrain based on 1500 equally likely combinations of the data of the key aquifer input parameters were calibrated and used for the scenario analysis. This was done to evaluate model non-uniqueness arising from uncertainties in the key aquifer parameters especially hydraulic conductivity and recharge by comparing the realizations and statistically determining the degree to which they differ from each other. Parameter standard deviations, computed from the calibrated data of the key parameters of hydraulic conductivity and recharge, were used as a yardstick for evaluating model non-uniqueness. All model realizations suggest horizontal hydraulic conductivity estimates in the range of 0.03–78.4 m/day, although over 70 % of the area has values in the range of 0.03–14 m/day. Low standard deviations of the horizontal hydraulic conductivity estimates from the 1500 solutions suggest that this range adequately reflects the properties of the material in the terrain. Lateral groundwater inflows and outflows appear to constitute significant components of the groundwater budgets in the terrain, although estimated direct vertical recharge from precipitation amounts to about 7 % of annual precipitation. High potential for groundwater development has been suggested in the simulations, corroborating earlier estimates of groundwater recharge. Simulation of groundwater abstraction scenarios suggests that the domain can sustain abstraction rates of up to 200 % of the current estimated abstraction rates of 12,960 m³/day under the current recharge rates. Decreasing groundwater recharge by 10 % over a 20-year period will not significantly alter the results of this abstraction scenario. However, increasing abstraction rates by 300 % over the period with decreasing recharge by 10 % will lead to drastic drawdowns in the hydraulic head over the entire terrain by up to 6 m and could cause reversals of flow in most parts of the terrain.     

Quantitative assessment of the impact of an inter-basin surface-water transfer project on the groundwater flow and groundwater-dependent eco-environment in an oasis in arid northwestern China

Inter-basin water transfer projects (IBWTPs) can involve basins as water donors and water receivers. In contrast to most studies on IBWTPs, which mainly impact the surface-water eco-environment, this study focuses on the impacts of an IBWTP on groundwater and its eco-environment in a water donor basin in an arid area, where surface water and groundwater are exchanged. Surface water is assumed to recharge groundwater and a groundwater numerical simulation model was constructed using MODFLOW. The model was used to quantitatively evaluate the impact of an IBWTP located in the upstream portion of Nalenggele River (the biggest river in the Qaidam basin, Northwest China). The impact involved decrease in spring flow, drawdown of groundwater, reduction in oasis area, and an increase in species replacement of oasis vegetation in the midstream and downstream of the river. Results show that the emergence sites of springs at the front of the oasis will move 2–5 km downstream, and the outflow of springs will decrease by 42 million m³/a. The maximum drawdown of groundwater level at the front of the oasis will be 3.6 m and the area across which groundwater drawdown exceeds 2.0 m will be about 59.02 km², accounting for 2.71% of the total area of the oasis. Under such conditions, reeds will gradually be replaced by Tamarix, shrubs, and other alternative plant species. These findings have important implications for the optimization of water resource allocation and protection of the eco-environment in arid regions.     

Groundwater mixing in a sand-island freshwater lens: density-dependent flow and stratigraphic controls

This paper focuses on a small back-barrier sand-island on the southeast coast of Queensland. The freshwater lens in the study area exhibits anomalously high short-range salinity gradients at shallow depths, which cannot be explained using a standard seawater intrusion model. The island groundwater system consists of two aquifers: a semiconfined aquifer hosting saline to hypersaline groundwater and an overlying unconfined freshwater aquifer. The deeper aquifer is semiconfined within an incised paleovalley, and groundwater flow is restricted to an east – west direction. Tidal response observations show that the tidal signal propagates far more rapidly and is of much higher magnitude in the semiconfined aquifer than the unconfined aquifer. The tidal wave-pulse amplitude is also subject to greater attenuation in the unconfined aquifer. A conceptual hydrogeological model illustrates how upwelling of hypersaline groundwater, induced by density-dependent flow and tidal pumping, has contaminated the shallow groundwater resource. Salinisation at shallow depths is restricted to an area proximal to the paleovalley aquifer. The spatial distribution of lithological heterogeneity is an initial limiting control on the movement of the upwelling saline plume. The extent of shallow groundwater contamination is also limited by the presence of a baroclinic field, resulting from lateral variations in fluid density. Hydrochemical signatures have been used to support the model hypothesis and link the salinisation of fresh groundwater with the semiconfined aquifer as opposed to the surrounding estuarine surface water. The geometry and thickness of the freshwater lens are further controlled by the presence of the largely impermeable bedrock paleosurface between 9 and 12 m depth. The combination of hypersaline groundwater and hydraulically restrictive lithology at shallow depths has produced excessive thinning of the freshwater lens, demonstrating that the application of a model such as the Dupuit – Ghyben – Herzberg relationship would grossly overestimate the available groundwater resource.     

Reassessing the management of groundwater use from sandy aquifers: acidification and base cation depletion exacerbated by drought and groundwater withdrawal on the Gnangara Mound, Western Australia

The combined effects of low rainfall, groundwater withdrawal in excess of 300 GL/year and reduced recharge in areas covered by pine plantations has caused the water table in a sandy unconfined aquifer on the Gnangara Mound in Western Australia to drop by up to 5 m and aquifer storage to decline by about 500 GL over the last 20 years. Groundwater has become acidic in areas of high drawdown, with pH values typically being less than 5.0 at the water table, and elevated concentrations of SO₄ ^2?, Al, Fe, Zn, Cu, Ni and Pb. Trends of increasing acidity and base cation concentrations in deep water supply wells in the Mirrabooka wellfield indicate that about 0.7 keq/ha/year of base cations are being leached from soil within cones of depression of pumping wells. These results indicate that the assessment of the sustainable yields of aquifers under conditions of low rainfall needs to consider geochemical interactions between groundwater, aquifer sediments, soils and vegetation, and not be just based on aquifer hydraulics and water-balance changes.     

An approach to interpretation of step drawdown tests

To understand the behaviour of drawdown with discharge under site-specific conditions, a step drawdown test (SDT) was conducted on a tubewell in alluvium near Delhi, India, and the data were analyzed to find the value of well efficiency. The entrance velocity of groundwater into the well screen was computed to see if it exceeded the safety limit of 0.03 m/s. Reynold's number (Re) was also calculated to study the nature of flow at the well screen. The decrease in efficiency of the well at higher discharge was attributed to an increase in turbulence and curvature of the flow path of water. An alternative, more efficient approach has been put forward, using a spreadsheet programme to fit a polynomial trend line on a plot of drawdown versus discharge and deriving a polynomial trend line equation. This equation predicts the behaviour of drawdown with discharge under site-specific conditions. The calculated efficiency of the tubewell can, at best, be regarded as a reflection of head loss on account of the laminar flow from the aquifer.     

How appropriate is the Thiem equation for describing groundwater flow to actual wells?

The Thiem equation of radial groundwater flow to a well is more than 100 years old and is still commonly used. Here, deviations caused by some of its simplifications are quantified by comparing the analytical to a numerical model that allows the implementation of more complex geometries. The assumption of horizontal flow in the Thiem equation, which necessitates uniform inflow over the entire screen length of the fully penetrating well, was found to cause deviations from actual pumping wells where the pump is placed above the screen, resulting in non-uniform inflow and additional drawdown. The same applies to partially penetrating wells, where inflow peaks and additional drawdown occur, especially when the well is screened in the lower part of the aquifer. The use of the Thiem equation in the near-field of a well should thus be restricted to situations where the screen inflow is relatively uniformly distributed, e.g. when it covers large portions of the aquifer thickness. The presence of a gravel pack and a background gradient, on the other hand, are of limited importance.     

Modelling the response of an alluvial aquifer to anthropogenic and recharge stresses in the United States Southern Great Plains

This paper uses Visual MODFLOW to simulate potential impacts of anthropogenic pumping and recharge variability on an alluvial aquifer in semi-arid northwestern Oklahoma. Groundwater withdrawal from the aquifer is projected to increase by more than 50% (relative to 1990) by the year 2050. In contrast, climate projections indicate declining regional precipitation over the next several decades, creating a potential problem of demand and supply. The following scenarios were simulated: (1) projected groundwater withdrawal, (2) a severe drought, (3) a prolonged wet period, and (4) a human adjustment scenario, which assumes future improvements in water conservation measures. Results indicate that the combined impacts of anthropogenic pumping and droughts would create drawdown of greater than 12 m in the aquifer. Spatially, however, areas of severe drawdown will be localized around large-capacity well clusters. The worst impacts of both pumping and droughts will be on stream–aquifer interaction. For example, the projected aquifer pumpage would lead to a total streamflow loss of 40%, creating losing stream system regionally. Similarly, a severe drought would lead to a total streamflow loss of >80%. A post-audit of the model was also carried out to evaluate model performance. By simulating various stress scenarios on the alluvial aquifer, this study provides important information for evaluating management options for alluvial aquifers.     

Evaluation of unconfined aquifer parameters from flow to partially penetrating wells in Tailan River basin, China

Effective evaluation, management and abstraction of groundwater resources of any aquifer require accurate and reliable estimates of its hydraulic parameters. This study, therefore, looks at the determination of hydraulic parameters of an unconfined aquifer using both analytical and numerical approaches. A long-duration pumping test data obtained from an unconfined aquifer system within the Tailan River basin in Xinjiang Autonomous Region in the northwest of China is used, in this study, to investigate the best method for estimating the parameters of the aquifer. The pumping test was conducted by pumping from a radial collector well and measuring the response in nine observation wells; all the wells used in the test were partially penetrating. Using two well-known tools, namely AquiferTest and MODFLOW, as an aid for the analytical and numerical approaches, respectively, the parameters of the aquifer were determined and their outputs compared. The estimated horizontal hydraulic conductivity, vertical hydraulic conductivity, and specific yield for the analytical approach are 38.1–50.30 m/day, 3.02–9.05 m/day and 0.204–0.339, respectively, while the corresponding numerical estimates are 20.50–35.24 m/day, 0.10–3.40 m/day, and 0.27–0.31, respectively. Comparing the two, the numerical estimates were found to be more representative of the aquifer in the study area since it simulated the groundwater flow conditions of the pumping test in the aquifer system better than the analytical solution.     

Three-dimensional groundwater flow modeling approach for the groundwater management options for the Dakhla oasis,Western Desert,Egypt

In Dakhla oasis, Western Desert of Egypt, groundwater is the only resource for all anthropogenic activities. During the last 50 years, the Nubian Sandstone Aquifer System (NSAS) has been undergoing serious stress through withdrawing its storage. Plans for expanding the agricultural areas in Dakhla oasis were given by the government. This article is an attempt to investigate the best management option that meets development ambitions and groundwater availability. Based on a calibrated regional three-dimensional groundwater flow model for the NSAS using FEFLOW, a refined (high resolution) local scale model was developed to simulate and predict the impact of applying the actual and planned extractions rates on Dakhla oasis. Five management scenarios were suggested. The application of the actual extraction rate of 1.2 × 10⁶ m³/day for the oasis for the next 90 years resulted in a drawdown of 75 m and a depth to groundwater up to 75 m with an annual change in hydraulic head of 0.57 m. At the end of this simulation, only a few wells at the west of the oasis will still be free flowing. The application of the planned extraction rate (1.7 × 10⁶ m³/day) resulted in great depths to groundwater (>100 m) and formed huge cones of depressions that connected together to cover the whole oasis and extend further beyond its borders. It was found that the best option for groundwater management in the oasis is the implementation of an extraction rate of 1.46 × 10⁶ m³/day, as the depths to groundwater will never exceed the 100 m limit.     

Modeling of groundwater flow for Mujib aquifer, Jordan

Jordan is an arid country with very limited water resources. Groundwater is the main source for its water supply. Mujib aquifer is located in the central part of Jordan and is a major source of drinking water for Amman, Madaba and Karak cities. High abstraction rates from Mujib aquifer during the previous years lead to a major decline in water levels and deterioration in groundwater quality. Therefore, proper groundwater management of Mujib aquifer is necessary; and groundwater flow modeling is essential for proper management. For this purpose, Modflow was used to build a groundwater flow model to simulate the behavior of the flow system under different stresses. The model was calibrated for steady state condition by matching observed and simulated initial head counter lines. Drawdown data for the period 1985–1995 were used to calibrate the transient model by matching simulated drawdown with the observed one. Then, the transient model was validated by using drawdown data for the period 1996–2002. The results of the calibrated model showed that the horizontal hydraulic conductivity of the B2/A7 aquifer ranges between 0.001 and 40m/d. Calibrated specific yield ranges from 0.0001 to 0.15. The water balance for the steady state condition of Mujib aquifer indicated that the total annual direct recharge is 20.4 × 10⁶m³, the total annual inflow is 13.0 × 10⁶ m³, springs discharge is 15.3 × 10⁶ m³, and total annual outflow is 18.7 × 10⁶ m³. Different scenarios were considered to predict aquifer system response under different conditions. The results of the sensitivity analysis show that the model is highly sensitive to horizontal hydraulic conductivity and anisotropy and with lower level to the recharge rates. Also the model is sensitive to specific yield     

Hydrogeophysical approach for contamination assessment in NamSon landfill,Hanoi, Vietnam

Self potential (SP) and electrical resistivity tomography (ERT) methods are used together with the results of groundwater samples hydrogeochemical analysis to assess the impact of the water leak from the landfill garbage site at NamSon located in Northern Hanoi on causing pollution to the surrounding environment and affecting geological structure. Selected survey area covers an area of 180 × 300 m lying in the low land of the NamSon site with a slope ranging about 8 m in direction NW–SE. There are three geophysical measurements lines denoted as T1, T2 and T3. Processing 180 SP data points has allowed to draw maps of equipotential epoch in the two periods in 2015 and 2016. The maps show four zones of SP positive anomalies with maximum amplitudes of about +20 mV where the groundwater flow direction is downward and five zones of SP negative anomalies with minimum values in a range from ?180 to ?260 mV where the groundwater flow direction is upward. Resistivity values of the subsurface layers of soils and rocks have been aquired from 2D inverse model for measuring ERT in March 2015 and March 2016. The results of the ERT allowed to define the low resistivity in the range 15–20 Ωm related to leachate plume from NamSon landfill site. Results of the physico-chemical analysis of groundwater samples from the existing six boreholes show increases in concentration of the measured pollutant parameters indicating contamination of the groundwater as a result of solid waste leachate accumulation. This result is affirmative evidence for the survey results by geophysical technique. The rapid decrease in quality of groundwater over the last year is probably due to the influence of the leachate from the NamSon landfill site.     

Temperature-driven groundwater convection in cold climates

The aim was to study density-driven groundwater flow and analyse groundwater mixing because of seasonal changes in groundwater temperature. Here, density-driven convection in groundwater was studied by numerical simulations in a subarctic climate, i.e. where the water temperature was <4 °C. The effects of soil permeability and groundwater temperature (i.e. viscosity and density) were determined. The influence of impermeable obstacles in otherwise homogeneous ground was also studied. An initial disturbance in the form of a horizontal groundwater flow was necessary to start the convection. Transient solutions describe the development of convective cells in the groundwater and it took 22 days before fully developed convection patterns were formed. The thermal convection reached a maximum depth of 1.0 m in soil of low permeability (2.71 · 10^?9 m²). At groundwater temperature close to its density maximum (4 °C), the physical size (in m) of the convection cells was reduced. Small stones or frost lenses in the ground slightly affect the convective flow, while larger obstacles change the size and shape of the convection cells. Performed simulations show that “seasonal groundwater turnover” occurs. This knowledge may be useful in the prevention of nutrient leakage to underlying groundwater from soils, especially in agricultural areas where no natural vertical groundwater flow is evident. An application in northern Sweden is discussed.     

Study of geothermal water intrusion due to groundwater exploitation in the Puebla Valley aquifer system, Mexico

Significant intrusion of geothermal water into fresh groundwater takes place in the Puebla Valley aquifer system, Mexico. The decline in the potentiometric surface due to the overexploitation of the groundwater induces this intrusion. This hydrological system comprises three aquifers located in Plio-Quaternary volcanic sediments and Mesozoic calcareous rocks. The hydraulic balance of the aquifer shows that the annual output exceeds the natural inputs by 12 million m³. Between 1973 and 2002, a drop in the potentiometric surface, with an 80 m cone of depression, was identified in a 5-km-wide area located southwest of the city of Puebla. Chemical analyses performed on water samples since 1990 have shown an increase in total dissolved solids (TDS) of more than 500 mg/L, coinciding with the region showing a cone of depression in the potentiometric surface. A three-dimensional flow and transport model, based on the hydrogeological and geophysical studies, was computed by using the MODFLOW and MT3D software. This model reproduces the evolution of the aquifer system during the last 30 years and predicts for 2010 an additional drawdown in the potentiometric surface of 15 m, and an increase in the geothermal water intrusion.     

Potential contaminant transport in the regional Carbonate Aquifer beneath Yucca Mountain, Nevada, USA

Yucca Mountain, Nevada is the site of the proposed US geologic repository for spent nuclear fuel and high-level radioactive waste. The repository is to be a mine, sited approximately 300 m below the crest of the mountain, in a sequence of variably welded and fractured mid-Miocene rhylolite tuffs, in the unsaturated zone, approximately 300 m above the water table. Beneath the proposed repository, at a depth of 2 km, is a thick sequence of Paleozoic carbonate rocks that contain the highly transmissive Lower Carbonate Aquifer. In the area of Yucca Mountain the Carbonate Aquifer integrates groundwater flow from north of the mountain, through the Amargosa Valley, through the Funeral Mountains to Furnace Creek in Death Valley, California where the groundwater discharges in a set of large springs. Data that describe the Carbonate Aquifer suggest a concept for flow through the aquifer, and based upon the conceptual model, a one-layer numerical model was constructed to simulate groundwater flow in the Carbonate Aquifer. Advective transport analyses suggest that the predicted travel time of a particle from Yucca Mountain to Death Valley through the Carbonate Aquifer might be as short as 100 years to as long 2,000 years, depending upon the porosity.     

变异条件下内蒙古呼包平原地下水演化趋势

重点探讨气候变异对内蒙古呼包平原地下水资源、地下水流场和动态的影响。在介绍呼包平原水文地质条件的基础上,运用地下水模型软件PMWIN 5.1建立了研究区双层地下水流模型,并根据1998年地下水动态观测和统测资料对模型进行识别。通过对近51 a降水量的分析,确定将连续出现的2个特枯年作为地下水的变异条件,运用地下水模型对变异条件下地下水状态进行模拟,结果表明：2年间对地下水的严重超采,使地下水亏空量达75 296.34 万m³,潜水和承压含水层的地下水位大幅度下降,潜水位最大下降4 m左右,承压水位最大下降17 m左右;漏斗中心主要集中在开采量大的呼和浩特和包头市区。     

Non-Darcian flow toward a larger-diameter partially penetrating well in a confined aquifer

In this study, non-Darcian flow to a larger-diameter partially penetrating well in a confined aquifer was investigated. The flow in the horizontal direction was assumed to be non-Darcian and described by the Izbash equation, and the flow in the vertical direction was assumed to be Darcian. A linearization procedure was used to approximate the nonlinear governing equation. The Laplace transform associated with the finite cosine Fourier transform was used to solve such non-Darcian flow model. Both the drawdowns inside the well and in the aquifer were analyzed under different conditions. The results indicated that the drawdowns inside the well were generally the same at early times under different conditions, and the features of the drawdowns inside the well at late times were similar to those of the drawdowns in the aquifer. The drawdown in the aquifer for the non-Darcian flow case was larger at early times and smaller at late times than their counterparts of Darcian flow case. The drawdowns for a partially penetrating well were the same as those of a fully penetrating well at early times, and were larger than those for a fully penetrating well at late times. A longer well screen resulted in a smaller drawdown in the aquifer at late times. A larger power index n in the Izbash equation resulted in a larger drawdown in the aquifer at early times and led to a smaller drawdown in the aquifer at late times. A larger well radius led to a smaller drawdown at early times, but it had little impact on the drawdown at late times. The wellbore storage effect disappears earlier when n is larger.