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1.
This study investigated non‐Darcian flow to a well in a leaky aquifer considering wellbore storage and a finite‐thickness skin. The non‐Darcian flow is described by the Izbash equation. We have used a linearization procedure associated with the Laplace transform to solve such a non‐Darcian flow model. Besides, the Stehfest method has been used to invert the Laplace domain solutions for the drawdowns. We further analyzed the drawdowns inside the well for different cases. The results indicated that a smaller BD results in a smaller drawdown at late times and the leakage has little effect on the drawdown inside the well at early times, where BD is a dimensionless parameter reflecting the leakage. We have also found that the flow for the negative skin case approaches the steady‐state earlier than that for the positive skin. In addition, the drawdown inside the well with a positive skin is larger than that without skin effect at late times, and a larger thickness of the skin results in a greater drawdown inside the well at late times for the positive skin case. A reverse result has been found for the negative skin case. Finally, we have developed a finite‐difference solution for such a non‐Darcian flow model and compared the numerical solution with the approximate analytical solution. It has been shown that the linearization procedure works very well for such a non‐Darcian flow model at late times, and it underestimates the drawdowns at early times. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

2.
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.  相似文献   

3.
Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin was investigated. The Izbash equation is used to describe the non-Darcian flow in the horizontal direction, and the vertical flow is described as Darcian. The solution for the newly developed non-Darcian flow model can be obtained by applying the linearization procedure in conjunction with the Laplace transform and the finite Fourier cosine transform. The flow model combines the effects of the non-Darcian flow, partial penetration of the well, and the finite thickness of the well skin. The results show that the depression cone spread is larger for the Darcian flow than for the non-Darcian flow. The drawdowns within the skin zone for a fully penetrating well are smaller than those for the partially penetrating well. The skin type and skin thickness have great impact on the drawdown in the skin zone, while they have little influence on drawdown in the formation zone. The sensitivity analysis indicates that the drawdown in the formation zone is sensitive to the power index (n), the length of well screen (w), the apparent radial hydraulic conductivity of the formation zone (K r2), and the specific storage of the formation zone (S s2) at early times, and it is very sensitive to the parameters n, w and K r2 at late times, especially to n, while it is not sensitive to the skin thickness (r s).  相似文献   

4.
文章  刘凯  陈晓恋 《地球科学》2015,40(5):918-924
抽水井附近由于流速过快往往发生非达西流,而远离抽水井随着流速下降又变为达西流.为了描述这些特征,建立了承压含水层中非完整井附近“非达西-达西”两区渗流模型,即距离抽水井较近的区域由于流速较快假设发生非达西渗流,并利用Izbash公式刻画,而距离抽水井较远由于流速较慢假设仍然满足达西定律,含水层中垂向流速较小也利用达西定律描述.通过线性化近似方法结合Laplace变换和有限Fourier余弦变换对模型进行了求解,分析探讨了该两区模型下水位降深曲线特征.结果表明:抽水初期,非达西渗流区域水位降深与全非达西渗流模型结果吻合,而抽水后期两区模型非达西渗流区域的水位降深与全达西模型水位降深基本一致,但大于全非达西渗流模型的水位降深;抽水初期,两区模型中达西渗流区域的水位降深比全达西渗流模型结果大,但比全非达西渗流模型结果小;对不同时间的水位降深随井距变化曲线分析发现非达西渗流区域水位降深随Izbash公式中的幂指数n增大而减小,而在达西渗流区域水位降深基本不受n值的影响.研究成果对非完整井抽水试验参数反演具有重要理论意义.   相似文献   

5.
This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries. The mathematical modelling for the pumping-induced flow in aquifers with different boundaries is developed by employing image-well theory with the superposition principle, of which the non-Darcian effect is characterized by Izbash’s equation. The solutions are derived by Boltzmann and dimensionless transformations. Then, the non-Darcian effect and wellbore storage are especially investigated according to the proposed solution. The results show that the aquifer boundaries have non-negligible effects on pumping, and ignoring the wellbore storage can lead to an over-estimation of the drawdown in the first 10 minutes of pumping. The higher the degree of non-Darcian, the smaller the drawdown.  相似文献   

6.
A numerical analysis of non-Darcian flow to a pumping well in a confined aquifer using the strong-form mesh-free (MFREE) method is described. This technique is targeted at problems that use advanced numerical approaches for modeling non-Darcian flow and it supports the assumption that the non-Darcian flow follows the Forchheimer equation. Interpolation functions including the multi-quadrics (MQ) basis function (containing shape factors q and α) and the Gaussian (EXP) basis function (with shape factor ω) were found to be important defining parameters which had significant influence on the numerical results. A series of numerical experiments revealed that when q?=?2 and α?=?0.1, the mesh-free method yielded good results and the range of 10?6?–?10?3 might be a good choice for the shape factor ω in the EXP basis function. A comparison between the strong-form MFREE method and the finite difference method was done; the results showed that the strong-form MFREE method was very effective for solving non-Darcian flow near a pumping well in a confined aquifer, and was favorable over the finite-difference method, which could undergo oscillation and converging problems at early times.  相似文献   

7.
为了分析水层越流补给对煤层气井早期排水的影响,根据不稳定渗流理论,引入越流系数,建立了考虑层间越流现象的煤层中水的渗流数学模型。通过Laplace变换对模型求解,并利用Stehfest反演得到实空间的解,采用新的参数组合,分别绘制了压力和压力导数双对数曲线图版。从物理渗流机理上分析了层间越流对曲线形态的影响,随着越流系数的增大,径向流结束的时间越早;同时提出了利用典型图版拟合确定储层渗透率、表皮系数以及越流系数的方法。典型图版有助于定量评价越流的强弱,对煤层气井后续排采制度的调整具有指导意义。   相似文献   

8.
A mathematical model describing the constant pumping is developed for a partially penetrating well in a heterogeneous aquifer system. The Laplace‐domain solution for the model is derived by applying the Laplace transforms with respect to time and the finite Fourier cosine transforms with respect to vertical co‐ordinates. This solution is used to produce the curves of dimensionless drawdown versus dimensionless time to investigate the influences of the patch zone and well partial penetration on the drawdown distributions. The results show that the dimensionless drawdown depends on the hydraulic properties of the patch and formation zones. The effect of a partially penetrating well on the drawdown with a negative patch zone is larger than that with a positive patch zone. For a single‐zone aquifer case, neglecting the effect of a well radius will give significant error in estimating dimensionless drawdown, especially when dimensionless distance is small. The dimensionless drawdown curves for cases with and without considering the well radius approach the Hantush equation (Advances in Hydroscience. Academic Press: New York, 1964) at large time and/or large distance away from a test well. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

9.
A new analytical solution is developed for describing groundwater level fluctuations in a coupled leaky confined aquifer system which consists of an unconfined aquifer, confined aquifer, and an aquitard in between. The aquifer system has a tidal boundary at the seashore, a no flow boundary at remote inland side, and a confined aquifer extending under the sea and terminated with an outlet-capping. This new solution has shown to be a generalisation of most existing analytical solutions for a tidal aquifer system which includes single confined and leaky confined aquifers. In addition, the solution is used to explore the influences of the dimensionless leakance of the outlet-capping, the dimensionless hydraulic diffusivities, and the leakages of the inland and offshore aquitards on the head responses in the leaky confined aquifer.  相似文献   

10.
In this note, we examine the flow towards a well in a confined aquifer in the presence of an interaction force defined by the sum of three terms, namely, a Darcy term (linear in the velocity), a Forchheimer term (quadratic in the velocity), and an added‐mass term (linear in the acceleration). We obtain the exact dynamic solution for the piezometric head distribution around the well and investigate the relative importance of the non‐Darcian terms. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

11.
A new accurate numerical solution is presented for aquifer storage and recovery (ASR) systems in coastal aquifers; flow is approximated as radial Dupuit interface flow. The radial velocities of points on the interface are a function of time, the vertical coordinate, and the dimensionless parameter D (the discharge of the well divided by the product of the hydraulic conductivity, the square of the aquifer thickness, and the dimensionless density difference). The recovery efficiency of an ASR system (the ratio of the recovered volume of water divided by the injected volume of water) is determined by D and by the relative lengths of the injection, storage and recovery periods. Graphs are produced for the recovery efficiency as a function of parameter D for ASR operations with and without storage periods and for multiple cycles. The presented solutions and graphs are to be used as screening tools to assess the feasibility of specific injection, storage and recovery scenarios of planned ASR systems in saltwater aquifers without having to run complicated flow and transport models. When the screening tool indicates that recovery efficiencies are acceptable, the consideration of other features such as mixing and chemistry is warranted.  相似文献   

12.
A well-known analytical solution of Jacob (1950) for groundwater flow due to tidal-wave propagation, together with field measurements along a complete tidal cycle and geological data, were used to evaluate the heterogeneities in the hydraulic properties of a phreatic aquifer located next to the River Ajo in the coastal plain environment of the southern sector of the Samborombon Bay wetland, Argentina. From the analysis of water-table fluctuations in a set of monitoring wells located along a riverbank-normal transect, it was possible to quantify the piecewise spatial variations of the hydraulic diffusivity of the phreatic aquifer. The results show the strong lateral variations of the sedimentary environment due to the influence of the different transport and deposition agents that characterize the coastal plain. The known thickness of the phreatic aquifer and the estimated range of the specific yield allowed the hydraulic conductivity to be identified as the most influential factor. [Jacob CE (1950) Flow of ground water. In: Rouse H (ed) Engineering Hydraulics. Wiley, New York]  相似文献   

13.
用水位恢复数据反演越流承压含水层参数   总被引：1，自引：0，他引：1  
杨建民  郑刚 《岩土力学》2008,29(6):1602-1606
水文地质勘测中,由于水位恢复阶段没有人力和机械因素干扰,由测量数据可以画出平滑的曲线,更适宜于分析水文地质参数,但经典非稳定流Theis公式和Theis水位恢复法所依据的若干假设条件在实际中难以满足。针对越流承压含水层具有补给条件而很快稳定以及非稳定抽水阶段流量常“抖动”的特点,论证了利用稳定流量和Hantush-Jacob越流模型计算的可行性,并用扩展的卡尔曼滤波器反演水文地质参数,经文献中历史数据和实地抽水试验检验结果表明,由该方法反演的预测值和实测值吻合良好。  相似文献   

14.
指出承压含水层盖层的弯曲变形与开采井周围的径向地下水运动存在相互作用, 而这一效应在传统的井流理论中没有被认识到.通过引入弹性薄板理论, 建立了无越流的承压含水层井流-顶板弯曲效应的解析模型, 同时考虑了含水层和水的压缩性, 结果表明Theis井流方程给出的抽水降深偏小.在此基础上推导了有越流承压含水层井流-盖层弯曲效应的偏微分方程, 求出了解析解, 并与传统理论的结果进行了对比, 表明Hantush-Jacob公式计算的降深也是偏小的.在抽水井附近和抽水初期, 传统理论可能导致显著的相对误差.   相似文献   

15.
Among the risks of CO2 storage is the potential of CO2 leakage into overlaying formations and near-surface potable aquifers. Through a leakage, the CO2 can intrude into protected groundwater resources, which can lead to groundwater acidification followed by potential mobilisation of heavy metals and other trace metals through mineral dissolution or ion exchange processes. The prediction of pH buffer reactions in the formations overlaying a CO2 storage site is essential for assessing the impact of CO2 leakages in terms of trace metal mobilisation. For buffering the pH-value, calcite dissolution is one of the most important mechanisms. Although calcite dissolution has been studied for decades, experiments conducted under elevated CO2 partial pressures are rare. Here, the first study for column experiments is presented applying CO2 partial pressures from 6 to 43 bars and realising a near-natural flow regime. Geochemical calculations of calcite dissolution kinetics were conducted using PHREEQC together with different thermodynamic databases. Applying calcite surface areas, which were previously acquired by N2-BET or calculated based on grain diameters, respectively, to the rate laws according to Plummer et al. (Am J Sci 278:179–216, doi:10.2475/ajs.278.2.179, 1978) or Palandri and Kharaka (US Geol Surv Open file Rep 2004–1068:71, 2004) in the numerical simulations led to an overestimation of the calcite dissolution rate by up to three orders of magnitude compared to the results of the column experiments. Only reduction of the calcite surface area in the simulations as a fitting procedure allowed reproducing the experimental results. A reason may be that the diffusion boundary layer (DBL), which depends on the groundwater flow velocity and develops at the calcite grain surface separating it from the bulk of the solution, has to be regarded: The DBL leads to a decrease in the calcite dissolution rate under natural laminar flow conditions compared to turbulent mixing in traditional batch experiments. However, varying the rate constants by three orders of magnitudes in a field scale PHREEQC model simulating a CO2 leakage produced minor variations in the pH buffering through calcite dissolution. This justifies the use of equilibrium models when calculating the calcite dissolution in CO2 leakage scenarios for porous aquifers and slow or moderate groundwater flow velocities. However, the selection of the thermodynamic database has an impact on the dissolved calcium concentration, leading to an uncertainty in the simulation results. The resulting uncertainty, which applies also to the calculated propagation of an aquifer zone depleted in calcite through dissolution, seems negligible for shallow aquifers of approximately 60 m depth, but amounts to 35 % of the calcium concentration for aquifers at a depth of approximately 400 m.  相似文献   

16.
CO2 injection in saline aquifers induces temperature changes owing to processes such as Joule–Thomson cooling, endothermic water vaporization, exothermic CO2 dissolution besides the temperature discrepancy between injected and native fluids. CO2 leaking from the injection zone, in addition to initial temperature contrast due to the geothermal gradient, undergoes similar processes, causing temperature changes in the above zone. Numerical simulation tools were used to evaluate temperature changes associated with CO2 leakage from the storage aquifer to an above-zone monitoring interval and to assess the monitorability of CO2 leakage on the basis of temperature data. The impact of both CO2 and brine leakage on temperature response is considered for three cases (1) a leaky well co-located with the injection well, (2) a leaky well distant from the injector, and (3) a leaky fault. A sensitivity analysis was performed to determine key operational and reservoir parameters that control the temperature signal in the above zone. Throughout the analysis injection-zone parameters remain unchanged. Significant pressure drop upon leakage causes expansion of CO2 associated with Joule–Thomson cooling. However, brine may begin leaking before CO2 breakthrough at the leakage pathway, causing heating in the above zone. Thus, unlike the pressure which increases in response to both CO2 and brine leakage, the temperature signal may differentiate between the leaking fluids. In addition, the strength of the temperature signal correlates with leakage velocity unlike pressure signal whose strength depends on leakage rate. Increasing leakage conduit cross-sectional area increases leakage rate and thus increases pressure change in the above zone. However, it decreases leakage velocity, and therefore, reduces temperature cooling and signal. It is also shown that the leakage-induced temperature change covers a small area around the leakage pathway. Thus, temperature data will be most useful if collected along potential leaky wells and/or wells intersecting potential leaky faults.  相似文献   

17.
A modification is proposed of Torricelli’s (1608–1647) formula for the velocity of water discharging from a small hole at the bottom of a large tank filled with fractal solid material. The new formula takes proper account of the mechanical energy losses due to flow in the solid matrix, thus expanding the area of validity of the classical Torricelli’s formula. Moreover, it offers a convenient alternative to Darcy’s law for estimating the discharge rate from an aquifer. The new formula was derived from laboratory experiments, with a low-Reynolds number discharge flow (Darcian flow). It was tested in a natural karst aquifer where the flow is non-Darcian, at Almiros spring on the island of Crete (Greece). In both cases, the predictive capability of the modified formula is established.  相似文献   

18.
通过采用单位面积河流在单位水头差作用下的渗漏量来表征河流渗漏能力,建立渗流井取水理想模型,分别计算了在不同河流渗漏能力和含水层渗透性能条件下,竖井降深对渗流井出水量的影响。建立渗流井取水非稳定流模型,计算了在前期稳定竖井降深不同条件下,河流断流后渗流井出水量衰减过程及竖井降深发展过程。提出渗流井合理竖井降深应根据河流与地下水是否脱节以及含水层渗透性能,在岸边渗流井中部及一侧各布设一个观测孔,根据观测孔水位进行确定。对于含水层渗透性能较强地区,渗流井竖井降深应使得渗流井范围内地下水位与河流脱节,但高于辐射孔顶面;对于含水层渗透性能较差地区,渗流井竖井降深应使得侧部观测孔水位接近河床底面或刚出现脱节。  相似文献   

19.
Tracing fractures under glacial drift commonly involves costly and often unfeasible (in populated areas) geophysical methods or outcrop surveys, often far from the area of interest. A hypothesis is tested, that the specific capacity data for wells penetrating through glacial drift into a bedrock aquifer display two statistical populations: assuming uniform well construction, the wells with high specific capacity penetrate transmissive fracture zones, while those with low specific capacity encounter non-fractured rock characterized by primary porosity. The hypothesis was tested on 617 wells drilled into the Pennsylvanian Sharon Sandstone, Geauga County, Ohio (USA). Hydraulic conductivity, calculated using the Cooper and Jacob (1946) approximation to Theis’ non-equilibrium radial flow equation, followed quasi-log-normal distribution (geometric mean 9.88?×?10?6 m/s). The lower values presumably correspond to primary porosity, and higher values correspond to bedrock fracture zones. The higher hydraulic conductivity followed two distinct orientations (N34°E, N44°W), corresponding with the regional fracture pattern of the Allegheny Plateau. A variogram showed that the wells within a kilometer of each other correlate and that wells penetrating the thicker glacial blanket have lower hydraulic conductivity and larger drawdown. Cooper and Jacob (1946) A generalized graphical method for evaluating formation constants and summarizing well-field history, Am. Geoph. Union Trans. 27/4:526–534.  相似文献   

20.
An analytical solution is obtained for 2‐D steady Darcian flow under and through a cutoff wall partially obstructing a homogeneous isotropic foundation of a dam. The wall is leaky; that is, flow across it depends on the ratio of hydraulic conductivity of the wall and the wall thickness that results in the third‐type (Robin) boundary condition along the wall, as compared with the Terzaghi problem for an impermeable wall. The Laplace equation for the hydraulic head is meshlessly solved in a non‐standard flow tube. A Fredholm equation of the second kind is obtained for the intensity of leakage across the wall. The equation is tackled numerically, by adjusted successive iterations. Flow characteristics (total Darcian discharge and its components through the wall and the window between the wall top and horizontal bedrock, stream function, head distribution, and Darcian velocity along the wall and tailwater bed) are obtained for various conductivity ratios, head drops across the structure, thicknesses of the foundation, and the degree of its blockage by the wall. Comparisons with the Terzaghi limit of an impermeable wall show that for common wall materials and thicknesses, the leakage may constitute tens of percent of the discharge under the dam. The through‐flow hydraulic gradients on a vertical wall face (Robin's boundary condition) as well as the exit gradients along a horizontal tailwater boundary (Dirichlet's boundary condition) acting for decades have deleterious impacts on dam stability because of potential heaving, piping, and mechanical–chemical suffusion. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

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