scholarly journals Technical note: Analytical drawdown solution for steady-state pumping tests in two-dimensional isotropic heterogeneous aquifers

2016 ◽  
Vol 20 (5) ◽  
pp. 1655-1667 ◽  
Author(s):  
Alraune Zech ◽  
Sabine Attinger
Keyword(s):  
Steady State ◽  
Correlation Length ◽  
Heterogeneous Media ◽  
Radial Distance ◽  
Pumping Test ◽  
Two Dimensional ◽  
Aquifer Heterogeneity ◽  
Pumping Tests ◽  
Flow Solution ◽  
Ensemble Mean

Abstract. A new method is presented which allows interpreting steady-state pumping tests in heterogeneous isotropic transmissivity fields. In contrast to mean uniform flow, pumping test drawdowns in heterogeneous media cannot be described by a single effective or equivalent value of hydraulic transmissivity. An effective description of transmissivity is required, being a function of the radial distance to the well and including the parameters of log-transmissivity: mean, variance, and correlation length. Such a model is provided by the upscaling procedure radial coarse graining, which describes the transition of near-well to far-field transmissivity effectively. Based on this approach, an analytical solution for a steady-state pumping test drawdown is deduced. The so-called effective well flow solution is derived for two cases: the ensemble mean of pumping tests and the drawdown within an individual heterogeneous transmissivity field. The analytical form of the solution allows inversely estimating the parameters of aquifer heterogeneity. For comparison with the effective well flow solution, virtual pumping tests are performed and analysed for both cases, the ensemble mean drawdown and pumping tests at individual transmissivity fields. Interpretation of ensemble mean drawdowns showed proof of the upscaling method. The effective well flow solution reproduces the drawdown for two-dimensional pumping tests in heterogeneous media in contrast to Thiem's solution for homogeneous media. Multiple pumping tests conducted at different locations within an individual transmissivity field are analysed, making use of the effective well flow solution to show that all statistical parameters of aquifer heterogeneity can be inferred under field conditions. Thus, the presented method is a promising tool with which to estimate parameters of aquifer heterogeneity, in particular variance and horizontal correlation length of log-transmissivity fields from steady-state pumping test measurements.

scholarly journals Technical note: Analytical solution for the mean drawdown of steady state pumping tests in two-dimensional isotropic heterogeneous aquifers

2015 ◽  
Vol 12 (7) ◽  
pp. 6921-6944 ◽  
Author(s):  
A. Zech ◽  
S. Attinger
Keyword(s):  
Steady State ◽  
Analytical Solution ◽  
Correlation Length ◽  
Heterogeneous Media ◽  
Coarse Graining ◽  
Pumping Test ◽  
Two Dimensional ◽  
Aquifer Heterogeneity ◽  
Pumping Tests ◽  
Ensemble Mean

Abstract. A new method is presented which allows to interpret steady state pumping test in heterogeneous isotropic transmissivity fields. In contrast to mean uniform flow, the pumping test drawdowns in heterogeneous media cannot be described by a single effective or equivalent value of hydraulic transmissivity. A radially depending description of transmissivity is required, including the parameters of aquifer heterogeneity: mean, variance and correlation length. Such a model is provided by the upscaling procedure Radial Coarse Graining, which describes the transition of near well to far field transmissivity effectively. Based on the Radial Coarse Graining Transmissivity, an analytical solution for a steady state pumping test drawdown is derived. The so-called effective well flow solution is derived for two cases: the ensemble mean of pumping tests and the drawdown at an individual heterogeneous transmissivity field. The analytical form of the solution allows to inversely estimate the parameters of aquifer heterogeneity from pumping test data. This is shown making use of virtual pumping test data, for both cases the ensemble mean drawdown and pumping tests at individual transmissivity fields. The effective well flow solution reproduces the drawdown for two-dimensional pumping tests in heterogeneous media and is a promising tool to estimate parameters of aquifer heterogeneity, in particular for the horizontal correlation length.

scholarly journals Estimation of heterogeneous aquifer parameters using centralized and decentralized fusion of hydraulic tomography data from multiple pumping tests

2014 ◽  
Vol 11 (4) ◽  
pp. 4163-4208 ◽  
Author(s):  
A. H. Alzraiee ◽  
D. Baú ◽  
A. Elhaddad
Keyword(s):  
Correlation Length ◽  
Hydraulic Properties ◽  
Pumping Test ◽  
Hydraulic Head ◽  
Specific Storage ◽  
Pumping Tests ◽  
Hydraulic Tomography ◽  
Temporal Moment ◽  
Transient Data ◽  
Temporal Moments

Abstract. Characterization of spatial variability of hydraulic properties of groundwater systems at high resolution is essential to simulate flow and transport phenomena. This paper investigates two schemes to invert transient hydraulic head data resulting from multiple pumping tests for the purpose of estimating the spatial distributions of the hydraulic conductivity, K, and the specific storage, Ss, of an aquifer. The two methods are centralized fusion and decentralized fusion. The centralized fusion of transient data is achieved when data from all pumping tests are processed concurrently using a central inversion processor, whereas the decentralized fusion inverts data from each pumping test separately to obtain optimal local estimates of hydraulic parameter, which are consequently fused using the Generalized Millman Formula, an algorithm for merging multiple correlated or uncorrelated local estimates. For both data fusion schemes, the basic inversion processor employed is the Ensemble Kalman Filter, which is employed to assimilate the temporal moments of the transient hydraulic head measurements resulting from multiple pumping tests. Assimilating the temporal moments instead of the hydraulic head transient data themselves is shown to provide a significant improvement in computational efficiency. Additionally, different assimilation strategies to improve the estimation of Ss are investigated. Results show that estimation of the K and Ss distributions using temporal moment analysis is fairly good; however, the centralized inversion scheme consistently outperforms the decentralized inversion scheme. Investigations on the sensitivity of the inversion estimates to errors in geostatistical parameters of the random fields of K and Ss reveal that the estimates are not sensitive to errors in the correlation length and the variance of hydraulic properties, but are noticeably sensitive to errors in the stationary mean. The proposed inversion schemes are expanded to estimate the geostatistical parameters of the K and Ss fields. The results show that the estimation of the true stationary mean of the K field and, to a lesser degree, the stationary mean of the Ss field can be successfully achieved, while the estimation of correlation length and standard deviation for both the K and Ss fields are not as effective.

A Graphical Method for Storage Coefficient Determination from Quasi-Steady State Flow Data

1996 ◽  
Vol 27 (4) ◽  
pp. 247-254 ◽  
Author(s):  
Zekâi Şen
Keyword(s):  
Steady State ◽  
Graphical Method ◽  
Pumping Test ◽  
Quasi Steady State ◽  
Flow Data ◽  
Steady State Flow ◽  
Storage Coefficient ◽  
State Flow ◽  
Aquifer Test

A simple, approximate but practical graphical method is proposed for estimating the storage coefficient independently from the transmissivity value, provided that quasi-steady state flow data are available from a pumping test. In the past, quasi-steady state flow distance-drawdown data have been used for the determination of transmissivity only. The method is applicable to confined and leaky aquifers. The application of the method has been performed for various aquifer test data available in the groundwater literature. The results are within the practical limits of approximation compared with the unsteady state flow solutions.

Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number

2009 ◽  
Vol 626 ◽  
pp. 367-393 ◽  
Author(s):  
STEFAN MÄHLMANN ◽  
DEMETRIOS T. PAPAGEORGIOU
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Electric Field ◽  
Electric Fields ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Liquid Drops

The effect of an electric field on a periodic array of two-dimensional liquid drops suspended in simple shear flow is studied numerically. The shear is produced by moving the parallel walls of the channel containing the fluids at equal speeds but in opposite directions and an electric field is generated by imposing a constant voltage difference across the channel walls. The level set method is adapted to electrohydrodynamics problems that include a background flow in order to compute the effects of permittivity and conductivity differences between the two phases on the dynamics and drop configurations. The electric field introduces additional interfacial stresses at the drop interface and we perform extensive computations to assess the combined effects of electric fields, surface tension and inertia. Our computations for perfect dielectric systems indicate that the electric field increases the drop deformation to generate elongated drops at steady state, and at the same time alters the drop orientation by increasing alignment with the vertical, which is the direction of the underlying electric field. These phenomena are observed for a range of values of Reynolds and capillary numbers. Computations using the leaky dielectric model also indicate that for certain combinations of electric properties the drop can undergo enhanced alignment with the vertical or the horizontal, as compared to perfect dielectric systems. For cases of enhanced elongation and alignment with the vertical, the flow positions the droplets closer to the channel walls where they cause larger wall shear stresses. We also establish that a sufficiently strong electric field can be used to destabilize the flow in the sense that steady-state droplets that can exist in its absence for a set of physical parameters, become increasingly and indefinitely elongated until additional mechanisms can lead to rupture. It is suggested that electric fields can be used to enhance such phenomena.

Predicting Groundwater Flow and Solute Transport in the Heterogeneous Aquifer Sandbox Using Different Parameter Estimation Methods

2021 ◽  
Author(s):  
Liqun Jiang ◽  
Ronglin Sun ◽  
Xing Liang
Keyword(s):  
Steady State ◽  
Groundwater Flow ◽  
Solute Transport ◽  
Transport Process ◽  
Homogeneous Model ◽  
Estimation Methods ◽  
Aquifer Heterogeneity ◽  
Heterogeneous Aquifer ◽  
Tracer Distribution ◽  
Parameter Estimation Methods

<p>Protection and management of groundwater resources demand high-resolution distributions of hydraulic parameters (e.g., hydraulic conductivity (K) and specific storage (Ss)) of aquifers. In the past, these parameters were obtained by traditional analytical solutions (e.g., Theis (1935) or Cooper and Jacob (1946)). However, traditional methods assume the aquifer to be homogeneous and yield the equivalent parameter, which are averages over a large volume and are insufficient for predicting groundwater flow and solute transport process (Butler & Liu, 1993). For obtaining the aquifer heterogeneity, some scholars have used kriging (e.g., Illman et al., 2010) and hydraulic tomography (HT) (e.g., Yeh & Liu, 2000; Zhu & Yeh, 2005) to describe the K distribution.</p><p>In this study, the laboratory heterogeneous aquifer sandbox is used to investigate the effect of different hydraulic parameter estimation methods on predicting groundwater flow and solute transport process. Conventional equivalent homogeneous model, kriging and HT are used to characterize the heterogeneity of sandbox aquifer. A number of the steady-state head data are collected from a series of single-hole pumping tests in the lab sandbox, and are then used to estimate the K fields of the sandbox aquifer by the steady-state inverse modeling in HT survey which was conducted using the SimSLE algorithm (Simultaneous SLE, Xiang et al., 2009), a built-in function of the software package of VSAFT2. The 40 K core samples from the sandbox aquifer are collected by the Darcy experiments, and are then used to obtain K fields through kriging which was conducted using the software package of Surfer 13. The role of prior information on improving HT survey is then discussed. The K estimates by different methods are used to predict the process of steady-state groundwater flow and solute transport, and evaluate the merits and demerits of different methods, investigate the effect of aquifer heterogeneity on groundwater flow and solute transport.</p><p>According to lab sandbox experiments results, we concluded that compared with kriging, HT can get higher precision to characterize the aquifer heterogeneity and predict the process of groundwater flow and solute transport. The 40 K fields from the K core samples are used as priori information of HT survey can promote the accuracy of K estimates. The conventional equivalent homogeneous model cannot accurately predict the process of groundwater flow and solute transport in heterogeneous aquifer. The enhancement of aquifer heterogeneity will lead to the enhancement of the spatial variability of tracer distribution and migration path, and the dominant channel directly determines the migration path and tracer distribution.</p>

Two-Dimensional Spectroscopy for Vacuum Arc in Steady State and Decaying State under Free-Recovery Condition

2021 ◽  
Author(s):  
Yuto Hatanaka ◽  
Takamitsu Miyazaki ◽  
Yusuke Nakano ◽  
Yasunori Tanaka ◽  
Yoshihiko Uesugi ◽  
...  
Keyword(s):  
Steady State ◽  
Vacuum Arc ◽  
Two Dimensional ◽  
Recovery Condition

scholarly journals Thermal Robustness of Entanglement in a Dissipative Two-Dimensional Spin System in an Inhomogeneous Magnetic Field

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1066
Author(s):  
Gehad Sadiek ◽  
Samaher Almalki
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Nearest Neighbor ◽  
Quantum Phase Transitions ◽  
Inhomogeneous Magnetic Field ◽  
Steady States ◽  
Inhomogeneous Field ◽  
Spin States ◽  
Two Dimensional ◽  
Spin Lattice

Recently new novel magnetic phases were shown to exist in the asymptotic steady states of spin systems coupled to dissipative environments at zero temperature. Tuning the different system parameters led to quantum phase transitions among those states. We study, here, a finite two-dimensional Heisenberg triangular spin lattice coupled to a dissipative Markovian Lindblad environment at finite temperature. We show how applying an inhomogeneous magnetic field to the system at different degrees of anisotropy may significantly affect the spin states, and the entanglement properties and distribution among the spins in the asymptotic steady state of the system. In particular, applying an inhomogeneous field with an inward (growing) gradient toward the central spin is found to considerably enhance the nearest neighbor entanglement and its robustness against the thermal dissipative decay effect in the completely anisotropic (Ising) system, whereas the beyond nearest neighbor ones vanish entirely. The spins of the system in this case reach different steady states depending on their positions in the lattice. However, the inhomogeneity of the field shows no effect on the entanglement in the completely isotropic (XXX) system, which vanishes asymptotically under any system configuration and the spins relax to a separable (disentangled) steady state with all the spins reaching a common spin state. Interestingly, applying the same field to a partially anisotropic (XYZ) system does not just enhance the nearest neighbor entanglements and their thermal robustness but all the long-range ones as well, while the spins relax asymptotically to very distinguished spin states, which is a sign of a critical behavior taking place at this combination of system anisotropy and field inhomogeneity.

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