Steady-state Pumping Research Articles

Groundwater modeling and estimation of the safe pumping rate for the sustainable use of groundwater resources in Kombolcha town, upper Borkena watershed, Ethiopia

ABSTRACT The rate of groundwater extraction is increasing due to population growth. Balancing pumping rates with natural recharge is necessary for sustainable use. The safe groundwater pumping rate was determined using the groundwater model ModelMuse. To determine the safe pumping rate, 39 borehole data points were gathered and adjusted for 4, 8, and 12 h of pumping scenarios for 50 years in a steady-state pumping condition. The recharge rates in the study area were calculated using four empirical approaches in addition to the water balance method. Of the four empirical methods, the water balance technique provided the most accurate estimates of groundwater recharge, with an estimated average recharge rate of 176.75 mm per year. The ModelMuse model water balance report demonstrated that there was positive storage for all boreholes to be pumped simultaneously under 4- and 8-h pumping rate scenarios, but that there would be a significant drawdown under 12-h pumping from the stress period of 2039–2065, and the summation of inflow and outflow would become negative, indicating that the withdrawal rate is greater than the recharge rate. Thus, the safe pumping rate for Borkena groundwater was calculated to be 975 L/s in 8-h pumping rate scenarios.

Unraveling Interactions between Asymmetric Tidal Turbulence, Residual Circulation, and Salinity Dynamics in Short, Periodically Weakly Stratified Estuaries

AbstractAsymmetric tidal turbulence (ATT) strongly influences estuarine health and functioning. However, its impact on the three-dimensional estuarine dynamics and the feedback of water motion and salinity distribution on ATT remain poorly understood, especially for short estuaries (estuarine length ≪ tidal wavelength). This study systematically investigates the abovementioned interactions in a short estuary for the first time, considering periodically weakly stratified conditions. This is done by developing a three-dimensional semi-analytical model (combining perturbation method with finite element method) that allows a dissection of the contributions of different processes to ATT, estuarine circulation, and salt transport. The generation of ATT is dominated by (i) strain-induced periodic stratification and (ii) asymmetric bottom-shear-generated turbulence, and their contributions to ATT are different both in amplitude and phase. The magnitude of the residual circulation related to ATT and the eddy viscosity–shear covariance (ESCO) is about half of that of the gravitational circulation (GC) and shows a “reversed” pattern as compared to GC. ATT generated by strain-induced periodic stratification contributes to an ESCO circulation with a spatial structure similar to GC. This circulation reduces the longitudinal salinity gradients and thus weakens GC. Contrastingly, the ESCO circulation due to asymmetric bottom-shear-generated turbulence shows patterns opposite to GC and acts to enhance GC. Concerning the salinity dynamics at steady state, GC and tidal pumping are equally important to salt import, whereas ESCO circulation yields a significant seaward salt transport. These findings highlight the importance of identifying the sources of ATT to understand its impact on estuarine circulation and salt distribution.

Interpretation of Pumping Tests in Heterogeneous Aquifers with Constant Head Boundary.

This paper investigates the impact of heterogeneity of the transmissivity field on the interpretation of steady-state pumping test data from aquifer systems delimited by constant head boundaries such as aquifers adjacent to lakes or rivers. Spatially variable transmissivity fields are randomly generated and used to simulate the drawdown due to a pumping well located at different distances from a constant head boundary. The steady-state drawdown simulated at different observation wells are then interpreted using the Hantush method (Hantush 1959). The numerical simulations show that, in contrast to the case of infinite aquifer domains, the interpreted transmissivity varies depending on well locations and the separation distance between pumping well and boundary relative to the correlation length. The ensemble-averaged estimated transmissivity varies between the geometric mean and the arithmetic mean, and can even exceed the arithmetic mean in a narrow domain adjacent to the boundary. It approaches the geometric mean of the underlying transmissivity field only if the distance between the pumping well is more than 20 times the characteristic length of the transmissivity field.

Measurements of quantum dot level populations using an optical waveguide

A scheme is proposed for measuring electron level populations in a semiconductor quantum dot embedded in a multimode waveguide. The photon transmittance of the waveguide under steady-state pumping is shown to depend on the presence of an electron in the ground state of the quantum dot. The influence of waveguide, quantum dot, and photon source parameters on the electron detection process is examined. It is shown that, even at a moderate mode Q-factor (104 to 105), the measurement contrast and signal-to-noise ratio are rather high (above 104). The feasibility of using the proposed method for probing the state of a charge qubit is discussed.

Response of dual-zone heterogeneous wedge-shaped aquifers under steady-state pumping and regional flow

Natural hydrogeological settings may delineate wedge-shaped aquifers that are sandwiched between streams, lakes or sea water bodies along arbitrary-oriented boundary lines. This is the case in multiple river basins, river deltas, alluvial fans, and coastal promontories and heterogeneity patterns are likely to arise because of sedimentation zoning. The aim of present study is to provide a steady-state analytical solution describing the nature of well extraction in heterogeneous wedge-shaped aquifers formed by intersection of arbitrary-oriented streams. This laterally bounded aquifer comprises two zones of constant but differing transmissivity (hydraulic conductivity) which are hydraulically connected through a common interface. First, the method of Green's function constructs a closed-form expression for the spatial distribution of dual-zone potential. Next, the stream function is derived from the integration of Cauchy-Riemann equations which in turn completes an analytical representation of the flow net. The stream depletion rates are shown to be explicitly linked to the stream function. This leads to simple expressions for the stream depletion rates, demonstrating that the lateral recharge from adjacent streams varies linearly with the angular position of pumping well without any dependency on the aquifer heterogeneity. The present solution encompasses a number of existing solutions for homogeneous aquifer system as subsets. Flow nets are generated for hypothetical test cases whereby stagnation points are identified semi-analytically. The present formulation ensures preservation of water balance for a capture zone subject to regional flow. Sensitivity analysis is conducted to address how drawdown at a certain observation point responds to a heterogeneity perturbation. Wider wedges appear more sensitive to variation of heterogeneity. The formulation is extended to account for rainfall-induced recharge over a dual-zone unconfined aquifer. In each case, the computed head profiles agree well with numerical counterparts from finite element method.

Does In Situ State of Stress Affect Fracture Flow in Crystalline Settings?

AbstractWhether in situ state of stress affects fracture flow in approximately 1‐km‐deep crystalline rock setting is investigated by analyzing a unique fracture database, consisting of 193,698 discrete fractures out of which 6,223 were detected as flowing during steady state pumping. The database is based on fracture data acquired in deep surface‐based holes drilled during the site investigations for underground high‐level spent nuclear fuel repositories in Finland and Sweden. By computing effective normal and shear stress magnitudes on the planes of all identified fractures, we show that the probability for critically stressed fractures to be flowing is low and low normal stress values provide a slightly better indicator for fracture flow. Our results further show that at shallow settings, fracture criticality is driven by low normal stresses as the distributions of shear stress values for flowing and nonflowing fractures are very similar. The results also show that the effect of in situ stress on fracture flow is relatively low and in situ stress or its associated derivatives (shear and normal stresses) cannot be used directly in a deterministic manner for the prediction of fracture flow. As a consequence, if hydromechanical concepts are invoked for modeling fracture flow, a probabilistic approach is needed. In such an approach, we emphasize the role of low normal stresses over the concept of critically stressed fractures, as the use of normal stresses does not require the selection of a certain friction coefficient value, defining the boundary between critical and noncritical fractures.

Comparison of the fully penetrating well drawdown in leaky aquifers between fiite and infiite radius of inflence under steady-state pumping conditions

Comparison of the fully penetrating well drawdown in leaky aquifers between fiite and infiite radius of inflence under steady-state pumping conditions

Gauge freedom in observables and Landsberg's nonadiabatic geometric phase: Pumping spectroscopy of interacting open quantum systems

We set up a general density-operator approach to geometric steady-state pumping through slowly driven open quantum systems. This approach applies to strongly interacting systems that are weakly coupled to multiple reservoirs at high temperature, illustrated by an Anderson quantum dot, but shows potential for generalization. Pumping gives rise to a nonadiabatic geometric phase that can be described by a framework originally developed for classical dissipative systems by Landsberg. This geometric phase is accumulated by the transported observable (charge, spin, energy) and not by the quantum state. It thus differs radically from the adiabatic Berry-Simon phase, even when generalizing it to mixed states, following Sarandy and Lidar. Importantly, our geometric formulation of pumping stays close to a direct physical intuition (i) by tying gauge transformations to calibration of the meter registering the transported observable and (ii) by deriving a geometric connection from a driving-frequency expansion of the current. Our approach provides a systematic and efficient way to compute the geometric pumping of various observables, including charge, spin, energy and heat. Our geometric curvature formula reveals a general experimental scheme for performing geometric transport spectroscopy that enhances standard nonlinear spectroscopies based on measurements for static parameters. We indicate measurement strategies for separating the useful geometric pumping contribution to transport from nongeometric effects. Finally, we highlight several advantages of our approach in an exhaustive comparison with the Sinitsyn-Nemenmann full-counting statistics (FCS) approach to geometric pumping of an observable`s first moment. We explain how in the FCS approach an "adiabatic" approximation leads to a manifestly nonadiabatic result involving a finite retardation time of the response to parameter driving.

Charge translocation by mitochondrial NADH:ubiquinone oxidoreductase (complex I) from Yarrowia lipolytica measured on solid-supported membranes

The charge translocation by purified reconstituted mitochondrial complex I from the obligate aerobic yeast Yarrowia lipolytica was investigated after adsorption of proteoliposomes to solid-supported membranes. In presence of n-decylubiquinone (DBQ), pulses of NADH provided by rapid solution exchange induced charge transfer reflecting steady-state pumping activity of the reconstituted enzyme. The signal amplitude increased with time, indicating ‘deactive→active’ transition of the Yarrowia complex I. Furthermore, an increase of the membrane-conductivity after addition of 5-(N-ethyl-N-isopropyl)amiloride (EIPA) was detected which questiones the use of EIPA as an inhibitor of the Na+/H+-antiporter-like subunits of complex I. This investigation shows that electrical measurements on solid-supported membranes are a suitable method to analyze transport events and ‘active/deactive’ transition of mitochondrial complex I.

Extending Theis' solution: Using transient pumping tests to estimate parameters of aquifer heterogeneity

AbstractA framework for interpreting transient pumping tests in heterogeneous transmissivity fields is developed to infer the overall geostatistical parameters of the medium without reconstructing the specific heterogeneous structure point wise. The methodology of Radial Coarse Graining is applied to deduce an effective radial description of multi‐Gaussian transmissivity. It was used to derive an Effective Well Flow Solution for transient flow conditions including not only the storativity, but also the geometric mean, the variance, and the correlation length of log‐transmissivity. This solution is shown to be appropriate to characterize the pumping test drawdown behavior in heterogeneous transmissivity fields making use of ensembles of simulated pumping tests with multiple combinations of statistical parameters. Based on the Effective Well Flow Solution, a method is developed for inferring heterogeneity parameters from transient pumping test drawdown data by inverse estimation. Thereby, the impact of statistical parameters on the drawdown is analyzed, allowing to determine the dependence of reliability of parameter estimates on location and number of measurements. It is shown, that the number of measurements can be reduced compared to steady state pumping tests. Finally, a sampling strategy for single aquifer analysis is developed, which allows to estimate the statistical parameters, in particular variance and correlation length for individual heterogeneous transmissivity fields making use of transient pumping test measurements at multiple locations.

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

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.

Electrophysiological Characterization of Na,K-ATPases Expressed in Xenopus laevis Oocytes Using Two-Electrode Voltage Clamping.

The transport of three Na(+) per two K(+) means that the Na,K-ATPase is electrogenic, and though the currents generated by the ion pump are small compared to ion channel currents, they can be measured using electrophysiology, both steady-state pumping and individual steps in the transport cycle. Various electrophysiological techniques have been used to study the endogenous pumps of the squid giant axon and of cardiac myocytes from for example rabbits. Here, we describe the characterization of heterologously expressed Na,K-ATPases using two-electrode voltage clamping (TEVC) and oocytes from the Xenopus laevis frog as the model cell. With this system, the effects of particular mutations can be studied, including the numerous mutations that in later years have been found to cause human diseases.

Estimating parameters of aquifer heterogeneity using pumping tests – implications for field applications

The knowledge of subsurface heterogeneity is a prerequisite to describe flow and transport in porous media. Of particular interest are the variance and the correlation scale of hydraulic conductivity. In this study, we present how these aquifer parameters can be inferred using empirical steady state pumping test data. We refer to a previously developed analytical solution of “effective well flow” and examine its applicability to pumping test data as under field conditions. It is examined how the accuracy and confidence of parameter estimates of variance and correlation length depend on the number and location of head measurements. Simulations of steady state pumping tests in a confined virtual aquifer are used to systematically reduce sampling size while determining the rating of the estimates at each level of data density. The method was then applied to estimate the statistical parameters of a fluvial heterogeneous aquifer at the test site Horkheimer Insel, Germany. We conclude that the “effective well flow” solution is a simple alternative to laboratory investigations to estimate the statistical heterogeneity parameter using steady state pumping tests. However, the accuracy and uncertainty of the estimates depend on the design of the field study. In this regard, our results can help to improve the conceptual design of pumping tests with regard to the parameter of interest.

Optimal design of an in-situ bioremediation system using support vector machine and particle swarm optimization

A methodology based on support vector machine and particle swarm optimization techniques (SVM-PSO) was used in this study to determine an optimal pumping rate and well location to achieve an optimal cost of an in-situ bioremediation system. In the first stage of the two stage methodology suggested for optimal in-situ bioremediation design, the optimal number of wells and their locations was determined from preselected candidate well locations. The pumping rate and well location in the first stage were subsequently optimized in the second stage of the methodology. The highly nonlinear system of equations governing in-situ bioremediation comprises the equations of flow and solute transport coupled with relevant biodegradation kinetics. A finite difference model was developed to simulate the process of in-situ bioremediation using an Alternate-Direction Implicit technique. This developed model (BIOFDM) yields the spatial and temporal distribution of contaminant concentration for predefined initial and boundary conditions. BIOFDM was later validated by comparing the simulated results with those obtained using BIOPLUME III for the case study of Shieh and Peralta (2005). The results were found to be in close agreement. Moreover, since the solution of the highly nonlinear equation otherwise requires significant computational effort, the computational burden in this study was managed within a practical time frame by replacing the BIOFDM model with a trained SVM model. Support Vector Machine which generates fast solutions in real time was considered to be a universal function approximator in the study. Apart from reducing the computational burden, this technique generates a set of near optimal solutions (instead of a single optimal solution) and creates a re-usable data base that could be used to address many other management problems. Besides this, the search for an optimal pumping pattern was directed by a simple PSO technique and a penalty parameter approach was adopted to handle the constraints in the PSO. The results showed that the costs involved in the proposed management solution were consistent with that resulting from other nontraditional optimization techniques which use embedded/linked bioremediation simulation models. Moreover, an optimal transient pumping strategy resulted in an overall reduction in pumping cost by almost 20% when compared to cases where a steady state pumping strategy was adopted. A considerable reduction in the number of simulations was achieved using the SVM approach.

Line profiles of Ni-like collisional XUV laser amplifiers: Particle correlation effects

We present a detailed analysis of the different processes that contribute to the spectral broadening of the Ni-like Ag XUV laser line, including the effects of particle correlations on the broadening due to the radiator motion (Doppler broadening). We consider two different regimes of collisional excitation pumping: the transient pumping for which the ionic temperature is relatively low and the plasma coupling parameter is large, and the quasi steady-state pumping for which the ionic temperature is higher and the plasma coupling parameter is of the order of 1. In both cases, by using classical molecular dynamics simulation techniques, we show that ionic correlations actually modify the radiator-motion broadened profiles and cannot be neglected in evaluating the Doppler effect. The subsequent narrowing of the Doppler component is small compared to the overall linewidth, which includes the effect of homogeneous collisional broadening. However, ionic correlations will also affect the amplification of the lasing line, especially when the laser enters the saturation regime, because it will lead to a homogenization of the spectral profile.

Analytical solutions for anisotropic time-dependent heat equations with Robin boundary condition for cubic-shaped solid-state laser crystals

The problem of finding analytical solutions for time-dependent or time-independent heat equations, especially for solid-state laser media, has required a lot of work in the field of thermal effects. However, to calculate the temperature distributions analytically, researchers often have to make some approximations or employ complex methods. In this work, we present full analytical solutions for anisotropic time-dependent heat equations in the Cartesian coordinates with various source terms corresponding to various pumping schemes. Moreover, the most general boundary condition of Robin (or impedance boundary condition), corresponding to the convection cooling mechanism, was applied. This general condition can be easily switched to constant temperature and thermal insulation as special cases. To this end, we first proposed a general approach to solving time-dependent heat equations with an arbitrary heat source. We then applied our approach to explore the temperature distribution for three cases: steady-state pumping or long transient, single-shot pumping or short transient, and repetitively pulsed pumping. Our results show the possibility of an easier and more accurate approach to analytical calculations of the thermal dispersion, thermal stresses (strains), thermal bending, thermal phase shift, and other thermal effects.

The Extended Thiem's solution: Including the impact of heterogeneity

In this study we present a formula for the hydraulic head describing the mean drawdown of a three dimensional steady state pumping test in heterogeneous anisotropic porous media effectively. By modeling the hydraulic conductivity as spatial random function and using the upscaling method Coarse Graining we succeed in deriving a closed form solution hefw (r) which we understand as an extension of Thiem's formula to heterogeneous media. The solution hefw (r) does not only depend on the radial distance r but accounts also for the statistics of , namely geometric mean KG, variance σ2, horizontal correlation length ℓ and anisotropy ratio e. We perform a sensitivity analysis on the parameters of hefw (r) and implement an inverse estimation strategy. Using numerical pumping tests we show the applicability of hefw (r) on the interpretation of drawdown data. This will be done for both, an ensemble of as well as for single pumping tests. Making use of the inverse estimation method we find excellent agreement of estimated parameters with initial values, in particular for the horizontal correlation length.

Calculation of energy characteristics for Si1–x Ge x –Si structures with single quantum wells

Introduction. The elemental semiconductors Si and Ge have different crystal-lattice constants. The misfit of their values is 4.2%. Therefore, Si1–xGex–Si structures experience mechanical stresses. An Si1–xGex–Si structure with x 0.85, of Ge. This produces a sharp change in the nature of the band gap of Si1–xGex–Si compounds as a function of the component composition. It should be noted that charge carriers, electrons and holes, are much more mobile in Ge than in Si because of the smaller effective masses of the electrons and holes. Therefore, the use of Si1–xGex compounds enables the speed of opto-electronic devices to be increased and new devices operating in the middle- and far-IR regions to be fabricated. The integration of Si1–xGex compounds into electronic and photonic devices is one of the contemporary areas of semiconductor technology. Application of silicon technology lowers the cost of production and expands the functional capabilities of integrated micro- and opto-components. For example, attempts to produce effective optical transitions in indirect-band Ge semiconductor by heavy doping of the crystal with P atoms or through the action of distensive stresses led to a noticeable emission of the Ge–Si structure and even optical amplification at wavelengths near 1.6 μm at room temperature and steady-state optical pumping. Herein the band structure of quantum-size Si1–xGex–Si systems is determined in terms of a 4-band k⋅pmethod. The results and analytical expressions for the energy h ω of optical band–band transitions enable the limits of change of h ω upon variation of the component composition and thickness of active and barrier layers to be defined rather accurately. Calculation by the k⋅p-Method. Spectral characteristics of quantum-size heterostructures are determined by the energy structure of the conduction band and active layer valence band. The effective mass approximation is widely used to calculate spectral characteristics of heterostructures with a one-dimensional boundary. In this instance, dispersion curves of the conduction and valence bands are written as a quadratic law:

Limiting thermal regimes of active disk elements under steady-state pumping and two-dimensional temperature distribution inside the disk

An analytic expression describing the stationary two-dimensional axially symmetric temperature distribution in a disk active element (AE) is derived upon pumping the entire disk whose thickness is 0.01 cm ≤ h ≤ 0.3 cm and the diameter-to-thickness ratio is 1 ≤ d/h ≤ 100. Thermomechanical stresses are calculated. It is shown that from the point of view of the disk damage, the tangential stress on the disk side face constitutes the major threat. For different scaling parameters x =d/h, the limiting lasing powers Plas are estimated in multimode approximation, which can be obtainedusing a disk AE in the case of end and side cooling for different heat exchange coefficients a (by the example of an Nd : YAG crystal). It is found that the side cooling can decrease Plas in some situations. The priority regions are established in the space of the parameters h, x, and a which, while increasing the pump intensity, are accompanied by one of the three events violating the normal operation of the laser: deterioration of spectral and luminescent AE parameters due to heating, malfunctioning of the cooling regime, or thermomechanical damage of the disk. It is shown that an increase in thescaling parameter x smoothes the radial temperature profile and the thermoelastic stress distribution profile.

Specific features of thermal regimes in rectangular laser slabs under steady-state pumping

We continue to investigate the phenomena related to smoothing of temperature profiles in rectangular laser slabs and to an increase in the thresholds of their breakdown under optical pumping with variations in the slab optical density [the effect of smoothing of thermooptical inhomogeneities (STOI effect)]. It is found that the STOI effect is observed not only with increasing but also with decreasing optical density if this occurs due to a decrease in the sample thickness. The dependence of the maximum temperature difference inside the slab on its optical density at the instant of its thermal breakdown is calculated. It is shown that the variations in the optical density caused by variations in both the absorption coefficient and geometric dimensions of the slab differently affect the order of occurrence of two undesirable events — destruction of the slab or boiling of cooling water — with increasing pump power. The calculated relationships reveal two optical density regions corresponding to different orders of occurrence of these events. The maximum allowable temperatures in each region are determined.