Sensitivity analysis of slug tests Part 2. Observation wells

As important parameters for characterizing heat transfer, thermal property parameters of aquifers and rock-soil skeletons have important research significance in the development and utilization of geothermal resources. The slug heat test is inspired by the slug test, and the heat is instantaneously excited in the test well so as to change the temperature of test section in the test well instantaneously. Based on the thermal radial convection-dispersion theory and the principle of heat conservation, the theoretical model of the slug heat test is established, and the model is solved by Laplace transform and inverse transform to obtain multiple sets of standard curves under different conditions. The slug heat tests were conducted in the indoor model, the slug heat test data under different hydrodynamic conditions were fitted with the standard curves and the thermal property parameters, including effective thermal conductivity, stagnant thermal conductivity, thermal mechanical dispersion coefficient, thermal dispersive degree, thermal diffusivity, heat capacity of aquifer, heat capacity and thermal conductivity of rock-soil skeletons, were accurately obtained. The test results are in good agreement with the empirical values. Meanwhile, the effective thermal conductivity of the aquifer also clearly increases with the increase of flow rate. The excitation temperature difference had little effect on the effective thermal conductivity of the aquifer. At the same time, numerical simulation methods are used to establish a numerical model consistent with the indoor test model, and the numerical model is assigned with the thermal property parameters obtained from the indoor slug heat test, and the measured values of temperature changes in the test well during the slug heat test under different hydrodynamic and excitation strength conditions are compared with the simulated values for verification. The research results show that the slug heat test has the characteristics of high applicability, simple operation and rapid testing, and can effectively determine the thermal properties parameters of aquifers and rock-soil skeletons.

A single-porosity model is developed to deal with a fracture zone slug test in a large dip angle by assuming the fracture zone causes a downward regional flow. For the oscillatory response, a larger dip angle causes larger amplitude while introduces little impact on period. The effective water length, an important parameter necessary for analyzing the oscillatory response, is proven to be independent of the dip angle and can be evaluated using the available horizontal formation methods. The dip angle effect is more pronounced for a larger storage coefficient. An empirical relationship is developed to evaluate the limiting dip angle, below which the dip angle effect is negligible. Field data analysis of a slug test in a 47° dip angle fracture zone indicates that neglecting the dip angle can result in a 27% transmissivity over estimation and a 53% storage coefficient under estimation.

Determination of skin and aquifer parameters for a slug test with wellbore-skin effect

Methods of analyzing ‘slug test’ data are reviewed, and additional type curves for the analysis of test data from formations with very low storage coefficients are presented.

An increasing need for surveillance of the quality of our ground water resources requires a comprehensive hydraulic modeling. A thorough knowledge of the hydraulic parameters is a necessity for reliable hydraulic modeling. Pumping and slug tests have usually been the main source of information about the hydraulic conductivity and the specific storage. Pumping tests result in conductivities and storage coefficients averaged over large volumes, and slug tests are often seriously affected by the well screens and filter packs. A new method for in situ determination of the hydraulic conductivity and the specific storage has been developed at the University of Aarhus. By making use of a hollow auger drill stem it is possible to inject water directly into the formation and measure the rise in hydraulic head at a short distance from the injection point. Other procedures for in situ determination of hydraulic parameters have been developed (Fejes and J6sa, 1990). The measured data (the transient hydraulic head variations) are interpreted using an inversion algorithm based on a least squares iterative formalism. To make the problem more linear the inversion is carried out in the log parameter space. The model response applied is the transient head variations due to a point source in a homogenous isotropic fullspace, where the source is considered as a step source. Since there are only three model parameters to be estimated and typically more than one hundred data, the inverse problem is strongly overdetermined.

This note develops a general mathematical model for describing the transient hydraulic head response for constant-head test, constant-flux test, and slug test in a radial confined aquifer system with a partially penetrating well. The Laplace-domain solution for the model is derived by applying the Laplace transform with respect to time and finite Fourier cosine transform with respect to the z-direction. This new solution has been shown to reduce to the constant-head test when discounting the wellbore storage and maintaining a constant well water level. This solution can also be reduced to the constant-flux test solution when discounting the wellbore storage and keeping a constant pumping rate in the well. Moreover, the solution becomes the slug test solution when there is no pumping in the well. This general solution can be used to develop a single computer code to estimate aquifer parameters if coupled with an optimization algorithm or to assess the effect of well partial penetration on hydraulic head distribution for three types of aquifer tests.

Groundwater management or remediation requires the knowledge of the main hydrodynamic parameters of the hydrological system. The aim of the study focused on the investigation of the reliability of the methods used for the estimation of these important parameters. Several pumping and slug tests were performed in the Hydraulics Laboratory of University of Calabria, where a high controlled experimental apparatus was designed and constructed. The data collected during the experiments have been used to estimate the hydraulic conductivity and the storage coefficient of the porous medium. The analysis was carried out both through classical analytical methods and by the development of an ad hoc three-dimensional finite element model of the apparatus working in transient conditions. An extreme variability in the results was observed but the estimates obtained by the inverse numerical modelling were the ones returning, on average, the best outcomes among all the characterisation methods.

The correct characterization of aquifer parameters is essential for water-supply and water-quality investigations. Slug tests are widely used for these purposes. While free software is available to interpret slug tests, some codes are not user-friendly, or do not include a wide range of methods to interpret the results, or do not include automatic, inverse solutions to the test data. The private sector has also generated several good programs to interpret slug test data, but they are not free of charge. The computer program SlugIn 1.0 is available online for free download, and is demonstrated to aid in the analysis of slug tests to estimate hydraulic parameters. The program provides an easy-to-use Graphical User Interface. SlugIn 1.0 incorporates automated parameter estimation and facilitates the visualization of several interpretations of the same test. It incorporates solutions for confined and unconfined aquifers, partially penetrating wells, skin effects, shape factor, anisotropy, high hydraulic conductivity formations and the Mace test for large-diameter wells. It is available in English and Spanish and can be downloaded from the web site of the Geological Survey of Spain. Two field examples are presented to illustrate how the software operates.

Knowledge of the hydraulic conductivity distribution is of utmost importance in understanding the dynamics of an aquifer and in planning the consequences of any action taken upon that aquifer. Slug tests have been used extensively to measure hydraulic conductivity in the last 50 years since Hvorslev's (1951) work. A general nonlinear model based on the Navier-Stokes equation, nonlinear frictional loss, non-Darcian flow, acceleration effects, radius changes in the wellbore, and a Hvorslev model for the aquifer has been implemented in this work. The nonlinear model has three parameters: beta, which is related primarily to radius changes in the water column; A, which is related to the nonlinear head losses; and K, the hydraulic conductivity. An additional parameter has been added representing the initial velocity of the water column at slug initiation and is incorporated into an analytical solution to generate the first time step before a sequential numerical solution generates the remainder of the time solution. Corrections are made to the model output for acceleration before it is compared to the experimental data. Sensitivity analysis and least squares fitting are used to estimate the aquifer parameters and produce some diagnostic results, which indicate the accuracy of the fit. Finally, an example of field data has been presented to illustrate the application of the model to data sets that exhibit nonlinear behavior. Multiple slug tests should be taken at a given location to test for nonlinear effects and to determine repeatability.

Analysis of the hydromechanical behavior of a flat-lying fracture during a slug test

This study presents a comparative analysis of various optimization algorithms—Differential Evolution (DE), Particle Swarm Optimization (PSO), Arithmetic Optimization Algorithm (AOA), and Hippopotamus Optimization Algorithm (HOA)—for parameter identification in photovoltaic (PV) models. By utilizing RTC France solar cell data, we demonstrate that accurate parameter estimation is crucial for enhancing the efficiency of PV systems, ultimately supporting sustainable energy solutions. Our results indicate that DE achieves the lowest root mean square error (RMSE) of 0.0001 for the double-diode model (DDM), outperforming other methods in terms of accuracy and convergence speed. Both the HOA and PSO also show competitive RMSE values, underscoring their effectiveness in optimizing parameters for PV models. This research not only contributes to improved PV model precision but also aids in the broader effort to advance renewable energy technologies, thereby fostering a more sustainable future.

A mathematical formulation is presented in this paper which includes wellbore inertial and frictional effects during a slug test or the flow period of a drillstem test from naturally fractured reservoirs. This formulation is obtained by coupling a wellbore equation and the diffusivity equation for double-porosity reservoirs. The wellbore equation represents a transient momentum balance relating liquid level in the wellbore and bottomhole pressure. Wellbore storage and skin effect are considered in the coupling conditions. A simplified formulation resulting from the assumptions of a small slug and friction losses for laminar flow in the wellbore is solved by applying the Laplace transformation with numerical inversion. Solutions obtained in this study show a distinctive double-porosity behavior for some naturally fractured reservoirs. For those naturally fractured reservoirs with double-porosity behavior, an estimate of the interporosity flow parameter, λ, and of the storativity ratio, ω, can be obtained in addition to fissures transmissivity, kfh/µ, and skin effect factor, s. On the other hand, during the practical range of time, the response of other naturally fractured reservoirs follow either the response for a single-porosity reservoir with the properties of the fracture system or the response of a single-porosity reservoir with the combined properties of the fractures and matrix blocks. Criteria to estimate the magnitude of wellbore inertial and frictional effects for practical systems are developed from an analysis of results obtained in this study. Also, the solution method proposed in this paper can be used to forecast or match bottomhole flowing pressures during a drillstem test from estimates of the properties that describe a naturally fractured reservoir.

In this article, an adaptive dynamic surface control approach is proposed for uncertain strict‐feedback systems (SFSs) to guarantee both the prescribed transient tracking performance and the asymptotic tracking while realizing the accurate parameter estimation. It is assumed that SFSs are subject to linearly parametric uncertainties in both the drift terms and the control coefficients. A new inequality on the arctangent function, which can be widely used in the robust or the adaptive control designs, is established. Owing to this inequality, nonlinear robust filters with arctangent functions are designed and embedded into the backstepping control algorithm to avoid the “differential explosion” problem. Moreover, an improved forgetting‐factor‐based parameter estimation error reconstruction mechanism is proposed. And the obtained parameter estimation errors are integrated into the adaptive laws to achieve the accurate parameter estimation. Furthermore, the projection operator is applied to avoid the singularity problem of the control law. Besides, an asymmetric error transformation is introduced to restrict the tracking error within the prescribed performance envelope. It is proved that the tracking error and the parameter estimation errors asymptotically converge to zero and the tracking error satisfies the prescribed transient performance. Finally, the effectiveness of the proposed control approach is validated in terms of the single‐link manipulator actuated by a brush DC motor.

This paper presents focus on physical feature extraction and parameter estimation for satellites in space. In the context of increasingly prominent space security issues, it is necessary to improve the security and protection capabilities of the space system, especially the refined feature extraction and recognition technology of space targets. However, the feature extraction methods based on optical or radar imagery are limited by resolution and observation conditions, making it difficult to extract refined features. This paper is based on the attribute scattering center theory, using high-frequency electromagnetic wave detection method. Through the attribute parameter estimation result of the scattering center, the scattering structure on the space target can be identified and its distribution position can be analyzed, and the structure and size of the typical parts in the space target can be extracted. Aiming at the problem of high parameter dimension and large amount of calculation, an attributed scattering centers parameter estimation method with amplitude and phase separation is proposed, which reduces the time complexity of parameter estimation by an order of magnitude, saves system resources and increases the parameter estimation rate, and the estimation accuracy is better than 90%. In terms of the efficiency and accuracy of parameter estimation from simulation and experimental data, the effectiveness of the proposed method in this paper is verified.

A general method for estimating ground‐water solute mass transfer rate parameters from field test data is presented. The method entails matching solute concentration and hydraulic head data collected during the recovery phase of a pumping test through application of a simulation‐regression technique. Estimation of hydraulic conductivity and mass transfer rate parameter values is performed by fitting model simulations to the data. Parameter estimates are utilized to assess cleanup times for pump‐and‐treat aquifer remediation scenarios. Uncertainty in the cleanup time estimate is evaluated using statistical information obtained with the parameter estimation technique.Application of the method is demonstrated using a hypothetical ground‐water flow and solute transport system. Simulations of field testing, parameter estimation, and remedial time frames are performed to evaluate the usefulness of the method. Sets of random noise that signify potential field and laboratory measurement errors are combined with the hypothetical data to provide rigorous testing of the method. Field tests are simulated using ranges of values for data noise, the mass transfer rate parameters, the test pumping rates, and the duration of recovery monitoring to evaluate their respective influence on parameter and cleanup time estimates. The demonstration indicates the method is capable of yielding accurate estimates of the solute mass transfer rate parameters. When the parameter values for the hypothetical system are well estimated, cleanup time predictions are shown to be more accurate than when calculated using the local equilibrium assumption.