How to Find Aquifer Statistics Utilizing Pumping Tests? Two Field Studies Using welltestpy

We present a workflow to estimate geostatistical aquifer parameters from pumping test data using the Python package welltestpy . The procedure of pumping test analysis is exemplified for two data sets from the Horkheimer Insel site and from the Lauswiesen site, Germany. The analysis is based on a semi-analytical drawdown solution from the upscaling approach Radial Coarse Graining, which enables to infer log-transmissivity variance and horizontal correlation length, beside mean transmissivity, and storativity, from pumping test data. We estimate these parameters of aquifer heterogeneity from type-curve analysis and determine their sensitivity. This procedure, implemented in welltestpy , is a template for analyzing any pumping test. It goes beyond the possibilities of standard methods, for example, based on Theis' equation, which are limited to mean transmissivity and storativity. A sensitivity study showed the impact of observation well positions on the parameter estimation quality. The insights of this study help to optimize future test setups for geostatistical aquifer analysis and provides guidance for investigating pumping tests with regard to aquifer statistics using the open-source software package welltestpy .     

A Type-Curve Method for the Analysis of Pumping Tests with Piecewise-Linear Pumping Rates

Aquifer hydraulic parameters are commonly inferred from constant-rate pumping tests, while variable pumping rates are frequently encountered in actual field conditions. In this study, we propose a generally applicable dimensionless form of the analytical solution for variable-rate pumping tests in confined aquifers. In particular, we adopt a piecewise-linear fitting of variable pumping rates and propose a new type-curve method for estimating the hydraulic conductivity (K ) and specific storage (S_s ) of the investigated confined aquifer. For each test, a series of type curves, which depend on the variable pumping rates, the location of observation wells and the introduced first dimensionless inflection time, need to be provided for matching the observed drawdown data on a log-log graph. We first demonstrate the applicability and robustness of this method through a synthetic pumping test. Subsequently, we apply this method to analyze drawdown data from four pumping tests conducted within a multilayered aquifer/aquitard system in Wuxi city, Jiangsu Province, China. The parameter estimates are then compared with those reported by PEST. The K and S_s values estimated by the new type-curve method are found to be quite close to PEST-based estimates. Parameter estimation results demonstrate the difference in K and S_s values between observation wells. The difference could be attributed to the spatial heterogeneity in K and S_s . A future research topic may focus on the characterization of K and S_s heterogeneity with the currently available drawdown data from variable-rate pumping tests.     

Determining anisotropic transmissivity using a simplified Papadopulos method

The straight-line method presented by Papadopulos requires a minimum of three observation wells for determining the transmissivity tensor of a homogeneous and anisotropic aquifer. A simplification of this method was developed for fractured aquifers where the principal directions of the transmissivity tensor are known prior to implementation, such as when fracture patterns on outcropping portions of the aquifer may be used to infer the principal directions. This new method assumes that observation wells are drilled along the two principal directions from the pumped well, thus reducing the required number of observation wells to two. This method was applied for an aquifer test in the fractured Navajo Sandstone of southwestern Utah and yielded minimum and maximum principal transmissivity values of 70 and 1800 m(2)/d, respectively, indicating an anisotropy ratio of approximately 24 to 1.     

A new method for the interpretation of pumping tests in leaky aquifers

A novel methodology for the interpretation of pumping tests in leaky aquifer systems, referred to as the double inflection point (DIP) method, is presented. The method is based on the analysis of the first and second derivatives of the drawdown with respect to log time for the estimation of the flow parameters. Like commonly used analysis procedures, such as the type-curve approach developed by Walton (1962) and the inflection point method developed by Hantush (1956), the mathematical development of the DIP method is based on the assumption of homogeneity of the leaky aquifer layers. However, contrary to the two methods developed by Hantush and Walton, the new method does not need any fitting process. In homogeneous media, the two classic methods and the one proposed here provide exact results for transmissivity, storativity, and leakage factor when aquifer storage is neglected and the recharging aquifer is unperturbed. The real advantage of the DIP method comes when applying all methods independently to a test in a heterogeneous aquifer, where each method yields parameter values that are weighted differently, and thus each method provides different information about the heterogeneity distribution. Therefore, the methods are complementary and not competitive. In particular, the combination of the DIP method and Hantush method is shown to lead to the identification of contrasts between the local transmissivity in the vicinity of the well and the equivalent transmissivity of the perturbed aquifer volume.     

The use of MRS in the determination of hydraulic transmissivity: The case of alluvial aquifers

Magnetic Resonance Sounding (MRS) is nowadays accepted as a new geophysical method that can be used for a reliable determination of the ground water content distribution in the top 150 m. A great effort has also been made in MRS development to deduce the hydraulic transmissivity, based on empiric relationships of the permeability with a factor F which is calculated with NMR parameters measured at laboratory scale. To use this relationship under field conditions a calibration coefficient C_T = T_pt / F has to be previously established, which demands the knowledge of the transmissivity T_pt evaluated in the pumping test. The transmissivity can then be calculated at any other site of the same aquifer using the relation T_mrs = C_TF. The C_T values reported suggest a certain relationship with the lithology, but with a great dispersion and contradictory results. MRS surveys carried out in alluvial aquifers in Spain have shown that the value of C_T evaluated at one site may not be valid at another place of the same aquifer, because of the great heterogeneity of this kind of geological environment. The demand of a pumping test at each site where a MRS is measured invalidates the method actually used for MRS transmissivity evaluation. More than 50 MRS have been used to propose a new methodology. The aquifers visited cover a great range of transmissivities (from 2 × 10^− 6 to 9 × 10^− 3 m²/s). The MRS signal amplitude varies between 20 and 1400 nV, the signal/noise ratio is in the range from 0.6 to 42, and the value of the decay time constant varies from 200 to 800 ms. It has been demonstrated that when the transmissivity increases, the value of F decreases, and C_T increases, except for certain groups of MRS taken at the same aquifer or part of one aquifer, for which F increases with T_pt, keeping C_T constant. A function C_T(F) of the type C_T = mF^− n has been obtained that allows the transmissivity evaluation without the need of T_pt. Considering that both values of transmissivity, T_pt and T_mrs, are subjected to deviations due to the experimental errors as well as due to evaluation errors, the prediction achieved by the proposed equation is rather good. To perform a better evaluation of the values of the coefficients m and n it is necessary to have a greater number of MR soundings of good quality and with a trustworthy inversion at locations where a really comparable and good performed pumping test is available, covering a sufficient range of transmissivities. Though the data we have used do not always fulfil these conditions, the result is promising. Once a trustable function is available, the forecast of the transmissivity using MRS will not need the existence of any pumping test in the area. The general extension of this methodology demands the availability of MRS taken at all kinds of geological and hydrogeological environments, which is impossible without the existence of a universal MRS data base.     

PUMPING TESTS ON OPEN WELLS IN PALAR ALLUVIUM,NEAR MADRAS CITY,INDIA AN APPLICATION OF THE PAPADOPULOS-COOPER METHOD

Abstract

The non-equilibrium formula of Theis has hitherto been found to be inadequate to analyse drawdown data from open wells, due to the influence of effects of well-storage on early drawdown data. Recently, a reliable type-curve method was proposed by Papadopulos and Cooper to analyse drawdowns in wells of large diameter. In order to study its practical validity, the Papadopulos-Cooper method was applied to drawdown data from six open wells, tapping the alluvial sands of the river Palar, near Madras city, India. The study has indicated that the method has considerable practical utility in analysing drawdown data from large diameter open wells. Besides, the method also offers an easy way of computing the duration over which the effects of well-storage are likely to influence drawdown data, in terms of aquifer transmissibility and well-radius. If a rough idea of aquifer trans-missibility is available from existing data, then, such a computation, to determine the duration over which wellstorage affects drawdown, could be initially made to advantage, so that proper judgement could be exercised in using other conventional methods of analysis, such as that of Jacob or that of Theis. (Key Words: Pumping tests; Open wells; Papadopulos-Cooper method.)     

Hydraulic properties of groundwater systems in the saprolite and sediments of the wheatbelt, Western Australia

Hydraulic properties of deeply weathered basement rocks and variably weathered sedimentary materials were measured by pumping and slug-test methods. Results from over 200 bores in 13 catchments, and eight pumping-test sites across the eastern and central wheatbelt of Western Australia were analysed. Measurements were made in each of the major lithological units, and emphasis placed on a ubiquitous basal saprolite aquifer. Comparisons were made between alternative drilling and analytical procedures to determine the most appropriate methods of investigation.

Aquifers with an average hydraulic conductivity of 0.55 m day⁻¹ occur in variably weathered Cainozoic sediments and poorly weathered saprolite grits (0.57 m day⁻¹). These aquifers are separated by an aquitard (0.065 m day⁻¹) comprising the mottled and pallid zones of the deeply weathered profile. Locally higher values of hydraulic conductivity occur in the saprolite aquifer, although after prolonged periods of pumping the values decrease until they are similar to those obtained from the slug-test methods. Hydraulic conductivities measured in bores drilled with rotary auger rigs were approximately an order of magnitude lower than those measured in the same material with bores drilled by the rotary air-blast method.

Wheatbelt aquifers range from predominantly unconfined (Cainozoic sediments), to confined (saprolite grit aquifer). The poorly weathered saprolite grit aquifer has moderate to high transmissivities (4–50 m² day⁻¹) and is capable of producing from less than 5 to over 230 kl day⁻¹ of ground water, which is often of a quality suitable for livestock. Yields are influenced by the variability in the permeability of isovolumetrically weathered materials from which the aquifer is derived.

The overlying aquitard has a low transmissivity (< 1 m² day⁻¹), especially when deeply weathered, indurated and silicified. The transmissivity of the variably weathered sedimentary materials ranges from less than 0.5 m² day⁻¹ to over 10 m² day⁻¹, depending on the texture of the materials and their position within the landscape. Higher transmissivity zones may occur as discrete layers of coarser textured materials. The salinity of the saprolite and sedimentary aquifers ranges from less than 2000 mgl⁻¹ to greater than 250000 mgl⁻¹ (total dissolved solids; TDS), depending on position within the landscape. Secondary soil salinization develops when groundwater discharge occurs from either saprolite or sedimentary aquifers.     

Comparison of Oil Transmissivity Methods Using Bail‐Down Test Data

This paper evaluates the results from three methods commonly used to estimate oil transmissivity: the modified Cooper solution (Beckett and Lyverse 2002), the modified Bouwer and Rice method (Kirkman 2013), and the modified Jacob and Lohman method (Huntley 2000). Determining the validity of oil transmissivity values is important (e.g., when used in extraction system design and operation) and not straightforward as these methods are based on different assumptions and boundary conditions and introduce different simplifying assumptions to allow for estimating oil drawdown. Data from 289 bail‐down tests performed during an oil remediation project were used in this evaluation. Analysis of these tests produced realistic transmissivity values and good correlation between these three methods, giving the authors confidence in the oil transmissivity values as this correlation is reflected across a significant number of data sets. Secondly, the nature of oil and water recharge to the wells interpreted from Kirkman's J‐ratio values largely validates the Huntley (2000) simplifying assumption that the potentiometric surface will be relatively constant during the test, allowing the use of the modified Bouwer and Rice method. Finally, the impact of oil extraction on measured oil thickness and estimated oil transmissivity was also assessed. The study showed a clear general decrease in both measured oil thicknesses and estimated oil transmissivity during the oil recovery project. However, measured oil thickness and estimated oil transmissivity are not clearly correlated, and, as a consequence, the range of decrease in one parameter does not allow any prediction of the range of decrease in the second parameter.     

Interpretation of a Pumping Test with Interference from a Neighboring Well

In confined aquifers, the influence of neighboring active wells is often neglected when interpreting a pumping test. This can, however, lead to an erroneous interpretation of the pumping test data. This paper presents simple methods to evaluate the transmissivity (T) and storativity (S) of a confined aquifer under Theis conditions, when an interfering well starts pumping in the neighborhood of the tested well before the beginning of the test. These new methods yield better estimates of the T and especially S values than when the interfering well influence is neglected. They also permit to distinguish between interfering wells and other deviations from the Cooper‐Jacob straight line, such as impermeable boundaries. The new methods were then applied on data obtained from a numerical model. The new methods require knowing the pumping rate of the interfering well and the time elapsed since the pumping started in each well, but contrary to previous methods, they do not require the aquifer natural level at the beginning of the test, which is often unknown if the interfering well has started pumping before the tested well.     

A novel analytical solution for a slug test conducted in a well with a finite-thickness skin

An aquifer containing a skin zone is considered as a two-zone system. A mathematical model describing the head distribution is presented for a slug test performed in a two-zone confined aquifer system. A closed-form solution for the model is derived by Laplace transforms and Bromwich integral. This new solution is used to investigate the effects of skin type, skin thickness, and the contrast of skin transmissivity to formation transmissivity on the distributions of dimensionless hydraulic head. The results indicate that the effect of skin type is marked if the slug-test data is obtained from a radial two-zone aquifer system. The dimensionless well water level increases with the dimensionless positive skin thickness and decreases as the dimensionless negative skin thickness increases. In addition, the distribution of dimensionless well water level due to the slug test depends on the hydraulic properties of both the wellbore skin and formation zones.     

Role of Geological and Geophysical Data in Modeling a Southwestern Alluvial Basin

A parameter-estimation technique based on existing hydrological, geophysical, and geological data was developed to approximate transmissivity values for use in a ground-water flow model of the Animas Valley, southwest New Mexico. Complete Bouguer gravity anomaly maps together with seismic-refraction profiles, geologic maps, geologic, geophysical, and drillers' logs, water levels, and pumping-test data provide insight into the transmissivity of bolson deposits throughout the basin. The transmissivity distribution was primarily based on reported pumping and specific-capacity tests in conjunction with complete Bouguer gravity anomaly maps and well log data. Reported transmissivity values were characterized by gravity values and well log data. In grid blocks lacking pumping and specific-capacity tests, transmissivity values were assigned based on the relationship of gravity values and well log data within the grid block to gravity values and well log data within other grid blocks for which transmissivity values are available. A two-dimensional, finite-difference, ground-water flow computer code was used to evaluate the effectiveness of the parameter-estimation technique. Although the trial-and-error method of calibration was employed, the actual computer time necessary for model calibration was minimal. The conceptually straightforward approach for parameter estimation utilizing existing hydrological, geophysical, and geological data provides realistic parameter estimates.     

An Analytical Model for Hydraulic Fracturing in Shallow Bedrock Formations

A theoretical method is proposed to estimate post‐fracturing fracture size and transmissivity, and as a test of the methodology, data collected from two wells were used for verification. This method can be employed before hydrofracturing in order to obtain estimates of the potential hydraulic benefits of hydraulic fracturing. Five different pumping test analysis methods were used to evaluate the well hydraulic data. The most effective methods were the Papadopulos‐Cooper model (1967), which includes wellbore storage effects, and the Gringarten‐Ramey model (1974), known as the single horizontal fracture model. The hydraulic parameters resulting from fitting these models to the field data revealed that as a result of hydraulic fracturing, the transmissivity increased more than 46 times in one well and increased 285 times in the other well. The model developed by dos Santos (2008) , which considers horizontal radial fracture propagation from the hydraulically fractured well, was used to estimate potential fracture geometry after hydrofracturing. For the two studied wells, their fractures could have propagated to distances of almost 175 m or more and developed maximum apertures of about 2.20 mm and hydraulic apertures close to 0.30 mm. Fracturing at this site appears to have expanded and propagated existing fractures and not created new fractures. Hydraulic apertures calculated from pumping test analyses closely matched the results obtained from the hydraulic fracturing model. As a result of this model, post‐fracturing geometry and resulting post‐fracturing well yield can be estimated before the actual hydrofracturing.     

Comparison of Two Computational Methods for Estimating Transmissivity Based on the Picking Equation

A comparison is presented of two computational methods, PICKINGmodel and PPC-Recovery, to estimate transmissivities based on the Picking equation using water-level recovery data from brief pumping tests of relatively low-yielding domestic wells. The tests were performed by the United States Geological Survey (USGS) in 50 domestic bedrock wells in south-central New York State, and USGS staff performed the analysis using PICKINGmodel based on the Picking equation. The results indicated that the estimated transmissivities ranged from 0.86 to 2900 ft²/d (0.080 to 270 m²/d) with a median of 41 ft²/d (3.8 m²/d). The same data were later analyzed using PPC-Recovery also based on the Picking equation. The two sets of estimated transmissivities were compared and statistically had the same median value at a probability of 95%. In another analysis, the PPC-Recovery method was applied to the same data that had been truncated at the point when the slope of the recovery data curve began to deviate from a straight line aligned with the middle portion of the recovery data. Comparing these resulting estimates of transmissivity with values originally obtained using the PICKINGmodel, the two had statistically the same median value for transmissivity at a probability of 95%. It was concluded that using PPC-Recovery in this manner to estimate transmissivity in low-yielding domestic wells will yield transmissivity values sufficiently close to the results had PICKINGmodel been used, and with less time and effort.     

Asymptotic analysis of cross-hole pneumatic injection tests in unsaturated fractured tuff

We present a new method to interpret three-dimensional pressure interference tests, which is based on an asymptotic analysis of late time pressure transient data. The approach yields reliable estimates of equivalent permeability and porosity without resorting to type-curve fitting or numerical inverse models. This is accomplished by analyzing the late-time behavior of type-curve solutions for pressure interference tests. We use our approach to infer the permeability and porosity of fractured tuff from cross-hole pneumatic injection test data. Their values are found to be in good agreement with those inferred from more complicated methods of data analysis. We analyze the statistical properties of the estimated equivalent permeability and porosity and observe a weak correlation between the two.     

A Comparative Study of Specific Yield Determinations for a Shallow Sand Aquifer

Using the type-curve methods of Boulton (1963) and Neuman (1972), and comparisons, at various times, of the cumulative volume of water pumped to the volume of the water-table drawdown cone (volume-balance method), values of specific yield were obtained from pumping test data from numerous piezometers in an unconfined sand aquifer. The long-term value of specific yield for the aquifer was determined from measurements of the laboratory drainage curve of the aquifer material. The volume-balance method gave specific yield values of 0.02, 0.05, 0.12, 0.20, 0.23, and 0.25 at times of 0.25, 0.66, 10, 26, 45, and 65 hours, respectively, indicating a gradual increase in specific yield and an asymptotic approach to the long-term value of 0.30 determined from the laboratory method. The type-curve methods provided values of 0.07 and 0.08, which correspond to the volume-balance values at early times, but which are less than one-third of the value obtained from the laboratory method and from the volume-balance method applied at the end of the pumping test (2.7 days). The type-curve procedures therefore provide unrealistically low values of specific yield for application to problems concerning the long-term yield characteristics of the aquifer. The observed trend towards increasing values of specific yield with increasing duration of pumping, and the vertical hydraulic head profiles that were measured during the pumping test indicate that both delayed drainage from above the water table and downward hydraulic gradients in the saturated zone can be important hydraulic effects contributing to the delayed-drawdown segment that is characteristic of time-drawdown graphs for unconfined aquifers.     

A single recovery type curve from Theis'' exact solution

The Theis type curve matching method and the Cooper-Jacob semilog method are commonly used for estimation of transmissivity and storage coefficient of infinite, homogeneous, isotropic, confined aquifers from drawdown data of a constant rate pumping test. Although these methods are based on drawdown data, they are often applied indiscriminately to analyze both drawdown and recovery data. Moreover, the limitations of drawdown type curve to analyze recovery data collected after short pumping times are not well understood by the practicing engineers. This often may result in an erroneous interpretation of such recovery data. In this paper, a novel but simple method is proposed to determine the storage coefficient as well as transmissivity from recovery data measured after the pumping period of an aquifer test. The method eliminates the dependence on pumping time effects and has the advantage of employing only one single recovery type curve. The method based on the conversion of residual drawdown to recovered drawdown (buildup) data plotted versus a new equivalent time (delta(t) x t(p)/t(p) + delta(t)). The method uses the recovery data in one observation point only, and does not need the initial water level h0, which may be unknown. The accuracy of the method is checked with three sets of field data. This method appears to be complementary to the Cooper-Jacob and Theis methods, as it provides values of both storage coefficient and transmissivity from recovery data, regardless of pumping duration.     

Stochastically conditioned flow paths and travel time distribution in highly heterogeneous synthesized aquifers / Chemins d’écoulement et distribution des temps de parcours au sein d’aquifères synthétiques hautement hétérogènes sous conditions stochastiques

Abstract

Abstract Characterization of heterogeneity at the field scale generally requires detailed aquifer properties such as transmissivity and hydraulic head. An accurate delineation of these properties is expensive and time consuming, and for many if not most groundwater systems, is not practical. As an alternative approach, stochastic representation of random fields is used and presented in this paper. Specifically, an iterative stochastic conditional simulation approach was applied to a hypothetical and highly heterogeneous pre-designed aquifer system. The approach is similar to the classical co-kriging technique; it uses a linear estimator that depends on the covariance functions of transmissivity (T), and hydraulic head (h), as well as their cross-covariances. A linearized flow equation along with a conditional random field generator constitutes the iterative process of the conditional simulation. One hundred equally likely realizations of transmissivity fields with pre-specified geostatistical parameters were generated, and conditioned to both limited transmissivity and head data. The successful implementation of the approach resulted in conditioned flow paths and travel-time distribution under different degrees of aquifer heterogeneity. This approach worked well for fields exhibiting small variances. However, for random fields exhibiting large variances (greater than 1.0), an iterative procedure was used. The results show that, as the variance of the ln[T] increases, the flow paths tend to diverge, resulting in a wide spectrum of flow conditions, with no direct discernable relationship between the degree of heterogeneity and travel time. The applied approach indicates that high errors may result when estimation of particle travel times in a heterogeneous medium is approximated by an equivalent homogeneous medium.     

Determination of Storage Coefficients During Pumping and Recovery

An aquifer test is used mostly to determine the storage coefficient and transmissivity. Although residual drawdown data are widely used in estimating the transmissivity of aquifers, the estimation of storage coefficients with recovery data is controversial. Some researchers have proposed methods to estimate storage coefficients with recovery data by assuming equality of storage coefficients for the recovery and pumping periods (S = S′). The aim of this study is to determine storage coefficients without such an assumption, that is, S≠S′. The method is a modified version of Banton‐Bangoy's method without considering drawdown data due to pumping. Drawdown is plotted vs. the logarithmic ratio (t′/t) or time since pumping stopped to the duration of pumping and the ratio of storage coefficient during recovery to the storage coefficient from the pumping period (S′/S). The method is verified with one case study and two synthetic examples. Thus, it is possible to determine storage coefficient of pumping period accurately without any data from pumping period by recovery data.     

Transmissivity and storage coefficient estimation by coupling the Cooper–Jacob method and modified fuzzy least-squares regression

Traditionally the Cooper–Jacob equation is used to determine the transmissivity and the storage coefficient for an aquifer using pump test results. This model, however, is a simplified version of the actual subsurface and does not allow for analysis of the uncertainty that comes from a lack of knowledge about the heterogeneity of the environment under investigation. In this paper, a modified fuzzy least-squares regression (MFLSR) method is developed that uses imprecise pump test data to obtain fuzzy intercept and slope values which are then used in the Cooper–Jacob method. Fuzzy membership functions for the transmissivity and the storage coefficient are then calculated using the extension principle. The supports of the fuzzy membership functions incorporate the transmissivity and storage coefficient values that would be obtained using ordinary least-squares regression and the Cooper–Jacob method. The MFLSR coupled with the Cooper–Jacob method allows the analyst to ascertain the uncertainty that is inherent in the estimated parameters obtained using the simplified Cooper–Jacob method and data that are uncertain due to lack of knowledge regarding the heterogeneity of the aquifer.     

Performance of methods for estimating the time of concentration in a watershed of a tropical region

The time of concentration (T_c) is a fundamental parameter in the design of hydrological projects for watersheds. In this study a graphical methodology is described for estimating T_c in a watershed, and this is applied to 17 rainfall–runoff events from a rural watershed located near the capital city of Mato Grosso do Sul State, in the Brazilian Cerrado. The T_c values obtained through the graphical method were compared to T_c values estimated using 20 equations from various references. The equations were selected by considering those that were not developed using data for urban watersheds, and the results of the graphical method were compared to those derived by applying the equations to sub-basin data. The graphical method was reliable in determining T_c, and Ventura’s equation was found to present the best performance for a rural watershed in a tropical climate region.