Cooper-Jacob Method Research Articles

Straight-Line Method Generalization for Aquifer Parameter Estimations

AbstractAquifer parameter determination in practical hydrogeological studies exposes one of the most significant steps in groundwater resources assessment and management. Successful parameter estimation necessitates both a reliable methodology and field data. Different analytical solutions in the forms of type curves depend on well and aquifer configuration such as porous or fractured media; confined, unconfined, and leaky conditions; and small- and large-diameter wells. Most often Cooper-Jacob (CJ) straight line is used for aquifer parameter estimations from late time-drawdown data in cases of confined and unconfined aquifers. This straight-line method is attractive because of its simplicity and straightforward calculations without tedious and dubious type-curve matching procedure. The warranty of the CJ method application depends on the fact that the late time-drawdown measurements fall along the final portion of the Theis type curve. The main purpose of this paper is to present a general type straight-...

Point-to-point connectivity, an abstract concept or a key issue for risk assessment studies?

Connectivity of high/low-permeability areas has been recognized to significantly impact groundwater flow and solute transport. The task of defining a rigorous quantitative measure of connectivity for continuous variables has failed so far, and thus there exist a suite of connectivity indicators which are dependent on the specific hydrodynamic processes and the interpretation method. Amongst the many existing indicators, we concentrate on those characterizing connectivity between the points involved in a hydraulic or tracer test. The flow connectivity indicator used here is based on the time elapsed for hydraulic response in a pumping test (e.g., the storage coefficient estimated by the Cooper–Jacob method, S est ). Regarding transport, we select the estimated porosity from the breakthrough curve ( ϕ est ) . According to Knudby and Carrera [Knudby C, Carrera J. On the relationship between indicators of geostatistical, flow and transport connectivity. Adv Water Resour 2005;28(4):405–21] these two indicators measure connectivity differently, and are poorly correlated. Here, we use perturbation theory to analytically investigate the intrinsic relationship between S est and ϕ est . We find that ϕ est can be expressed as a weighted line integral along the particle trajectory involving two parameters: the transmissivity point values, T, and the estimated values of S est along the particle path. The weighting function is linear with the distance from the pumping well, thus the influence of the weighting function is maximum at the injection area, whereas the hydraulic information close to the pumping well becomes redundant (null weight). The relative importance of these two factors is explored using numerical simulations in a given synthetic aquifer and tested against intermediate-scale laboratory tracer experiments. We conclude that the degree of connectivity between two points of an aquifer (point-to-point connectivity) is a key issue for risk assessment studies aimed at predicting the travel time of a potential contaminant.

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.

Multi-aquifer pumping test to determine cutoff wall length for groundwater flow control during site excavation in Tokyo, Japan

Multi-aquifer pumping tests, using a multi-screen pumping well and multi-level piezometers, were carried out for groundwater flow control in a large-scale excavation site in Tokyo, Japan. The site was underlain by multi-layered confined aquifers. In the tests, pumping was carried out using a multi-aquifer pumping well in which a screen depth was chosen arbitrarily. Changes in groundwater pressure heads in each aquifer were measured at each screen position of the multi-aquifer pumping well. Hydraulic conductivity (K) and specific storage (Ss) of not only aquifers, but also for low permeability layers between the aquifers, were estimated using the Cooper-Jacob method, and calibrated by a finite element method (FEM) groundwater model. Four different cutoff wall lengths were assumed for final excavation depth, and correlations among wall length, pumping discharge and drawdown at the back of the cutoff wall were obtained from simulations using the K and Ss parameters in the FEM model. Then, the most suitable wall length was selected based on the simulated correlations considering environmental condition, construction period and cost of the cutoff wall.

Interpretation of Transmissivity Estimates from Single‐Well Pumping Aquifer Tests

Interpretation of single-well tests with the Cooper-Jacob method remains more reasonable than most alternatives. Drawdowns from 628 simulated single-well tests where transmissivity was specified were interpreted with the Cooper-Jacob straight-line method to estimate transmissivity. Error and bias as a function of vertical anisotropy, partial penetration, specific yield, and interpretive technique were investigated for transmissivities that ranged from 10 to 10,000 m(2)/d. Cooper-Jacob transmissivity estimates in confined aquifers were affected minimally by partial penetration, vertical anisotropy, or analyst. Cooper-Jacob transmissivity estimates of simulated unconfined aquifers averaged twice the known values. Transmissivity estimates of unconfined aquifers were not improved by interpreting results with an unconfined aquifer solution. Judicious interpretation of late-time data consistently improved estimates where transmissivity exceeded 250 m(2)/d in unconfined aquifers.

A Distance‐Drawdown Aquifer Test Method for Aquifers with Areal Anisotropy

A new distance-drawdown method for aquifers with anisotropy on the horizontal plane is presented. The method uses scalar transformation to convert to an equivalent, isotropic medium, thus permitting application of the Cooper-Jacob Method. The method is applicable to cases where at least one ellipse of equal drawdown can be delineated but can also be applied where no ellipse can be discerned from the data. In the latter case, a least-squares regression approach can be employed to estimate the orientation and magnitude of the anisotropy. The regression R2 value provides a quantitative assessment of the degree to which the drawdown data are indicative of a systematic areal anisotropy in the aquifer or whether the data simply reflect natural aquifer heterogeneity. In addition to confined aquifers, this methodology, like the Cooper-Jacob Method, is also applicable to unconfined aquifers either before the onset of delayed drainage or following the completion of delayed drainage provided that the u value meets the recommended criterion.

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.

Aquifer Boundaries and Parameter Identification Simplified

A simple method is proposed for simultaneous and explicit identification of confined aquifer parameters and boundaries from drawdowns measured at an observation well during a constant rate pumping test. The method requires the determination of peaks of unimodal curves. Only a little subjectivity is involved in the method as the peak is a well-defined point. The method is applicable even when the first and second straight lines on the semilogarithmic characteristic drawdown curve are not fully developed. The calculations involved can be performed on a calculator. Results have also been presented for small arguments of the well functions defining the development of the straight lines. The times for initiation and development of straight lines are quantified. The minimum duration of a pumping test for a reliable identification of the aquifer parameters and boundaries using the proposed method is also quantified. Use of the new method suggests a much shorter duration pumping test for the accurate identification of aquifer parameters and boundaries. This would save considerable time and money. At least a 100-fold savings in time and money involved in a pumping test to locate a boundary is observed when compared to the use of the law of times in the Cooper-Jacob method. Application of the method to published data sets shows that reliable estimates of the aquifer parameters and distance to a boundary are obtained.

Response to pumping of wells in sloping fault zone aquifers

A number of short-term variable discharge pumping tests were conducted on sloping fault zones cutting serpentinites from a thrust complex in north Portugal. The fault zones were identified and geometrically characterized by geological mapping, interpretation of aerial photographs and electromagnetic survey. The evolution of specific drawdowns obeyed two different laws: (1) specific drawdown-time points fitted to straight lines in log–linear scatter plots. In these cases, test data were interpreted by the Cooper–Jacob method, as if fault zones were regular confined porous media aquifers; (2) specific drawdown-time points fitted to straight lines in bilinear scatter plots. Because the available theoretical models were unable to match the observed data, a new approach was developed. The approach introduces the concept of impermeable barrier with variable effective position, a barrier that is represented by the upper limit of the fault zone aquifer. The mechanics of the method is still based on the concepts and formulae of confined porous media aquifers, including the framework of the image well theory. The calculated transmissivities (T=7×10 −7–2×10 −4 m 2/ s) and storage coefficients ( S=2×10 −5–6.1×10 −4) are within those commonly found for confined aquifers in fractured rocks.

Confined Aquifer Parameters from Temporal Derivative of Drawdowns

A simple method that uses the time derivative of drawdowns is proposed for the evaluation of confined aquifer parameters. Explicit expressions are proposed for evaluation of the aquifer parameters as well as a graphical procedure. A reliable and accurate scheme to calculate the numerical derivative of drawdowns is developed based upon an analytical approach. The method requires early drawdown data (u > 0.01, where u is the argument of well function), and is shown to converge to the Cooper-Jacob method for late drawdowns (u ≤ 0.01). It does not require curve matching or an initial guess for the parameters. Calculations for the method can be performed on a hand-held calculator. The method has been applied to published data sets and the results have been compared with those obtained using traditional methods. The method accurately estimates the aquifer parameters using only early drawdown data, thereby indicating savings in time and money.

Simple Method for Confined-Aquifer Parameter Estimation

Early drawdown data, for which the argument u of the well function is >0.01, have often been considered unimportant in evaluating aquifer parameters. This paper shows that these early drawdown data, especially in the neighborhood of u = 0.43, can yield accurate values of aquifer parameters. A simple method has been presented for explicit determination of aquifer parameters using early drawdown data. The method does not require curve matching, initial guess of the parameters, or special care to check for u < 0.01, and the computations involved can be performed on a calculator. Application of the method on published data sets shows that the estimates of the aquifer parameters using only a few initial drawdowns are as good as those obtained by Theis curve matching when all data, including the late drawdowns (u ≤ 0.01), are used. The new method converges with the Cooper-Jacob method when the late drawdown data are considered. Thus, the late drawdown data also can be analyzed using the new method.

Estimation of Transmissivity in Two Wadis in the Kingdom of Saudi Arabia Using an Alternative Approach

Estimation of the parameters which describe groundwater flow continues to be an important topics. Transmissivity and hydraulic conductivity are the most important aquifer parameters in any study of groundwater problems. The availability and accuracy (reliability) of such information are essential for groundwater management and development studies. Methods of determining the magnitude of certain aquifer parameters are well established, however, these methods are very costly and time consuming. Thus some researchers and investigators turn to other techniques to determine these parameters in an indirect way. One of these techniques is the use of specific capacity approach which is considered in this paper. Case studies are presented which illustrate parameter estimation dealing with pumping test and specific capacity data of ten wells in both Wadi Tabalah and Yiba near the town of Bishah. Available pumping test data are used in the calculation of transmissivity values by Cooper-jacob's method. The recommended approach showed that the technique is valid, and versatile and can be used in estimating the aquifer parameters, especially in the case of scarce and limited data.

Hydraulics of a well pumped with linearly decreasing discharge

Abstract Varying the discharge rate of a well with time makes the Theis and Cooper-Jacob methods inapplicable for determination of the formation constants of an aquifer. Analytical and graphical solutions for variable discharge cases are available for a few empirical or functional relationships. A number of other modes of variation of discharge with time are physically possible. In this paper, a method has been developed with the help of analytical and graphical solutions to determine aquifer constants by pumping the well with linearly decreasing discharge. The linearly decreasing discharge was simulated on a horizontal Hele-Shaw model. The transmissivity and storage coefficient were evaluated by using the type curve developed for a linearly decreasing discharge well. The solution gave fairly satisfactory values of aquifer constants.