Constant-rate Pumping Research Articles

Abstract: Identifying Underutilized Ground Water Resources in the Coastal Bend Region of Texas

ABSTRACT Water supply planning in the twelve-county region of Texas has focused on surface water sources, especially the Choke Canyon/Lake Corpus Christi reservoir system. Long term growth in water demand in the Coastal Bend region will require the development of additional dependable water supplies. Water from Lake Texana in Jackson County, northeast of the Coastal Bend region, will be conveyed to the Corpus Christi regional water supply system via the Texana Pipeline. This pipeline bisects Refugio County, creating opportunities for integrating ground water resources in the Gulf Coast Aquifer under Refugio County into the regional water supply system. This study uses the numerical ground water model MODFLOW (McDonald and Harbaugh, 1988) to simulate the effects of ground water withdrawals on aquifer conditions in Refugio County. The model is a regional-scale model of a two-layer, leaky aquifer system. The model was calibrated to accurately reflect water level conditions reported from a comprehensive series of water level measurements undertaken in the 1961-62 period. These steady-state conditions, which more recent measurements have confirmed, have developed in Refugio County as a result of relatively constant pumping rates from only a limited number of larger wells. Model calibration results indicate a good fit of computed versus observed water levels for target wells selected from available data. The calibrated simulation model was used to evaluate two different well placement scenarios: a linear arrangement of wells along the Texana Pipeline route, and a well field arrangement with two separate sets of wells arranged in groups in areas that have greater thicknesses of the Lissie/Goliad Sand and lower dissolved solids levels. Each well placement scenario was used to test the effects of withdrawals ranging from 10,000 to 60,000 acre-feet per year. Model results show that both well arrangements could produce up to 60,000 acre-feet per year without de-watering the aquifer. The well fields produced slightly lower drawdown levels at each pumping rate than the wells along the pipeline. Significant drawdown occurred in each case and the effects were evident over a large portion of Refugio County. At least 30,000 acre-feet per year of ground water could be withdrawn from the Lissie/Goliad Sand in Refugio County without causing serious water quality problems or excessive drawdown. This amount of ground water is on the order of ten times greater than the predicted long-term water demands in Refugio County.

A new approach to fracturing test interpretation using the PKN model

A new approach to interpretation of fracturing test data obtained during shut-in decline test or flowback test has been developed. This approach allows us to determine a fracture closure pressure using downhole pressure measurements. It is based on a strictly formulated forward problem for the PKN model and a dimensional analysis of its solution. The entire set of forward problem solutions for pumping regimes with a constant pumping rate followed by shut-in or flowback is represented in a dimensionless form as a function of two variables, time and unknown fracture length at the end of pumping. For this reason, the interpretation procedure does not require multiple solving of the forward problem and is very fast and straightforward. After closure pressure determination, only the parameters HG 0 −2/3 , CG 0 1/3 and their algebraic combinations can be found from shut-in/flowback test data, where H is the fracture height, C is the leakoff coefficient and G 0 is the elastic modulus. The inverse problem with respect to other combinations of these parameters suffers from non-uniqueness. If H, C and G 0 are found somehow, the fracture length and the fracture volume at the end of pumping can be calculated.

Effects of the geological parameters on rock blasting using the Hopkinson split bar

A new approach to interpretation of fracturing test data obtained during shut-in decline test or flowback test has been developed. This approach allows us to determine a fracture closure pressure using downhole pressure measurements. It is based on a strictly formulated forward problem for the PKN model and a dimensional analysis of its solution. The entire set of forward problem solutions for pumping regimes with a constant pumping rate followed by shut-in or flowback is represented in a dimensionless form as a function of two variables, time and unknown fracture length at the end of pumping. For this reason, the interpretation procedure does not require multiple solving of the forward problem and is very fast and straightforward. After closure pressure determination, only the parameters HG−2/30, CG1/30 and their algebraic combinations can be found from shut-in/flowback test data, where H is the fracture height, C is the leakoff coefficient and G0 is the elastic modulus. The inverse problem with respect to other combinations of these parameters suffers from non-uniqueness. If H, C and G0 are found somehow, the fracture length and the fracture volume at the end of pumping can be caluclated.

A new approach to fracturing test interpretation using the PKN model

A new approach to interpretation of fracturing test data obtained during shut-in decline test or flowback test has been developed. This approach allows us to determine a fracture closure pressure using downhole pressure measurements. It is based on a strictly formulated forward problem for the PKN model and a dimensional analysis of its solution. The entire set of forward problem solutions for pumping regimes with a constant pumping rate followed by shut-in or flowback is represented in a dimensionless form as a function of two variables, time and unknown fracture length at the end of pumping. For this reason, the interpretation procedure does not require multiple solving of the forward problem and is very fast and straightforward. After closure pressure determination, only the parameters HG −2/3 0 , CG 1/3 0 and their algebraic combinations can be found from shut-in/flowback test data, where H is the fracture height, C is the leakoff coefficient and G 0 is the elastic modulus. The inverse problem with respect to other combinations of these parameters suffers from non-uniqueness. If H, C and G 0 are found somehow, the fracture length and the fracture volume at the end of pumping can be caluclated.

A consistent approach for applying numerical boundary conditions for multiphase subsurface flow

The partial differential equations which model multiphase subsurface flow are, in general, of mixed parabolic-hyperbolic type. A consistent and unified approach for handling a wide variety of boundary conditions under all flow conditions is presented. This method is conceptually simple, and numerically efficient. Test computations are presented which demonstrate this method for saturated-unsaturated models, and well as true three-phase simulations. Among the boundary conditions discussed are: seepage face conditions for three-phase problems and multi-node constant-rate pumping wells.

A Renewable Liquid Droplet as a Sampler and a Windowless Optical Cell. Automated Sensor for Gaseous Chlorine

A droplet of a reagent solution is formed at the tip of a tube centered in a cylindrical chamber through which a gas sample is aspirated. The solution is continuously pumped ; the drop grows, falls, and another drop grows again. The droplet serves not only as a reproducible collector for the sample gas flowing around it but also as a reactor for a chromogenic reaction and as a windowless optical cell. The design and characteristics of this dynamically growing/falling droplet-based gas sensor system are described ; the performance parameters are attractive relative to a static drop. In particular, such systems can be internally calibrated for any humidity effects : at a constant pumping rate, the drop period/frequency is a predictable function of sample relative humidity. The feasibility of the sensor is demonstrated by the fully automated and continuous determination of gaseous chlorine using tetramethylbenzidine solution as a chromogenic collection liquid. At levels relevant to industrial hygiene monitoring, an 18 μL droplet-based sensor equipped with a light-emitting diode photodiode-based detector shows a relative standard deviation of 1.2% (pCl 2 ∼900 ppbv, drop period 1.1 min) while the corresponding blank standard deviation is equivalent to ∼1 ppbv. There appears to be a great potential for such drop-based collectors with in situ photometric or electrochemical signal transducers as automated sensor devices in biphasic measurements (trace gases, solvent extraction, etc.).

A technique for the study of the fouling of microfiltration membranes using two membranes in series

This paper describes a technique for investigating the fouling of microfiltration membranes by measuring the pressure drops across two membranes fed in series by a constant rate pump, which enables a distinction to be made between surface fouling and internal fouling of the membrane. In the case of the microfiltration of BSA solutions, the technique shows how the type of pump and the operating temperature influence membrane fouling and how protein denaturation and adsorption give rise to different types of fouling. The technique is also used to investigate the microfiltration of beer and shows how this is affected by membrane properties and the aging of beer.

SEASONAL PUMPING VARIATION EFFECTS ON WELLHEAD PROTECTION AREA DELINEATION1

ABSTRACT: Delineation of a welihead protection area (WHPA) is the key element in welihead protection programs for drinking water supplies. WHPAs are often delineated under idealized conditions using simple steady‐state assumptions, which lead to an incorrect estimation of area and geometry. In this paper, we compare the results from a simple steady‐state procedure commonly employed in WHPA delineation with a more complex transient approach that allows consideration of seasonal variation in pumping rates. We also introduce a transient procedure to delineate time‐related capture zones using a numerical ground water flow and transport model. Welihead delineation is examined for two municipal wells in Tipton, Oklahoma, using a ten‐year time‐of‐travel criterion. In the steady‐state procedure, where we assumed constant pumping rates, we used GPTRAC, a semi‐analytical model, and MOC, a numerical model. The capture zone delineated by GPTRAC is comparable in shape with the capture zone delineated by MOC but not in size due to the differences in solution schemes. In the transient procedure, we used MOC and considered the seasonal variation in pumping rates. The capture zones delineated in this procedure were larger than the capture zones delineated by the steady‐state procedure using the same model. Further analysis showed that a higher drawdown was predicted in the transient procedure than in the steady‐state procedure, which is the reason for larger capture zones.

Hydrodynamics of the Capture Zone of a Partially Penetrating Well in a Confined Aquifer

In the pump and treat approach to the problem of managing a contaminated aquifer, a key problem is to design an effective capture system that collects only the polluted groundwater without allowing any of it to escape. At present, it is customary to design a capture system using fully penetrating withdrawal wells. Very often, however, only part of the vertical thickness of the aquifer is contaminated, so the question may arise whether a more efficient capture system can be achieved using partially penetrating wells. Very little work has been done on the application of partially penetrating wells to this problem. A new semianalytic method that can be used in determining the geometry of the capture zone for steady state flow to a partially penetrating well that is screened from the top (or from the bottom) of a confined aquifer has been developed. By combining the velocity potentials for flow to the well with that for the regional flow field, a three‐dimensional velocity potential that can be used in determining the complete geometry of the capture surface has been developed. The results have shown that with a constant pumping rate the maximum horizontal extent of the capture surface at the top (or bottom) of the aquifer increases as the degree of penetration decreases. As one would expect, the maximum vertical extent increases as the depth of penetration increases. Thus, if one knows the actual location of the contaminant plume, an appropriate combination of the degree of penetration and pumping rate can be selected to create an effective capture zone.

Analytical Solutions for Determination of Non‐Steady‐ State and Steady‐State Capture Zones

AbstractThis paper presents analytical solutions for determining non‐steady‐state capture zones produced by a single recovery well and steady‐state capture zones produced by multiple recovery wells. Analysis of non‐steady‐slate capture zones is based on the lime‐dependent location of caplure zone stagnation points and the geometric similarity between steady‐slate and non‐steady‐state capture zones. The analytical solution of steady‐state capture zones is obtained from spatial variations of discharge potential across the capture zone boundary. Both capture zone analyses are based on the assumptions of uniform flow field with a constant hydraulic conductivity, the Dupuit assumption of insignificant vertical flow, a negligible delayed yield, and a fully penetrating well with a constant pumping rate. For a ground water pump‐and‐trcat remediation program, the pumping rate and well location design variables can be adjusted to ensure containment of the ground water contaminant plume.

Effectiveness of a Prolapsed Bird's Nest Filter

The authors evaluated the variable deployment of the Bird's Nest filter, including frequency and extent of prolapse in clinical use, and analyzed the effects of this variability on clot-trapping efficiency with an in vitro model. In the clinical placement of 20 filters, the average length of cephalic filter wires from the center of the filter was measured from radiographs obtained immediately after placement. To analyze the effects of prolapse, a variable-rate pump was used to mimic the effects of respiration on IVC flow. Four clot sizes (5 x 20, 5 x 40, 10 x 20, and 10 x 40 mm) were evaluated with four filter configurations with wires stretched to different lengths in a cephalic direction from the center of the filter: 2 cm (normal-tight), 5 cm (normal-loose), 8 cm (moderate prolapse), and to a maximum of 12 cm (maximum prolapse). Ten passes for each clot size were performed with each filter configuration in both the horizontal and vertical positions. The smallest clots were also tested with a slower constant-rate pump. In clinical use, the average length of the filter wire was 5.4 cm (range, 1.2-9.0 cm). With the variable flow pump, the in vitro degree of prolapse did not significantly decrease the trapping efficiency for any but the smallest (5 x 20-mm) clots, for the maximum prolapse configuration in the horizontal position (P = .01). In addition, for these clot sizes, the filter was more efficient with the slower constant rate compared with the faster variable rate; this difference was only statistically significant in the horizontal position for the maximum prolapse configuration (P = .007). The results suggest that in clinical practice, a prolapsed Bird's Nest Filter remains effective for all but small clots.

Pumping tests in nonuniform aquifers: The radially asymmetric case

An analytical solution for the case of transient, pumping‐induced drawdown in a nonuniform aquifer is presented. The nonuniform aquifer is conceptualized as a uniform matrix into which a disk of anomalous properties has been placed. The disk can be arbitrarily located with respect to the pumping well. This solution can be used to develop considerable insight concerning the nature of drawdown in nonuniform systems. Changes in drawdown are sensitive to the hydraulic properties of a discrete portion of an aquifer for a time of limited duration. After that time, it is virtually impossible to gain further information about those properties. The volume of the aquifer controlling a given increment of drawdown at an observation well increases greatly as the distance between the pumping and observation well increases. At observation wells located at moderate to large distances from the pumping well, this volume is so large that the effect of spatial variations in flow properties may be negligible. In general, drawdown data from wells located at a distance from the pumping well should nicely fit the ideal models of the well hydraulics literature. When combined with previous work, these results demonstrate that constant rate pumping tests are not an effective tool for characterizing lateral variations in flow properties.

Optimal time‐varying pumping rates for groundwater remediation: Application of a constrained optimal control algorithm

A numerically efficient procedure is presented for computing optimal time‐varying pumping rates for remediation of contaminated groundwater described by two‐dimensional numerical models. The management model combines a pollutant transport model with a constrained optimal control algorithm. The transport model simulates the unsteady fluid flow and transient contaminant dispersion‐advection in a two‐dimensional confined aquifer. A Galerkin's finite element method coupled with a fully implicit time difference scheme is applied to solve the groundwater flow and contaminant transport equations. The constrained optimal control algorithm employs a hyperbolic penalty function. Several sample problems covering 5–15 years of remediation are given to illustrate the capability of the management model to solve a groundwater quality control problem with time‐varying pumping policy and water quality constraints. In our example, the optimal constant pumping rates are 75% more expensive than the optimal time‐varying pumping rates, a result that supports the need to develop numerically efficient optimal control‐finite element algorithms for groundwater remediation.

Modélisation physique de l'anesthésie par inhalation

A new physical model simulating the pharmacokinetics of volatile anaesthetics is presented. It consists in a ventilator connected to a water manometer. Gas is removed from the gaseous part of this manometer with a constant rate pump. This gas flow is directed thereafter into three capacitances with valves and pumps : one capacitance only contains air, representing the lungs, and the other two olive oil, representing the visceral and muscle compartments. Halothane, enflurane and isoflurane (1 vol%) were administered to this model with different values of cardiac output and alveolar ventilation. There was good concordance between the values of F A/F I that were measured in this model and those calculated by computer simulation. No correction factor was required. Such a physical model may therefore be used to test new techniques of administration of volatile agents.

Chronic Aminophylline Administration: Effect on Diaphragm Contractility and Fatigue ResistanceIn Vitro

The effects of acute and chronic administrations of aminophylline (AM) on diaphragm contractility and fatigue resistance were examined in 42 rats. In acute experiments (n = 22), the animals received an intravenous bolus of either AM (14 mg/kg; n = 11) or saline (n = 11). Serum AM level was determined 30 min after the bolus (17.8 +/- 0.8 mg/L, SD). In chronic experiments (n = 20), either AM (n = 10) or saline (n = 10) was infused subcutaneously via an osmotic minipump at a constant pumping rate of 2.5 microliters/h. Serum AM level was measured after 2 wk of pump infusion (12.3 +/- 2.0 mg/L, SD). For each animal in both acute and chronic experiments, a muscle strip from the right midcostal diaphragm was placed in an in vitro chamber containing Krebs solution and 12 microM/L curare. For the AM-treated group, AM was added to the tissue bath in a concentration similar to that in the serum. No AM was added to the bath for the control group. Forces were measured isometrically during direct muscle stimulation at different frequencies and standardized to muscle weight. Muscle fatigue was induced by repetitive stimulation at 40 pps, delivered in 330-ms trains, with one train presented each second. With either acute or chronic AM administration, a significant increase in diaphragm contractility was observed (p less than 0.01). In contrast, AM did not affect the rate of force decline during fatigue run.(ABSTRACT TRUNCATED AT 250 WORDS)

Characteristics of the radiation emitted by a pulsed CO2laser with an unstable resonator and an exit mirror with the reflectivity varying over the beam cross section

The energy and the angular divergence of the radiation emitted by a pulsed CO2 laser were determined at a constant pumping rate and for fixed parameters of the resonator using three different semitransparent exit mirrors and varying the thickness of the reflecting layer over the beam cross section. Radiation with a low angular divergence was generated in a wide range of pumping rates using an exit reflector with a smooth distribution of the reflectivity over the beam cross section.

Drawdowns for Constant‐Discharge One‐Dimensional Leaky Aquifer

A new mathematical solution was developed for the constant-discharge boundary condition for one-dimensional horizontal flow under nonsteady conditions in a semi-infinite leaky aquifer. The solution can be used to calculate aquifer drawdowns due to discharge into a line sink as a function of the aquifer parameters transmissivity, leakance, storage coefficient, and distance from the line sink and time since the discharge began. The solution is in the form of exponential and complementary error functions, and the polynomial approximation to the solution is easier to use, computationally, than an existing integral-form solution that requires numerical integration. In the solution, the discharge into the line sink is derived from artesian storage in the aquifer and from vertical leakage through the confining bed from a source bed that is at constant hydraulic head. As an example of its use, the solution could be used to analyze the results of a canal pumping test. In this application, aquifer parameters could be determined by analyzing transient drawdowns that resulted from abruptly lowering the canal water level by means of a constant pumping rate in a canal that incised a confined leaky aquifer.

Interpretation of hydrofrac pressure recordings using a simple fracture mechanics simulation model

Until now, most hydrofrac data interpretations for stress derivation only use singular pressure values of characteristics pressurization phases such as break-down, shut-in or fracture reopening. Valuable information of the total pressure record for hydrofrac propagation during constant-rate pumping tests is neglected. In addition, in most cases the interpretation of the characteristic pressure values is based on idealized assumptions such as elasticity, isotropy and homogeneity of the rock and perfect alignment of the frac direction with principal stresses. This approach per se neglects the fact that real materials such as rocks contain cracks of fractures into which the pressurizing fluid penetrates well before crack propagation. Instability for crack propagation is defined by the stress intensity at the crack tip and the material property fracture toughness. The stress intensity is given by the magnitude of the far-field stresses, the hydraulic pressure in the pressurized borehole section and the pressure distribution within the crack. The latter is generally unknown since it depends on numerous factors such as crack geometry, fluid viscosity, temperature, fluid injection rate and turbulence effects at the crack inlet, etc. The present simple hydrofrac model is an attempt to estimate these effects and to derive crustal stresses on the basis of fracture mechanics. The model will allow the estimation of the pressure drop at the fracture inlet and the pressure distribution within the hydraulic fracture. The model also yields quantitative information on elastic energy consumption during discrete crack growth as well as rock mass permeability data away from the disturbed region around the borehole.

Cycle Optimization Involving the Use of Filter Aids

ABSTRACT A method for optimizing the quantity of filter aid powders used In constant rate pumping operations In plate and frame, recessed plate, and leaf filters Is presented. In contrast to the usual assumption that there Is a fixed fraction of filter aid admix which yields the best results, we demonstrate that the optimum amount of filter aid varies with cake thickness, washing and dead times, and use of a membrane for expression or simply pressing out residual slurry In a filter press at the end of filtration. The specific problem treated in this paper relates to the adaptation of a constant rate pump to an existing filter equipped with cake squeezing membranes. The separation is limited by a specified pressure, and the maximum cake thickness Is fixed by the filter geometry. The optimum fraction of filter aid rises as cake thickness Increases.

Results of pumping tests in the Deccan Trap Basalts of Central India

The Satpura Hills Region of Central India is characterized by hilly to mountainous terrain, plateaus, and gently undulating country. The area is underlain by basalt, crystalline rocks and sandstone. Basalt rocks of Cretaceous age outcrop over about 60% of the area. During the past 14 years the authors, through their association with the Evangelical Lutheran Church (ELC) Water Development Project, have been involved in the development of groundwater resources for village, town, agricultural, and industrial uses. To date, over 700 wells have been drilled in the basalt rocks and aquifer pumping tests have been run on more than 200 wells. As a result of the controlled testing and detailed analysis of these pumping tests, it was possible to evaluate the applicability of standard analytical models for the analysis of pumping tests in basalt-rock aquifers. Step-drawdown pumping tests were run to determine the components of drawdown due to aquifer loss and well loss. Step-test data were analyzed by Rorabaugh's (1953) method and by a graphical method. The results indicate that well losses comprise a significant component of drawdown in most wells and these losses are probably a result of non-Darcian flow in the aquifer adjacent to a pumped well. Constant-rate pumping tests were run to determine aquifer transmissivity and specific capacity. Time-drawdown data were analyzed by the Cooper-Jacob (1946) approximation to the Theis (1935) equation and recovery data were analyzed by the residual-drawdown method. Aquifer transmissivity ranged over two to three orders of magnitude from less than 10m 2 day −1 to more than 300m 2 day −1. Pumping test results often enabled the prediction of aquifer conditions such as limited aquifers, recharge boundaries and aquifer dewatering.