Instantaneous Drainage Research Articles

Use of microgravity for identification of delayed gravity drainage and conceptual model selection in unconfined aquifers

The estimation of hydraulic parameters at the aquifer scale typically relies in the analysis of pumping tests. Drawdown data, from a frequently limited number of boreholes and piezometers, is used in conjunction with analytical formulas derived for conceptually simplified models in a history matching procedure. In unconfined aquifers it is well known that the drainage process is controlled by the unsaturated zone. Several models have been proposed in the literature for the calculation of drawdown caused by pumping. Approaches range from the assumption of instantaneous and complete drainage to the inclusion of a delay term or the full implementation of the unsaturated zone to represent the delayed drainage in the unsaturated zone. Because borehole drawdown data is not informative about the unsaturated zone processes, it is common for practitioners to rely in the simplest models available, usually in some pumping test interpretation software. For example, Neuman’s instantaneous drainage model is still widely used in the industry even when it has been demonstrated that under some circumstances provides incorrect estimations of key aquifer parameters. Additionally, as boreholes are scarce, spatial information is ignored and conceptual assumptions of axial-symmetry are a normal practice. In this work we show how the use of microgravity instruments, sensitive to storage variations in the near subsurface, could be a simple, cheap and convenient tool for the identification of delayed drainage processes in unconfined aquifers. The joint use of drawdown and gravity data can be utilized to select the most preferable conceptual model for the parameter estimation problem.

On Inflow to a Tunnel in a Fractured Double-Porosity Aquifer.

Inflow to a tunnel is a great public concern and is closely related to groundwater hydrology, geotechnical engineering, and mining engineering, among other disciplines. Rapid computation of inflow to a tunnel provides a timely means for quickly assessing the inflow discharge, thus is critical for safe operation of tunnels. Dewatering of tunnels is another engineering practice that should be planned. In this study, an analytical solution of the inflow to a tunnel in a fractured unconfined aquifer is obtained. The solution takes into account either the spherical or slab-shaped matrix block and the unsteady state interporosity flow. The instantaneous drainage water table and anisotropic hydraulic conductivities of the fractures network are also considered. Both uniform flux and uniform head boundary condition are considered to simulate the constant head boundary condition in the tunnel. The effects of the hydraulic parameters of the fractured aquifer on the inflow variation of the tunnel are explored. The application of the presented solution to obtain the optimum location and discharge of the well to minimize the inflow to a tunnel is illustrated.

Groundwater flow to a well in a strip-shaped unconfined-fractured aquifer system with a transition zone

Semi-infinite unconfined-fractured strip shaped aquifer systems are common in alluvial plain margins, but have received little attention in the hydrogeological community. Thus, the aim of this study is to present semi-analytical solutions of flow to a well in these aquifer systems. Two conceptual models are considered: 1-An unconfined aquifer with a lateral fractured aquifer and a pumping well installed in the unconfined aquifer (model I); 2-An unconfined aquifer with a lateral fractured aquifer and a pumping well installed in the fractured aquifer (model II). A transition zone is considered between two aquifers. Three-dimensional groundwater flows are considered in unconfined, fractured and transition zone aquifers. Homogeneous, anisotropic hydraulic conductivity and instantaneous drainage water table condition are assumed first but can be relaxed to accommodate delayed drainage water table condition if needed. The point sink/source solutions are obtained via finite and infinite Fourier transforms for space and Laplace transform for time. The line sink/source solutions are obtained via integration along the desired direction. The uniform flux and uniform head boundary conditions are considered for the pumping well. The vertical distribution of the flux toward the well screen is explored. The effects of inner well condition on the variation of the dimensionless drawdown and boundary depletion volume are investigated. We investigate the influences of the hydraulic parameters of the transition zone on the spatial and temporal variations of the sensitivity of the drawdown to hydraulic parameters of the aquifer system. Furthermore, the influences of the transition zone on the spatial distribution of the drawdown are explored. The results of this study can be utilized to evaluate head distribution in the aquifer system; to calculate the water budget of the alluvial aquifers near a fractured one; to analyze the influences of a transition zone on the head and flow distribution in the aquifer system.

Groundwater flow to a general well configuration in an unconfined aquifer overlying a fractured bedrock

Unconfined aquifers sometimes overlie fractured bedrocks, consisting of unconfined-fractured aquifer systems. Pumping induced hydrodynamics in such aquifer systems has not received much attention as in other types of aquifer systems. This paper aims to obtain semi-analytical solutions of flow to a general well configuration in such an unconfined-fractured two-layer aquifer system. The examples of general well configuration, specifically discussed here, include: 1) a horizontal well, 2) a vertical well, 3) a vertical well with one horizontal collector, and 4) a vertical well with two horizontal collectors which are perpendicular with each other. The methodology is general and can be extended to other types of wells with minor modifications of solutions developed in this study. The point sink/source solution is first obtained using double infinite Fourier and Laplace transformations (where sink is for pumping and source is for injection). The line sink/source solution is then obtained via integrating the point sink/source along the desired direction and following the principle of superposition. The de Hoog numerical inverse Laplace transform and Gaussian Quadrature are used to obtain time-domain dimensionless drawdown solutions. The instantaneous drainage of water table and the inter-porosity flow of the underlying fractured aquifer are taken into account. The effects of the length of horizontal well on dimensionless drawdown and dimensionless drawdown derivative, and scaled sensitivity of the hydraulic parameters of the underlying fractured aquifer are explored. The dimensionless drawdowns and drawdown derivatives of a vertical pumping well, a vertical well with a single horizontal collector and a vertical well with two perpendicular horizontal collectors are also compared. The scaled sensitivity of dimensionless drawdown to the hydraulic parameters of the underlying fractured aquifer of these different pumping well structures is explored. The results of this study can be used to evaluate the hydraulic parameters using the drawdown data collected during a pumping test performed in a general well configuration in a unconfined-fractured two-layer aquifer system. Furthermore, the presented solutions can be utilized to design the pumping well to minimize drawdown in low-permeability or thin aquifers. By eliminating the inter-porosity flow term from the underlying fractured aquifer, the solutions are applicable to groundwater flow to a pumping well in leaky aquifers.

Characterizing infiltration and internal drainage of South African dryland soils

AbstractSurface infiltration and internal drainage properties of five soil types from arid drylands of South Africa were studied under double ring infiltrometer, rainfall simulation plots (1 m2) and instantaneous drainage plots (9 m2). Changes in soil water content during 40 minute rainfall simulation for a rainstorm with average intensity of 1.61 mm min−1 and 30 day drainage period were measured at various depths by 1.5 m long capacitance soil water measuring (DFM) probe. Different (P < 0.05) mean surface steady infiltration rate ranged from 0.05 to 4.47 mm min−1 and had a negative power relationship (R2 = 0.65) with horizon clay plus fine silt content. Power regression (R2 ≥ 86%) described rainstorm infiltration and obtained steady rates within an average time of 15 minutes. Mean total infiltrated soil water content was lowest (P < 0.05) from surface horizons with either 47.7% clay plus fine silt content or bulk density of 1.91 g cm−3 and exchangeable sodium of not less than 44 mg kg−1. Surface horizons with lower surface bulk density and total sand fraction of more than 72% had infiltrated depth and mean total infiltrated soil water content up to 40 cm deeper and 0.55 mm mm−1 greater, respectively. Drainage rate at drained upper limit calculated from the Wilcox drainage model (R2 ≤ 0.97%) was 0.2 mm day−1 or less were from underlying horizons with either clay plus fine silt of 45% or soft calcium carbonate. Higher drainage rate with accumulative drainage amount greater than 60 mm were from soil profile horizons with clay plus fine silt content of less than 20% and above unity steady infiltration rates. Rainstorm infiltration and drainage rates was shown to depend on permeability and coarseness of the respective soil surface and subsurface horizons; a phenomenon critical for harnessing rain and flood water to recharge groundwater. Copyright © 2016 John Wiley & Sons, Ltd.

Gravity Drainage Visualization Experimental Study of Heavy Oil Reservoirs

Liaohe oilfield gravity drainage assisted steam flooding of heavy oil reservoir has made significant development effect, but the drain rule of condensate is unclear in the process of development. Heavy oil drainage microscopic visualization experimental study of using core model of glass etching, drainage process simulation of heavy oil reservoir and its influence factors were analyzed. Its method turns the drainage process of images into computer numerical signal through the image acquisition system, intuitive display flow pattern of drainage, and analyses the influence of homogeneity and the pressure differential regulation of drainage through the experimental data. The experiment results show that condensate around the steam chamber has a corresponding drainage channel, not uniform or diarrhea in the gravity drainage assisted steam flooding process. At the beginning of the drainage channels formation, the instantaneous drainage amount along with the change of pressure difference is not obvious. Instantaneous drainage amount increases with increasing pressure difference in the medium term. It tends to be stable in the later. The time of drainage channels to form homogeneous core is earlier than heterogeneous core. After the drainage channel, differential effects on heterogeneous core than homogeneous core of instantaneous drainage water.

In situ evaluation of internal drainage in duplex soils of the Tukulu, Sepane and Swartland forms

Internal drainage is a critical hydrological process in soil water conservation. Pedological and physical properties of the South African Tukulu, Sepane and Swartland soil types were studied in respect to soil water storage and hydraulic characteristics during internal drainage. Soil profiles were excavated and classified in situ alongside instantaneous drainage plots and saturated hydraulic conductivity experiments. Laboratory desorption experiments were used to establish the soil water characteristic curves (SWCC) of diagnostic horizons. Each SWCC was then fitted with the van Genuchten 1980 model and matric suction of soil water content corresponding to the 1 200 hours drainage curves were estimated. The pedocutanic B and prismatic C horizons in the Tukulu and Sepane soils had clay plus silt content of more than 40% and were characterised by abrupt transitions, signs of wetness and a sharp drop in hydraulic conductivity at higher soil water content. Consequently, deep drainage from the Tukulu and Sepane was about 40% less than that of the Swartland. The drained upper limit was located when drainage flux rate approached 0.001 mm h−1 irrespective of soil type. At this rate deep drainage losses over the seven-month fallow period are equivalent to 1% annual rainfall.

Semi-analytical solutions for flow to a well in an unconfined-fractured aquifer system

Semi-analytical solutions of flow to a well in an unconfined single porosity aquifer underlain by a fractured double porosity aquifer, both of infinite radial extent, are obtained. The upper aquifer is pumped at a constant rate from a pumping well of infinitesimal radius. The solutions are obtained via Laplace and Hankel transforms and are then numerically inverted to time domain solutions using the de Hoog et al. algorithm and Gaussian quadrature. The results are presented in the form of dimensionless type curves. The solution takes into account the effects of pumping well partial penetration, water table with instantaneous drainage, leakage with storage in the lower aquifer into the upper aquifer, and storativity and hydraulic conductivity of both fractures and matrix blocks. Both spheres and slab-shaped matrix blocks are considered. The effects of the underlying fractured aquifer hydraulic parameters on the dimensionless drawdown produced by the pumping well in the overlying unconfined aquifer are examined. The presented solution can be used to estimate hydraulic parameters of the unconfined and the underlying fractured aquifer by type curve matching techniques or with automated optimization algorithms. Errors arising from ignoring the underlying fractured aquifer in the drawdown distribution in the unconfined aquifer are also investigated.

Saturated–unsaturated flow in a compressible leaky-unconfined aquifer

An analytical solution is developed for three-dimensional flow towards a partially penetrating large-diameter well in an unconfined aquifer bounded below by a leaky aquitard of finite or semi-infinite extent. The analytical solution is derived using Laplace and Hankel transforms, then inverted numerically. Existing solutions for flow in leaky unconfined aquifers neglect the unsaturated zone following an assumption of instantaneous drainage due to Neuman. We extend the theory of leakage in unconfined aquifers by (1) including water flow and storage in the unsaturated zone above the water table, and (2) allowing the finite-diameter pumping well to partially penetrate the aquifer. The investigation of model-predicted results shows that aquitard leakage leads to significant departure from the unconfined solution without leakage. The investigation of dimensionless time-drawdown relationships shows that the aquitard drawdown also depends on unsaturated zone properties and the pumping-well wellbore storage effects.

The interaction between the unsaturated zone, aquifer, and stream during a period of groundwater withdrawal

► Specific yield estimates from analyses of core drainage and pumping tests coincide. ► Water release can be reproduced by Moench/Boulton type model. ► Pumping test estimate of specific yield depends on water release assumption. ► Assuming instantaneous drainage leads to biased specific yield estimate. ► Only prediction of early stream depletion depends on water release assumption. By combining laboratory and field experiments we study the release of water from above a falling water table and the implications this has on pumping test analysis and prediction of stream depletion. Undisturbed core samples from the field site were used in laboratory experiments to measure drainage responses to water-table drawdown. The responses can be sufficiently modeled by estimating the specific yield and five exponential time constants of a Moench/Boulton type model of delayed drainage. The average specific yield is thus estimated to 0.24 which is in agreement with previous small scale and large scale estimates. In addition two pumping tests were conducted near the stream. The drawdown analysis was made using a 3D numerical groundwater flow model facilitating use of the Moench/Boulton type boundary condition at the water table. The drawdown observations were fitted by calibrating two alternative models: one simulating the release of water at the water table as instantaneous; the other simulating the release of water as delayed. Comparing the calibration results for the two alternative models showed that they fit the drawdown observations nearly equally well, and most estimated parameter values are realistic and nearly identical. However, estimation of the specific yield is found to be sensitive to whether drainage is modeled as instantaneous or as delayed. In the first case the estimated specific yield is about half of the estimate from the core experiments and of the previous estimates; in the second case the estimate (0.17) is in better agreement with core and previous estimates (0.24). The analysis indicates that relatively fast drainage, and the existence of two drawdown dependent sources of groundwater recharge (the storage and the stream), complicates pumping test design to obtain unique parameter estimation. The analysis supports that an essential factor in parameter estimation by pumping test analysis for (at least some) unconfined aquifers is the use of a model that accounts for time-varying drainage from the vadose zone. Finally, when predicting stream depletion beyond 1 day of pumping it is acceptable in the present case to use a model simulating drainage as instantaneous if unbiased parameter estimates are used.

Three-dimensional semi-analytical solution to groundwater flow in confined and unconfined wedge-shaped aquifers

The Laplace domain solutions have been obtained for three-dimensional groundwater flow to a well in confined and unconfined wedge-shaped aquifers. The solutions take into account partial penetration effects, instantaneous drainage or delayed yield, vertical anisotropy and the water table boundary condition. As a basis, the Laplace domain solutions for drawdown created by a point source in uniform, anisotropic confined and unconfined wedge-shaped aquifers are first derived. Then, by the principle of superposition the point source solutions are extended to the cases of partially and fully penetrating wells. Unlike the previous solution for the confined aquifer that contains improper integrals arising from the Hankel transform [Yeh HD, Chang YC. New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions. Adv Water Resour 2006;26:471–80], numerical evaluation of our solution is relatively easy using well known numerical Laplace inversion methods. The effects of wedge angle, pumping well location and observation point location on drawdown and the effects of partial penetration, screen location and delay index on the wedge boundary hydraulic gradient in unconfined aquifers have also been investigated. The results are presented in the form of dimensionless drawdown-time and boundary gradient-time type curves. The curves are useful for parameter identification, calculation of stream depletion rates and the assessment of water budgets in river basins.

Quantitative measurements of liquid holdup and drainage in foam using NMRI

AbstractLiquid fraction profiles of a column of draining aqueous foam stabilized with sodium dodecyl sulfate were studied by nuclear magnetic resonance imaging (NMRI) at high spatial and temporal resolution. It was observed that the liquid holdup in the column is not locally homogeneous in the direction of the column axis with liquid holdup exhibiting periodic variation in time. This creates “ripples” in the liquid content profiles (that is, an approximately sinusoidal variation of liquid fraction in space). These ripples are seen to actually rise in the column as liquid drains down through the foam. This behavior may be explained by a simple mass balance: the rising velocity of the ripples multiplied by the gas fraction in the foam is equivalent to the liquid superficial drainage rate. Thus, NMRI is proposed as a powerful tool for studying drainage of foams because it provides a noninvasive method of measuring superficial drainage rate in foams that yields time‐resolved instantaneous drainage rates as a function of position in the column. The measured liquid drainage rates were compared with a dimensionless expression for the liquid drainage rate and excellent agreement was achieved. © 2006 American Institute of Chemical Engineers AIChE J, 2007

Pumping-induced vadose zone drainage and storage in an unconfined aquifer: A comparison of analytical model predictions and field measurements

Analytical models used to analyze hydraulic head data from pumping tests incorporate boundary conditions defined along the water table to account for drainage from the overlying vadose zone. Although these boundary conditions do not explicitly describe the details of flow in the vadose zone, they do specify a bulk vadose zone response. We have quantified this response in terms of the cumulative drainage flux through the water table and undrained vadose zone storage. A comparison of bulk vadose zone response predicted by analytical models and inferred from field measurements was performed using hydraulic head data and soil moisture content profiles obtained during a seven day pumping test at CFB Borden, Ontario. Three different analytical models (one assuming instantaneous drainage and two types of delayed drainage using exponential decay functions) were used to predict the bulk vadose zone response from the hydraulic head measurements. The pumping test analyses using these models gave reasonable values for aquifer parameters, and the model predictions of the transient hydraulic head response replicated the observed hydraulic head data. However, there are significant differences between the model predictions and field observations of the bulk vadose zone response. The instantaneous drainage model entirely neglected the substantial undrained storage that was observed. In the vicinity of the pumping well, the delayed drainage models significantly overestimated the cumulative drainage flux and underestimated the undrained storage determined from the field data. The delayed drainage models predicted a relatively rapid dissipation of the undrained storage while the observed undrained storage exhibited little, if any, decay throughout the entire pumping test. Our results indicate that the water table boundary conditions used in these analytical models do not adequately replicate the mechanisms controlling the vadose zone behavior during a pumping test.

Importance of the Vadose Zone in Analyses of Unconfined Aquifer Tests

Analytical models commonly used to interpret unconfined aquifer tests have been based on upper-boundary (water table) conditions that do not adequately address effects of time-varying drainage from the vadose zone. As a result, measured and simulated drawdown data may not agree and hydraulic parameters may be inaccurately estimated. A 72-hour aquifer test conducted in Cape Cod, Massachusetts, in a slightly heterogeneous, coarse-grained, glacial outwash deposit was found to be a good candidate for testing models with different upper-boundary conditions. In general, under the commonly invoked assumption of instantaneous drainage, measured and simulated drawdowns were found to agree with one another only at late time and early time. In the intermediate-time range, because of delayed drainage, measured drawdowns always exceeded simulated values, most noticeably in piezometers located near the water table. To reduce these discrepancies, an analytical model was developed that can fully account for time-varying drainage given that the aquifer is not strongly heterogeneous. The approach is flexible as the model, which makes use of empirical relations, does not constrain drainage to follow any particular functional relation. By this approach, measured and simulated drawdowns agree over the complete time range, and the estimated parameters are consistent with prior studies and with what is known about the aquifer geometry, stratigraphy, and composition. By properly accounting for vadose zone drainage, it was found that realistic estimates of all hydraulic parameters, including specific yield, could be obtained with or without the use of late-time data.

Analysis of compartmental models of type 4 nuclear renograms with calculation of flow rate parameters and instantaneous drainage rates.

To estimate the dynamic rates of arterial delivery and renal drainage in renograms with the Homsy sign, using optimized computed compartmental modelling. Eleven F-15 renograms and one F+15 renogram (using 99mTc-mercaptoacetyltriglycine) with the Homsy sign were studied, with 26 controls. Compartmental models were constructed for each renogram using components (blood, renal, bladder) linked by variables (arterial rate, drainage rate). Each model was optimized using the Marquadt least-squares method to numerical data from the time-activity curves (TACs). The model renal component at sample points along the TAC was minimized and the corresponding drainage rates calculated. The models were optimized, with a mean (range) r2 of 0.811 (0.68-0.88). There were continuous low drainage rates for all type 4 renograms, with no quadrupling of the flow rate, as predicted by the standard model. The standard model is unlikely to be correct and the Homsy sign is probably an artefact seen in patients with impeded urinary drainage. Computer modelling of individual renograms is feasible and can provide useful insights into the pathophysiology of renal uptake and drainage.

Groundwater flow to a horizontal or slanted well in an unconfined aquifer

New semianalytical solutions for evaluation of the drawdown near horizontal and slanted wells with finite length screens in unconfined aquifers are presented. These fully three‐dimensional solutions consider instantaneous drainage or delayed yield and aquifer anisotropy. As a basis, solution for the drawdown created by a point source in a uniform anisotropic unconfined aquifer is derived in Laplace domain. Using superposition, the point source solution is extended to the cases of the horizontal and slanted wells. The previous solutions for vertical wells can be described as a special case of the new solutions. Numerical Laplace inversion allows effective evaluation of the drawdown in real time. Examples illustrate the effects of well geometry and the aquifer parameters on drawdown. Results can be used to generate type curves from observations in piezometers and partially or fully penetrating observation wells. The proposed solutions and software are useful for the parameter identification, design of remediation systems, drainage, and mine dewatering.

A Microlysimeter Field Study of Solute Transport through a Structured Sandy Loam Soil

AbstractA 49‐d field experiment monitoring water and solute movement through a structured sandy loam is reported. Two field plots, each 15 by 30 m2 in area were instrumented with a 3 by 6 grid of small lysimeters containing undisturbed soil. Each lysimeter was weighed before and after irrigation and had effluent concentrations and drainage volumes recovered periodically. At the beginning of the experiment a pulse of KBr was added to the field and lysimeters with a mechanical lawn spreader and was leached into the soil with three water irrigations per week. Each plot received the same amount of water per irrigation but at intensities of 5.5 and 9.5 mm/h. Effluent breakthrough curves were constructed for each lysimeter. Substantial indication of preferential flow through part of the wetted pore space was observed in each lysimeter and the average breakthrough curves reflected substantial bypass. A statistical analysis of the drainage concentrations as a function of time showed the two fieldwide breakthrough curves to be identical. This not only showed that no intensity effect was apparent for solute movement on these plots but also indicated that the plot areas were large enough to incorporate all of the field scale variability within them. A calculation of solute flux from each lysimeter showed no correlation between instantaneous drainage and instantaneous solute concentration. As a consequence, we were able to show that the traditional method of estimating field scale solute flux as the product of average drainage and average concentration was adequate to describe solute leaching below the fields. Thirty‐six soil cores were taken in the two plots at the conclusion of the experiment. The average concentration depth patterns were similar for the two treatments and showed evidence of movement to at least 1.2 m during the lifetime of the experiment, implying that preferential flow continued to occur to greater depths.