Effects Of Partial Penetration Research Articles

Semi-analytical solution to pumping test data with barrier, wellbore storage, and partial penetration effects

There exist some difficulties in determining aquifer parameters based on pumping test data within a partially penetrated retaining walls using traditional Cooper-Jacob method. Many other site-specific factors, such as the effect of partially penetrating well and the large diameter of the wells, cannot easily be accommodated in theoretical well formulae. The semi-log drawdown-time curves affected by the effects of barrier, wellbore storage, and partial penetration well can be characterised by four distinct stages of drawdown: i) Stage I, drawdown is unaffected by the barrier, ii) Stage II, drawdown is significantly influenced by the barrier, iii) Stage III, the drawdown-time curve runs parallel to that deduced from greenfield conditions, and iv) Stage IV, the drawdown becomes a constant value. To handle the four distinct stages of drawdown, a semi-analytical method using the slope of the late-time drawdown asymptote of Stage III for determining the transmissivity is proposed. The horizontal intercept, resulting from an extension of the late-time drawdown asymptote from Stage II, is used for determining the storage coefficient. Pumping test data from a case history are analysed using the proposed semi-analytical method, and the results obtained are compared with those deduced from the numerical simulation. The comparison between the analytical results and those obtained from the numerical simulation appeared satisfactory.

Multidepth Pumping Tests in Deep Aquifers

Multidepth pumping tests (MDPTs), in which different sections of a screen are pumped in sequence, are not being used by hydrogeologists, despite the capability of such tests to resolve uncertainties in the estimation of aquifer characteristics. MDPTs can be used to discern the effects of partial penetration and vertical anisotropy. This article demonstrates the use of MDPTs for a deep and vertically anisotropic aquifer, based on a real and unique series of pumping tests conducted in the Indus Basin. Traditional single-layer methods, which incorporate partial penetration and vertical scaling, were employed to evaluate these tests. However, the drawdowns of the 19 piezometers at different depths for which times series data were available could not be matched, presumably because of the layered structure of the aquifer. Numerical (MODFLOW) and multilayer analytical (Hemker and Maas 1987; Hemker 1999) approaches were used to assess the benefits of using MDPTs in the analysis of deep layered and anisotropic aquifers. The multilayer analytical solution results are consistent with the measured and numerically computed drawdowns. The original step-drawdown data were used to verify the model independently. The results of statistical analyses indicate that the parameters for a three-layer system are uniquely estimated. A sensitivity analysis showed that aquifer depths greater than 900 m do not affect the drawdown. The multilayer analytical solution was implemented in MATLAB and can be found in the online version of this article. This multilayer analytical approach was implemented in MLU by Hemker and Randall (2013) for up to 40 layers. The results of this study will be useful in groundwater management, exploration, and optimal well depth estimation for the Indus Basin aquifer and other vertically heterogeneous aquifers.

A simple data reduction method for pumping tests with tidal, partial penetration, and storage effects

Single-well and group-well pumping tests were undertaken in a deep gravel formation of the Taipei basin to determine the hydraulic parameters and better understand the drawdown characteristics across the basin. The periodic drawdown fluctuation due to tidal loading from the overlying river resulted in a difficulty in determining the hydraulic parameters by those conventionally used graphic techniques. In addition, many other site-specific influencing factors, such as the partial penetration effect and the large diameter of the wells, had to be considered. In this paper, a simple data reduction method was presented to resolve the above-mentioned complications. It was demonstrated that the drawdown data induced by group-well pumping were well predicted using the shifted drawdown curve deduced by the proposed method.

Radial flow to a partially penetrating well with storage in an anisotropic confined aquifer

Drawdowns generated by extracting water from large diameter (e.g. water supply) well are affected by wellbore storage. We present an analytical solution in Laplace transformed space for drawdown in a uniform anisotropic aquifer caused by withdrawing water at a constant rate from partially penetrating well with storage. The solution is back transformed into the time domain numerically. When the pumping well is fully penetrating our solution reduces to that of Papadopulos and Cooper, 1967, Hantush, 1964 when the pumping well has no wellbore storage; Theis (1935) when both conditions are fulfilled and Yang (2006) when the pumping well is partially penetrating, has finite radius but lacks storage. Newly developed solution is then used to explore graphically the effects of partial penetration, wellbore storage and anisotropy on time evolutions of drawdown in the pumping well and in observation wells. We concluded after validating the developed analytical solution using synthetic pumping test.

Well function curves for different geometric situations in a large-diameter well

Movement and abstraction of groundwater in the geological formations are dependent on the hydro-geological parameters of the aquifers. The purpose of any aquifer test is to determine the hydro-geological parameters. Among the basic parameters are the specific storage, permeability and leakage coefficients. The hydro-geological parameters are hidden in the field test data and their identification is possible using the available physically plausible models suitable for the prevailing field circumstances. In this context, a generalized theoretical solution for the effect of partial penetration superimposed over the full penetration on draw-down in a large-diameter well in artesian aquifer discharging at a constant rate has been presented for non-dimensional quantities describing the variable geometries of wells. The well-function curves are developed by varying the percentage amount of drilling and the percentage amount of casing lowered which then control to vary the percentage amount of open-hole or screened interval for the three categories: when the diameter of the cased interval in which the water level changes is greater than, equal to, and less than the diameter of the open interval. The skin effect and the effect of leakage are neglected. A comparison of results with the published works has also been presented. The present study is useful in such areas where wells are located either in harder or in collapsible loose formations; and a decision is required that, at the planning, construction, or development stage, as to what extent the amount of drilling be reduced, and/or an additional amount of casing be lowered within the aquifer. Also this reduces the cost of well construction and development in a specific situation.

A User Interface for the Kansas Geological Survey Slug Test Model

The Kansas Geological Survey (KGS) developed a semianalytical solution for slug tests that incorporates the effects of partial penetration, anisotropy, and the presence of variable conductivity well skins. The solution can simulate either confined or unconfined conditions. The original model, written in FORTRAN, has a text-based interface with rigid input requirements and limited output options. We re-created the main routine for the KGS model as a Visual Basic macro that runs in most versions of Microsoft Excel and built a simple-to-use Excel spreadsheet interface that automatically displays the graphical results of the test. A comparison of the output from the original FORTRAN code to that of the new Excel spreadsheet version for three cases produced identical results.

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.

Computations of AC Loss in the ITER Magnets During Fast Field Transients

The calculation of AC loss due to the control currents in ITER is a cumbersome task. The reason is that control transients require small field changes (0.1 T or less) at moderate frequency (up to 10 Hz), where effects of partial penetration of the filaments and shielding are important and need to be taken into account to produce sound AC loss estimates. In this paper we describe models developed for AC loss calculation, in particular hysteresis and coupling current loss, that are suitable for the above regime. Both hysteresis and coupling loss models are adapted to the conductor analysed through few parameters (the effective filament diameter and time constants) that can be derived from measurement of loss on short samples. We report an example of calculations of AC loss in the ITER TF and PF coils for two vertical control scenarios (VS1 and VS2) during high beta operation at flattop.

A closed form solution for constant flux pumping in a well under partial penetration condition

An analytical model for the constant flux pumping test is developed in a radial confined aquifer system with a partially penetrating well. The Laplace domain solution is derived by the application of the Laplace transforms with respect to time and the finite Fourier cosine transforms with respect to the vertical coordinates. A time domain solution is obtained using the inverse Laplace transforms, convolution theorem, and Bromwich integral method. The effect of partial penetration is apparent if the test well is completed with a short screen. An aquifer thickness 100 times larger than the screen length of the well can be considered as infinite. This solution can be used to investigate the effects of screen length and location on the drawdown distribution in a radial confined aquifer system and to produce type curves for the estimation of aquifer parameters with field pumping drawdown data.

A flowing partially penetrating well in a finite-thickness aquifer: a mixed-type initial boundary value problem

An analytical approach using integral transform techniques is developed to deal with a well hydraulics model involving a mixed boundary of a flowing partially penetrating well, where constant drawdown is stipulated along the well screen and no-flux condition along the remaining unscreened part. The aquifer is confined of finite thickness. First, the mixed boundary is changed into a homogeneous Neumann boundary by discretizing the well screen into a finite number of segments, each of which at constant drawdown is subject to unknown a priori well bore flux. Then, the Laplace and the finite Fourier transforms are used to solve this modified model. Finally, the prescribed constant drawdown condition is reinstated to uniquely determine the well bore flux function, and to restore the relation between the solution and the original model. The transient and the steady-state solutions for infinite aquifer thickness can be derived from the semi-analytical solution, complementing the currently available dual integral solution. If the distance from the edge of the well screen to the bottom/top of the aquifer is 100 times greater than the well screen length, aquifer thickness can be assumed infinite for times of practical significance, and groundwater flow can reach a steady-state condition, where the well will continuously supply water under a constant discharge. However, if aquifer thickness is smaller, the well discharge decreases with time. The partial penetration effect is most pronounced in the vicinity of the flowing well, decreases with increasing horizontal distance, and vanishes at distances larger than 1–2 times the aquifer thickness divided by the square root of aquifer anisotropy. The horizontal hydraulic conductivity and the specific storage coefficient can be determined from vertically averaged drawdown as measured by fully penetrating observation wells. The vertical hydraulic conductivity can be determined from the well discharge under two particular partial penetration conditions.

Well Test Analysis of Multi-Layered Naturally Fractured Reservoirs with Variable Thickness and Variable Fracture Spacing

Introduction. This technical note is a synopsis of paper 2001–091. The readers are referred to the full-length paper for additional details, nomenclature and illustrations. Outcrop information, cores, images, and well logs have shown that in some cases, naturally fractured reservoirs are composed of many layers(1). The thinner the layer, the smaller the fracture spacing (or distance between natural fractures). This is illustrated in Figure 1, which is a photo of the Cardium sandstone outcrop at Seebe Dam near Calgary, Alberta.For this type of reservoir, some fractures may be intersected by the wellbore and others may not, as is shown in the schematic of Figure 2. A production log would show only the fluid entrance points into the wellbore.The production log would not give an indication of net pay in this naturally fractured reservoir, only an indication of where the wellbore intersects the most important fractures.It is not unusual to see, from a production log, that out of 30 m perforated in a fractured reservoir, only 2 to 3 m contribute production into the wellbore, even if the 30 m are true net pay. This is the result of a typical situation that occurs in most naturally fractured reservoirs we are familiar with; i.e., the matrix has a very low permeability, which does not permit efficient fluid flow into the wellbore. This same tight matrix, however, can flow very efficiently into the natural fractures(1). Various papers have contributed to our understanding of transient behaviour in multi-layered reservoirs(2–6).Aguilera et al.(7) evaluated data from the naturally fractured Palm Valley gas field using analytical and numerical simulation techniques. Both approaches provided approximately the same results. In a subsequent paper, Aguilera(8) used a numerical simulator to examine the behaviour of a naturally fractured reservoir with ten layers and with fracture permeabilities ranging between 6.91 and 1,232.41 mD. The geometric mean permeability was 40 mD. The thickness of each layer (1.6 m) and the fracture spacing (3.35 m) were constant. From this analysis, it was concludedthat multi-layered behaviour could be recognized by a pressure derivative indicating partial penetration effects, even if the well was perforated in all layers. The partial penetration effects correspond to a derivative with a slope equal to about - 0.5. This was followed by an indication of linear flow; i.e., aslope of the pressure derivative equal to approximately +0.5. This technical note is a continuation of the research published by Aguilera(8). In the present paper, we are using the same numerical model, but in addition to variations in fracture permeability, we include variations in layer thickness, fracture spacing, and fracture porosity(9).FIGURE 1: Outcrop of the Cardium sandstone showing variations in layer thickness and fracture spacing (Seebe Dam, Alberta, Canada). Width of shown outcrop is approximately 25 m.Results. Most reservoir parameters have been kept as in the previous study(8). Pay thickness for the reservoir is 16 m. Matrix porosity is 4.8% Matrix permeability is 0.023 mD. Gas saturation in the matrix is 42%, and gas saturation in the fractures is 99%.

Well Test Analysis of Multi-Layered Naturally Fractured Reservoirs with Variable Thickness and Variable Fracture Spacing

Introduction This technical note is a synopsis of paper 2001–091. The readers are referred to the full-length paper for additional details, nomenclature and illustrations. Outcrop information, cores, images, and well logs have shown that in some cases, naturally fractured reservoirs are composed of many layers(1). The thinner the layer, the smaller the fracture spacing (or distance between natural fractures). This is illustrated in Figure 1, which is a photo of the Cardium sandstone outcrop at Seebe Dam near Calgary, Alberta. For this type of reservoir, some fractures may be intersected by the wellbore and others may not, as is shown in the schematic of Figure 2. A production log would show only the fluid entrance points into the wellbore. The production log would not give an indication of net pay in this naturally fractured reservoir, only an indication of where the wellbore intersects the most important fractures. It is not unusual to see, from a production log, that out of 30 m perforated in a fractured reservoir, only 2 to 3 m contribute production into the wellbore, even if the 30 m are true net pay. This is the result of a typical situation that occurs in most naturally fractured reservoirs we are familiar with; i.e., the matrix has a very low permeability, which does not permit efficient fluid flow into the wellbore. This same tight matrix, however, can flow very efficiently into the natural fractures(1). Various papers have contributed to our understanding of transient behaviour in multi-layered reservoirs(2–6). Aguilera et al.(7) evaluated data from the naturally fractured Palm Valley gas field using analytical and numerical simulation techniques. Both approaches provided approximately the same results. In a subsequent paper, Aguilera(8) used a numerical simulator to examine the behaviour of a naturally fractured reservoir with ten layers and with fracture permeabilities ranging between 6.91 and 1,232.41 mD. The geometric mean permeability was 40 mD. The thickness of each layer (1.6 m) and the fracture spacing (3.35 m) were constant. From this analysis, it was concludedthat multi-layered behaviour could be recognized by a pressure derivative indicating partial penetration effects, even if the well was perforated in all layers. The partial penetration effects correspond to a derivative with a slope equal to about - 0.5. This was followed by an indication of linear flow; i.e., aslope of the pressure derivative equal to approximately +0.5. This technical note is a continuation of the research published by Aguilera(8). In the present paper, we are using the same numerical model, but in addition to variations in fracture permeability, we include variations in layer thickness, fracture spacing, and fracture porosity(9). FIGURE 1: Outcrop of the Cardium sandstone showing variations in layer thickness and fracture spacing (Seebe Dam, Alberta, Canada). Width of shown outcrop is approximately 25 m. Results Most reservoir parameters have been kept as in the previous study(8). Pay thickness for the reservoir is 16 m. Matrix porosity is 4.8% Matrix permeability is 0.023 mD. Gas saturation in the matrix is 42%, and gas saturation in the fractures is 99%.

Well-Test Characterization of Wedge-Shaped, Faulted Reservoirs

Summary Two offshore, wedge-shaped reservoirs in south Louisiana were interpreted with pressure-buildup responses by comparing the results from simulated finite-element model studies. The importance of knowing the correct reservoir shape, and how it is used to interpret the generated boundary-pressure responses, is briefly discussed. Two different 3D computer models incorporating different wedge-shaped geometries simulated the test pressure-buildup response patterns. Variations in the two configurations are topologically expressed as a constant thickness and a nonconstant thickness, with smooth-surface, wedged-shaped reservoir models. The variable-thickness models are pinched-out updip at one end and faulted at the other end. Numerical well-test results demonstrated changes in the relationships between the pressure-derivative profile, the wellbore location, and the extent of partial penetration in the reservoir models. The wells were placed along the perpendicular bisector (top view) at distances starting from the apex at 5, 10, 20, 40, 50, 60, 80, and 90% of the reservoir length. Results demonstrate that boundary distance identification (such as distance, number, and type) based solely on the log-log derivative profile in rectangular and triangular wedge-shaped reservoirs should be strongly discouraged. Partial-penetration effects (PPE's) in wedge-shaped reservoirs are highly dependent on the wellbore location relative to the wedge, and the well-test-data analysis becomes more complex.

Aquifer response to stream-stage and recharge variations. II. Convolution method and applications

In this second of two papers, analytical step-response functions, developed in the companion paper for several cases of transient hydraulic interaction between a fully penetrating stream and a confined, leaky, or water-table aquifer, are used in the convolution integral to calculate aquifer heads, streambank seepage rates, and bank storage that occur in response to stream-stage fluctuations and basinwide recharge or evapotranspiration. Two computer programs developed on the basis of these step-response functions and the convolution integral are applied to the analysis of hydraulic interaction of two alluvial stream–aquifer systems in the northeastern and central United States. These applications demonstrate the utility of the analytical functions and computer programs for estimating aquifer and streambank hydraulic properties, recharge rates, streambank seepage rates, and bank storage. Analysis of the water-table aquifer adjacent to the Blackstone River in Massachusetts suggests that the very shallow depth of water table and associated thin unsaturated zone at the site cause the aquifer to behave like a confined aquifer (negligible specific yield). This finding is consistent with previous studies that have shown that the effective specific yield of an unconfined aquifer approaches zero when the capillary fringe, where sediment pores are saturated by tension, extends to land surface. Under this condition, the aquifer's response is determined by elastic storage only. Estimates of horizontal and vertical hydraulic conductivity, specific yield, specific storage, and recharge for a water-table aquifer adjacent to the Cedar River in eastern Iowa, determined by the use of analytical methods, are in close agreement with those estimated by use of a more complex, multilayer numerical model of the aquifer. Streambank leakance of the semipervious streambank materials also was estimated for the site. The streambank-leakance parameter may be considered to be a general (or lumped) parameter that accounts not only for the resistance of flow at the river–aquifer boundary, but also for the effects of partial penetration of the river and other near-stream flow phenomena not included in the theoretical development of the step-response functions.

Unsteady Flow to Wells Partially Penetrating in Two-Layered Aquifers

The unsteady flow of water to well in a layered aquifer with an interlayer flow is examined in this paper. The system studied comprises an aquifer consisting of two productive layers of finite thickness that are in a perfect hydraulic contact and a well which partially penetrates in one of the layers. Each layer is assumed to be homogeneous and isotropic and the water contained in the aquifer is of identical physical properties and small compressibility. The analytical solutions are derived for the case when the system is characterised by equality of hydraulic diffusivity of layers. These solutions give the results accurate enough for practical applications and allow to estimate the effects of partial penetration and contrast in parameters of formation on distribution of the flow potential both at large distances from wells and at the wells. The obtained solutions also provide a basis for predicting the interlayer flow arising from the performance of a pumping well as well as between a pair of wells which have an open interval located in different layers of the aquifer. Two cases have been analysed: (1) a pumping pair of wells which is used to prevent water inflow to the productive well, and (2) a pumping-injection pair of wells providing the demanded mixing of water from adjacent layers. Some examples of flow patterns and specially computed diagrams are given to illustrate the operation of such systems.

Variations in Capture‐Zone Geometry of a Partially Penetrating Pumping Well in an Unconfined Aquifer

AbstractDesign of effective and efficient pump‐and‐treat systems requires capture zones of recovery wells to closely circumscribe the contaminant plume. Overestimation of capture zones incurs the undesired expense of treating clean water. Underestimation of capture zones enables contaminants to escape downgradient. Recovery wells in unconfined aquifers commonly penetrate only part of the aquifer either because of its large saturated thickness or the shallow vertical extent of contamination. The capture‐zone geometry of a partially penetrating pumping well can differ greatly from that of a fully penetrating one because of vertical flow components near the well. The differences in geometry are far greater if the medium is anisotropic (Kh≠ Kv).To estimate the capture‐zone geometry of a partially penetrating pumping well, a steady‐state, finite‐difference model was constructed to simulate flow to a well in a regional flow system. The model was used to simulate differences in the velocity field created by changes in (1) the depth of well penetration, (2) the magnitude of the regional hydraulic gradient, and (3) the degree of anisotropy. Following each simulation particle tracking was performed to determine the maximum width, depth, and distance to the stagnation point of the capture zone. Graphs were developed between capture‐zone width, relative capture‐zone depth, distance to the stagnation point, versus the ratio of Q/q (pumping rate/specific discharge). The graphs enable estimates to be made of these geometric parameters for a variety of pumping rates, regional hydraulic gradients, hydraulic conductivities, anisotropy ratios, and degrees of partial penetration. The results show that for isotropic conditions, particularly for small ratios of Q/q and wells that penetrate less than 40 percent of the aquifer, the shape of a capture zone can deviate significantly from that of a fully penetrating well. For anisotropic conditions, these differences are more pronounced and apply to a wider range of Q/q ratios and well penetration depths.In sequences of sediment, anisotropy is produced by textural, architectural, and stratigraphic elements that occur at different scales. Capture zones should be estimated using Kh:Kv ratios determined from pumping tests. This assures that the measured degree of anisotropy is commensurate with the scale of elements encountered by the stress created by a pumping well. Tabulated Kh:Kv ratios from analysis of pumping tests in unconfined aquifers suggest there are few isotropic sand and gravel aquifers. Recognition of this characteristic and consideration of the effects of partial penetration and regional hydraulic gradient on the geometry of capture zones may lead to the design of more efficient and effective pump‐and‐treat systems.

Slug Tests in Unconfined Formations: An Assessment of the Bouwer and Rice Technique

AbstractThe slug test is one of the most common techniques for the in situ estimation of hydraulic conductivity in unconfined flow systems. Recently, a mathematical model describing the flow of ground water in response to a slug test in an unconfined flow system has been proposed. This model incorporates the effects of partial penetration, anisotropy, an upper constant‐head boundary, and, in its most complete form, well skins of either higher or lower permeability than the formation itself. This model is useful in identifying conditions when conventional approaches (i.e., the Bouwer and Rice model) introduce large errors into parameter estimates. For slug tests performed in homogeneous, isotropic formations that would be classified as aquifers, the Bouwer and Rice model provides estimates within 30% of actual field values. In less‐permeable, clay‐rich formations, however, estimates may overpredict formation conductivity by more than 100%. The Bouwer and Rice model introduces the largest error (can easily exceed an order of magnitude) in the presence of a low‐permeability skin. Uncertainty about anisotropy can also be the source of considerable error. The semianalytical solution to the mathematical model described here can be employed for parameter estimation under conditions when the Bouwer and Rice model introduces unacceptably large errors into parameter estimates. This solution can be rapidly evaluated, allowing easy incorporation into an automated well‐test analysis package and/or ready generation of type curves.

Slug tests in partially penetrating wells

A semianalytical solution is presented to a mathematical model describing the flow of groundwater in response to a slug test in a confined or unconfined porous formation. The model incorporates the effects of partial penetration, anisotropy, finiteradius well skins, and upper and lower boundaries of either a constant‐head or an impermeable form. This model is employed to investigate the error that is introduced into hydraulic conductivity estimates through use of currently accepted practices (i.e., Hvorslev, 1951; Cooper et al., 1967) for the analysis of slug‐test response data. The magnitude of the error arising in a variety of commonly faced field configurations is the basis for practical guidelines for the analysis of slug‐test data that can be utilized by field practitioners.

Specific Yield as Determined by Type‐Curve Analysis of Aquifer‐Test Data

AbstractType‐curve analysis of water‐table aquifer pumping‐test data has often resulted in values of specific yield that are unrealistically low when compared with values obtained by volume‐balance calculations. It has been suggested that such values are the result of inadequate representation of drainage processes in the unsaturated zone. The commonly used analytical solution developed by Neuman for a homogeneous, water‐table aquifer assumes that the drainage of pores in the zone above the water table due to lowering of the water table occurs instantaneously. Published pumping‐test data from three relatively homogeneous, unconsolidated, granular aquifers with significantly different hydraulic conductivities are used to show that type‐curve analysis based on the Neuman model will result in estimates of specific yield that agree with volume‐balance calculations, provided that established procedures are followed. These involve the use of composite plots of drawdown observed at more than one location and inclusion of effects of partial penetration. Noninstantaneous drainage of pores in the unsaturated zone accounts for the finding that both type‐curve analysis and volume‐balance calculations yield values of specific yield that are slightly less than those obtained from laboratory column‐drainage experiments. It may also account for a slight underestimation of vertical hydraulic conductivity as obtained by type‐curve analysis.

In Situ Soil Remediation Using Vapor Extraction Wells, Development and Testing of a Three‐Dimensional Finite‐Difference Model

AbstractSoil vapor extraction technology is becoming increasingly popular in soil remediation in removing volatile and semivolatile organic compounds from the vadose zone. The rate and extent of removal of volatile organic compounds from the vadose zone by active or passive vapor extraction systems are known to be affected by a number of factors, including soil permeability, soil moisture content, applied suction, air flow rate, temperature, vapor pressure, and external boundary conditions. Some techniques used to describe the dynamics of gas flow are based on simplifying assumptions which limit their application in “real world” situations. This paper describes the development and testing of a three‐dimensional gas flow model “GAS3D” for the design of soil venting systems. The model takes into account the effect of partial penetration and partial screening of vapor extraction wells as well as the nonhomogeneity and anisotropy of the soil. The simulated pressure around a vapor extraction well by the developed GAS3D model was verified and validated by comparing the results of the finite‐difference solution to the actual field measurements and the results of an analytical solution under homogeneous and isotropic conditions. The model was used in a case study to demonstrate the utility of the developed model under heterogeneous and anisotropic conditions for designing a vapor extraction system.