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ASTM D5981/D5981M-18

(Guide)

Standard Guide for Calibrating a Groundwater Flow Model Application

Standard Guide for Calibrating a Groundwater Flow Model Application

SIGNIFICANCE AND USE
5.1 Most site-specific groundwater flow models must be calibrated prior to use in predictions. In these cases, calibration is a necessary, but not sufficient, condition which must be obtained to have confidence in the model's predictions.  
5.2 Often, during calibration, it becomes apparent that there are no realistic values of the hydraulic properties of the soil or rock which will allow the model to reproduce the calibration targets. In these cases the conceptual model of the site may need to be revisited or the construction of the model may need to be revised. In addition, the source and quality of the data used to establish the calibration targets may need to be reexamined. For example, the modeling process can sometimes identify a previously undetected surveying error, which would results in inaccurate hydraulic head targets.  
5.3 This guide is not meant to be an inflexible description of techniques for calibrating a groundwater flow model; other techniques may be applied as appropriate and, after due consideration, some of the techniques herein may be omitted, altered, or enhanced.
Note 1: Users of the inverse method should be aware that the method may have several solutions, all equally well calibrated. (1)4
SCOPE
1.1 This guide covers techniques that can be used to calibrate a groundwater flow model. The calibration of a model is the process of matching historical data, and is usually a prerequisite for making predictions with the model.  
1.2 Calibration is one of the stages of applying a groundwater modeling code to a site-specific problem (see Guide D5447). Calibration is the process of refining the model representation of the hydrogeologic framework, hydraulic properties, and boundary conditions to achieve a desired degree of correspondence between the model simulations and observations of the groundwater flow system.  
1.3 Flow models are usually calibrated using either the manual (trial-and-error) method or an automated (inverse) method. This guide presents some techniques for calibrating a flow model using either method.  
1.4 This guide is written for calibrating saturated porous medium (continuum) groundwater flow models. However, these techniques, suitably modified, could be applied to other types of related groundwater models, such as multi-phase models, non-continuum (karst or fracture flow) models, or mass transport models.  
1.5 Guide D5447 presents the steps to be taken in applying a groundwater modeling code to a site-specific problem. Calibration is one of those steps. Other standards have been prepared on environmental modeling, such as Guides D5490, D5609, D5610, D5611, D5718, and Practice E978.  
1.6 Units—The values stated in either SI units or inch-pound units (given in brackets) are to be regarded separately as standard. The values stated in each system may not be exact equivalents; therefore, each system shall be independently of the other. Combining values from the two systems may result in non-conformance with the standard.  
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.8 This guide offers an organized collection of information or a series of options and does not recommend a specific course of action. This document cannot replace education or experience and should be used in conjunction with professional judgment. Not all aspects of this guide may be applicable in all circumstances. This ASTM standard is not intended to represent or replace the standard of care by which the adequacy of a given professional service must be judged, nor should this document be applied without consideration of a project's many unique aspects. The word “Standard” in the title of this document means only that the...

General Information

Status
Published
Publication Date
31-Dec-2017
ICS
13.060.10 - Water of natural resources
Technical Committee
D18 - Soil and Rock
Drafting Committee
D18.21 - Groundwater and Vadose Zone Investigations
Current Stage
Ref Project

Relations

Refers
ASTM D5611-94(2016) - Standard Guide for Conducting a Sensitivity Analysis for a Groundwater Flow Model Application
Effective Date
01-Jan-2016
Refers
ASTM D5609-16 - Standard Guide for Defining Boundary Conditions in Groundwater Flow Modeling
Effective Date
01-Mar-2016
Refers
ASTM D5447-17 - Standard Guide for Application of a Numerical Groundwater Flow Model to a Site-Specific Problem
Effective Date
15-Dec-2017
Refers
ASTM D653-14 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
Effective Date
01-Aug-2014

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ASTM D5981/D5981M-18 - Standard Guide for Calibrating a Groundwater Flow Model ApplicationASTM D5981/D5981M-18 - Standard Guide for Calibrating a Groundwater Flow Model Application
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ASTM D5981/D5981M-18 - Standard Guide for Calibrating a Groundwater Flow Model Application
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This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: D5981/D5981M − 18
Standard Guide for
1
Calibrating a Groundwater Flow Model Application
This standard is issued under the fixed designation D5981/D5981M; the number immediately following the designation indicates the
year of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last
reapproval. A superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope* responsibility of the user of this standard to establish appro-
priate safety, health, and environmental practices and deter-
1.1 This guide covers techniques that can be used to
mine the applicability of regulatory limitations prior to use.
calibrateagroundwaterflowmodel.Thecalibrationofamodel
1.8 This guide offers an organized collection of information
is the process of matching historical data, and is usually a
or a series of options and does not recommend a specific
prerequisite for making predictions with the model.
course of action. This document cannot replace education or
1.2 Calibration is one of the stages of applying a ground-
experience and should be used in conjunction with professional
water modeling code to a site-specific problem (see Guide
judgment. Not all aspects of this guide may be applicable in all
D5447). Calibration is the process of refining the model
circumstances. This ASTM standard is not intended to repre-
representation of the hydrogeologic framework, hydraulic
sent or replace the standard of care by which the adequacy of
properties, and boundary conditions to achieve a desired
a given professional service must be judged, nor should this
degree of correspondence between the model simulations and
document be applied without consideration of a project’s many
observations of the groundwater flow system.
unique aspects. The word “Standard” in the title of this
document means only that the document has been approved
1.3 Flow models are usually calibrated using either the
manual (trial-and-error) method or an automated (inverse) through the ASTM consensus process.
method. This guide presents some techniques for calibrating a
1.9 This international standard was developed in accor-
flow model using either method.
dance with internationally recognized principles on standard-
ization established in the Decision on Principles for the
1.4 This guide is written for calibrating saturated porous
Development of International Standards, Guides and Recom-
medium (continuum) groundwater flow models. However,
mendations issued by the World Trade Organization Technical
these techniques, suitably modified, could be applied to other
Barriers to Trade (TBT) Committee.
types of related groundwater models, such as multi-phase
models, non-continuum (karst or fracture flow) models, or
2. Referenced Documents
mass transport models.
2
2.1 ASTM Standards:
1.5 Guide D5447 presents the steps to be taken in applying
D653 Terminology Relating to Soil, Rock, and Contained
a groundwater modeling code to a site-specific problem.
Fluids
Calibration is one of those steps. Other standards have been
D5447 Guide for Application of a Numerical Groundwater
prepared on environmental modeling, such as Guides D5490,
Flow Model to a Site-Specific Problem
D5609, D5610, D5611, D5718, and Practice E978.
D5490 Guide for Comparing Groundwater Flow Model
1.6 Units—The values stated in either SI units or inch-
Simulations to Site-Specific Information
pound units (given in brackets) are to be regarded separately as
D5609 Guide for Defining Boundary Conditions in Ground-
standard. The values stated in each system may not be exact
water Flow Modeling
equivalents; therefore, each system shall be independently of
D5610 GuideforDefiningInitialConditionsinGroundwater
the other. Combining values from the two systems may result
Flow Modeling
in non-conformance with the standard.
D5611 Guide for Conducting a Sensitivity Analysis for a
1.7 This standard does not purport to address all of the
Groundwater Flow Model Application
safety concerns, if any, associated with its use. It is the
D5718 Guide for Documenting a Groundwater Flow Model
Application
1
This guide is under the jurisdiction ofASTM Committee D18 on Soil and Rock
and is the direct responsibility of Subcommittee D18.21 on Groundwater and
Vadose Zone Investigations.
2
Current edition approved Jan. 1, 2018. Published February 2018. Originally For referenced ASTM standards, visit the ASTM website, www.astm.org, or
approved in 1996. Last previous edition approved in 2002 as D5981 – 96 (2008), contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
which was withdrawn January 2017 and reinstated in J
...

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3.1 The success of a sampling event is influenced by adequate planning and preparation. Use of this guide will help the groundwater sampler to methodically execute the planning and preparation.  
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1.1 This guide covers planning and preparing for a groundwater sampling event. It includes technical and administrative considerations and procedures. Example checklists are also provided as Appendices.  
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ASTM D6771-21(Practice)
Standard Practice for Low-Flow Purging and Sampling Used for Groundwater Monitoring

SIGNIFICANCE AND USE
5.1 Method Considerations—The objective of most groundwater sampling programs is to obtain samples that are similar in composition to that of the formation water near the well screen. The low-flow purging and sampling method uses the stabilization of indicator parameters to determine when the pump discharge is considered to represent a flow-weighted average of the formation water. Measurements of operational parameters are used to determine potential sampling bias (for example, artifactual turbidity and increased temperature) that may have been introduced by pumping operations and to ensure that the sample is representative of formation water. The low-flow purge rate minimizes lowering of the ambient groundwater level and thereby minimizes potential entrainment of blank-riser pipe (and potentially stagnant) water above or below the screen into the screened-zone of the well. This sampling method assumes that the well has been properly designed and constructed as described in Practices D5092/D5092M and D6725/D6725M, adequately developed as described in Guide D5521/D5521M, and has received proper well maintenance and rehabilitation as described in Guide D5978/D5978M (see Note 1).
Note 1: This Standard is not intended to replace or supersede any regulatory requirements, standard operating procedure (SOP), quality assurance project plan (QAPP), ground water sampling and analysis plan (GWSAP) or site-specific regulatory permit requirements. The procedures described in this Standard may be used in conjunction with regulatory requirements, SOPs, QAPPs, GWSAPs or permits where allowed by the authority with jurisdiction.  
5.2 Applicability—Low-flow purging and sampling may be used in a monitoring well that can be pumped at a constant low-flow rate without continuously increasing drawdown in the well (2). If a well cannot be purged without continuously increasing drawdown even at very low pumping rates (for example, 50 – 100 mL/min), the well should not be sampled using th...
SCOPE
1.1 This practice describes the method of low-flow purging and sampling used to collect groundwater samples from wells to assess groundwater quality.  
1.2 The purpose of this procedure is to collect groundwater samples that represent a flow-weighted average of solute and colloid concentrations transported through the formation near the well screen under ambient conditions. Samples collected using this method can be analyzed for groundwater contaminants and/or naturally occurring analytes.  
1.3 This practice is generally not suitable for use in wells with very low-yields and cannot be conducted using grab sampling or inertial lift devices. This practice is not suitable for use in wells with non-aqueous phase liquids.  
1.4 Units—The values stated in SI units are to be regarded as standard. The values given in parentheses are approximate mathematical conversions to inch-pound units that are provided for information only and are not considered standard.  
1.5 This practice offers a set of instructions for performing one or more specific operations. This document cannot replace education or experience and should be used in conjunction with professional judgment. Not all aspects of this practice may be applicable in all circumstances. This ASTM standard is not intended to represent or replace the standard of care by which the adequacy of a given professional service must be judged, nor should this document be applied without consideration of a project's many unique aspects. The word “standard” in the title means only that the document has been approved through the ASTM consensus process.  
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ASTM D6001/D6001M-20(Guide)
Standard Guide for Direct-Push Groundwater Sampling for Environmental Site Characterization

SIGNIFICANCE AND USE
5.1 Direct-push groundwater sampling and profiling are economical methods for obtaining discrete interval groundwater quality samples in many soils and unconsolidated formations without the expense of permanent monitoring well installation (1-10).4 Many of these devices can be used to profile groundwater quality or contamination and/or hydraulic conductivity with depth by performing repetitive sampling and testing events. DP groundwater sampling is often used in expedited site characterization (Practice D6235) and as a means to accomplish high resolution site characterization (HRSC) (11, 12). The formation to be sampled should be sufficiently permeable to allow filling of the sampler in a relatively short time. The zone to be sampled and/or slug tested can be isolated by matching sampler screen length to obtain discrete samples of thin saturated, permeable layers. Use of these sampling and hydraulic testing techniques will result in more detailed characterization of sites containing multiple aquifers. The field conditions, sampler design and data quality objectives should be reviewed to determine if development (Guide D5521/D5521M) of the screened formation is appropriate. The samplers do not have a filter pack designed to retain fines like conventional wells, but only a slotted screen or wire-mesh covered ports. So, obtaining low turbidity samples may be difficult or even impossible in formations with a significant proportion of fine-grained materials. With most systems turbidity will always be high so consult Guide D6564/D6564M if field filtration of samples is required. Discrete water sampling, combined with knowledge of location and thickness of target aquifers, may better define conditions in thin multiple aquifers than monitoring wells with long screened intervals that can intersect and allow for intercommunication of multiple aquifers (4, 6, 11-15). DP sampling performed without knowledge of the location and thickness of target aquifers can result in sampling...
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1.1 This guide covers a review of methods for sampling groundwater at discrete points or in increments by insertion of groundwater sampling devices using Direct Push Methods (D6286/D6286M, see 3.3.2). By directly pushing the sampler, the soil is displaced and helps to form an annular seal above the sampling zone. Direct-push water sampling can be one time, or multiple sampling events. Knowledge of site specific geology and hydrogeologic conditions is necessary to successfully obtain groundwater samples with these devices.  
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1.3 This guide covers several types of groundwater samplers; sealed screen samplers, profiling samplers, dual tube sampling systems, and simple exposed screen samplers. In general, sealed screen samplers driven to discrete depth provide the highest quality water samples. Profiling samplers using an exposed screen(s) which are purged between sampling events allow for more rapid sample collection at multiple depths. Simple exposed screen samplers driven to a test zone with no purging prior to sampling may result in more questionable water quality if exposed to upper contaminated zones, and in that case, would be considered screening devices.  
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ASTM D5472/D5472M-20(Practice)
Standard Practice for Determining Specific Capacity and Estimating Transmissivity at the Control Well

SIGNIFICANCE AND USE
5.1 Assumptions of the Theis (1) equation affect specific capacity and transmissivity estimated from specific capacity. These assumptions are given below:  
5.1.1 Aquifer is homogeneous and isotropic.  
5.1.2 Aquifer is horizontal, of uniform thickness, and infinite in areal extent.  
5.1.3 Aquifer is confined by impermeable strata on its upper and lower boundaries.  
5.1.4 Density gradient in the flowing fluid must be negligible and the viscous resistance to flow must obey Darcy's Law.  
5.1.5 Control well penetrates and receives water equally from the entire thickness of the aquifer.  
5.1.6 Control well has an infinitesimal diameter.  
5.1.7 Control well discharges at a constant rate.  
5.1.8 Control well operates at 100 percent efficiency.  
5.1.9 Aquifer remains saturated throughout the duration of pumping.  
5.2 Implications of Assumptions and Limitations of Method.  
5.2.1 The simplifying assumptions necessary for solution of the Theis equation and application of the method are never fully met in a field situation. The satisfactory use of the method may depend upon the application of one or more empirical correction factors being applied to the field data.  
5.2.2 Generally the values of transmissivity derived from specific capacity vary from those values determined from aquifer tests utilizing observation wells. These differences may reflect 1) that specific-capacity represents the response of a small part of the aquifer near the well and may be greatly influenced by conditions near the well such as a gravel pack or graded material resulting from well development, and 2) effects of well efficiency and partial penetration.  
5.2.3 The values of transmissivity estimated from specific capacity data are considered less accurate than values obtained from analysis of drawdowns that are observed some distance from the pumped well.
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1.1 This practice describes a procedure for conducting a specific capacity test, computing the specific capacity of a control well, and estimating the transmissivity in the vicinity of the control well. Specific capacity is the well yield per unit drawdown at an identified time after pumping started.  
1.2 This practice is used in conjunction with Test Method D4050 for conducting withdrawal and injection well tests.  
1.3 The method of determining transmissivity from specific capacity is a variation of the nonequilibrium method of Theis  (1)2 for determining transmissivity and storage coefficient of an aquifer. The Theis nonequilibrium method is given in Practice D4106.  
1.4 Limitations—The limitations of the technique for determining transmissivity are primarily related to the correspondence between the field situation and the simplifying assumptions of the Theis method.  
1.5 The scope of this practice is limited by the capabilities of the apparatus.  
1.6 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice D6026.  
1.6.1 The procedures used to specify how data are collected/recorded and calculated in this practice are regarded as the industry standard. In addition, they are representative of the significant digits that should generally be retained. The procedures used do not consider material variation, purpose for obtaining the data, special purpose studies, or any considerations for the user’s objectives; and it is common practice to increase or reduce significant digits of reported data to commensurate with these considerations. It is beyond the scope of this practice to consider significant digits used in analysis methods for engineering design.  
1.7 Units—The values stated in SI units or inch-pound units are to be regarded separately as standard. The values stated in each system may not be exact equivalents; therefore, each system...

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ASTM D5270/D5270M-20(Practice)
Standard Practice for (Analytical Procedures) Determining Transmissivity and Storage Coefficient of Bounded, Nonleaky, Confined Aquifers

SIGNIFICANCE AND USE
5.1 Assumptions:  
5.1.1 The well discharges at a constant rate.  
5.1.2 Well is of infinitesimal diameter and is open through the full thickness of the aquifer.  
5.1.3 The nonleaky confined aquifer is homogeneous, isotropic, and areally extensive except where limited by linear boundaries.  
5.1.4 Discharge from the well is derived initially from storage in the aquifer; later, movement of water may be induced from a constant-head boundary into the aquifer.  
5.1.5 The geometry of the assumed aquifer and well are shown in Fig. 1 or Fig. 2.  
5.1.6 Boundaries are vertical planes, infinite in length that fully penetrate the aquifer. No water is yielded to the aquifer by impermeable boundaries, whereas recharging boundaries are in perfect hydraulic connection with the aquifer.  
5.1.7 Observation wells represent the head in the aquifer; that is, the effects of wellbore storage in the observation wells are negligible.  
5.2 Implications of Assumptions:  
5.2.1 Implicit in the assumptions are the conditions of a fully-penetrating control well and observation wells of infinitesimal diameter in a confined aquifer. Under certain conditions, aquifer tests can be successfully analyzed when the control well is open to only part of the aquifer or contains a significant volume of water or when the test is conducted in an unconfined aquifer. These conditions are discussed in more detail in Practice D4105/D4105M.  
5.2.2 In cases in which this practice is used to locate an unknown boundary, a minimum of three observation wells is needed. If only two observation wells are available, two possible locations of the boundary are defined, and if only one observation well is used, a circle describing all possible locations of the image well is defined.  
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SCOPE
1.1 This practice covers an analytical procedure for determining the transmissivity, storage coefficient, and possible location of boundaries for a confined aquifer with a linear boundary. This practice is used to analyze water-level or head data from one or more observation wells or piezometers during the pumping of water from a control well at a constant rate. This practice also applies to flowing artesian wells discharging at a constant rate. With appropriate changes in sign, this practice also can be used to analyze the effects of injecting water into a control well at a constant rate.  
1.2 The analytical procedure in this practice is used in conjunction with the field procedure in Test Method D4050.  
1.3 Limitations—The valid use of this practice is limited to determination of transmissivities and storage coefficients for aquifers in hydrogeologic settings with reasonable correspondence to the assumptions of the Theis nonequilibrium method (see Practice D4106) (see 5.1), except that the aquifer is limited in areal extent by a linear boundary that fully penetrates the aquifer. The boundary is assumed to be either a constant-head boundary (equivalent to a stream or lake that hydraulically fully penetrates the aquifer) or a no-flow (impermeable) boundary (equivalent to a contact with a significantly less permeable rock unit). The Theis nonequilibrium method is described in Practices D4105/D4105M and D4106.  
1.4 Units—The values stated in either SI units or inch-pound units are to be regarded separately as standard. The values stated in each system may not be exact equivalents; therefore, each system shall be used independently of the other. Combining values from the two systems may result in nonconformance with the standard. Reporting of results in units other than SI shall not be regarded as nonconformance with this standard.  
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ASTM D4104/D4104M-20(Practice)
Standard Practice for (Analytical Procedures) Determining Transmissivity of Nonleaky Confined Aquifers by Overdamped Well Response to Instantaneous Change in Head (Slug Tests)

SIGNIFICANCE AND USE
5.1 Assumptions of Solution of Cooper et al (1):  
5.1.1 The head change in the control well is instantaneous at time t  = 0.  
5.1.2 Well is of finite diameter and fully penetrates the aquifer.  
5.1.3 Flow in the nonleaky aquifer is radial.
Note 2: The exact conservation equation of Richards (5)with the volumetric water content can be simplified to take the form used in the solution of (1)with the storage coefficient, which implies several assumptions including that of constant total stresses (6).  
5.2 Implications of Assumptions:  
5.2.1 The mathematical equations applied ignore inertial effects and assume the water level returns the static level in an approximate exponential manner. The geometric configuration of the well and aquifer are shown in Fig. 1.
FIG. 1 Cross Section Through a Well in Which a Slug of Water is Suddenly Injected  
5.2.2 Assumptions are applicable to artesian or confined conditions and fully penetrating wells. However, this practice is commonly applied to partially penetrating wells and in unconfined aquifers where it may provide estimates of hydraulic conductivity for the aquifer interval adjacent to the open interval of the well if the horizontal hydraulic conductivity is significantly greater than the vertical hydraulic conductivity.
Note 3: Slug and pumping tests implicitly assume a porous medium. Fractured rock and carbonate settings may not provide meaningful data and information.  
5.2.3 As pointed out by Cooper et al (1) the determination of storage coefficient by this practice has questionable reliability because of the similar shape of the curves, whereas, the determination of transmissivity is not as sensitive to choosing the correct curve. However, the curve selected should not imply a storage coefficient unrealistically large or small.
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SCOPE
1.1 This practice covers the determination of transmissivity from the measurement of force-free (overdamped) response of a well-aquifer system to a sudden change of water level in a well. Force-free response of water level in a well to a sudden change in water level is characterized by recovery to initial water level in an approximate exponential manner with negligible inertial effects.  
1.2 The analytical procedure in this practice is used in conjunction with the field procedure in Test Method D4044/D4044M for collection of test data.  
1.3 Limitations—Slug tests are considered to provide an estimate of transmissivity. Although the assumptions of this practice prescribe a fully penetrating well (a well open through the full thickness of the aquifer), the slug test is commonly conducted using a partially penetrating well. Such a practice may be acceptable for application under conditions in which the aquifer is stratified and horizontal hydraulic conductivity is much greater than vertical hydraulic conductivity. In such a case the test would be considered to be representative of the average hydraulic conductivity of the portion of the aquifer adjacent to the open interval of the well.  
1.4 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice D6026.  
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ASTM D5473/D5473M-20(Practice)
Standard Practice for (Analytical Procedures) Analyzing the Effects of Partial Penetration of Control Well and Determining the Horizontal and Vertical Hydraulic Conductivity in a Nonleaky Confined Aquifer

SIGNIFICANCE AND USE
5.1 Assumptions:  
5.1.1 Control well discharges at a constant rate, Q.  
5.1.2 Control well is of infinitesimal diameter and partially penetrates the aquifer.  
5.1.3 The nonleaky artesian aquifer is homogeneous, and aerially extensive. The aquifer may also be anisotropic and, if so, the directions of maximum and minimum hydraulic conductivity are horizontal and vertical, respectively. The methods may be used to analyze tests on unconfined aquifers under conditions described in a following section.
Note 1: Slug and pumping tests implicitly assume a porous medium. Fractured rock and carbonate settings may not provide meaningful data and information.  
5.1.4 Discharge from the well is derived exclusively from storage in the aquifer.  
5.1.5 The geometry of the assumed aquifer and well conditions are shown in Fig. 2.  
5.2 Implications of Assumptions—The vertical flow components in the aquifer are induced by a control well that partially penetrates the aquifer, that is, a well that is not open to the aquifer through its full thickness. The effects of vertical flow components are measured in piezometers near the control well, that is, within a distance, r, in which vertical flow components are significant, that is:
5.3 Application of Method to Unconfined Aquifers:  
5.3.1 Although the assumptions are applicable to artesian or confined conditions, Weeks (1) has pointed out that the solution may be applied to unconfined aquifers if drawdown is small compared with the saturated thickness of the aquifer or if the drawdown is corrected for reduction in thickness of the aquifer, and the effects of delayed gravity response are small. The effects of gravity response become negligible after a time as given, for piezometers near the water table, by the equation:
for values of ar/b  
for greater values of ar/b.  
5.3.2 Drawdown in an unconfined aquifer is also affected by curvature of the water table or free surface near the control well, and b...
SCOPE
1.1 This practice covers an analytical solution for determining the horizontal and vertical hydraulic conductivity of an aquifer by analysis of the response of water levels in the aquifer to the discharge from a well that partially penetrates the aquifer. This standard uses data derived from Test Method D4050.  
1.2 Limitations—The limitations of the technique for determination of the horizontal and vertical hydraulic conductivity of aquifers are primarily related to the correspondence between the field situation and the simplifying assumption of this practice.  
1.3 Units—The values stated in either SI units or inch-pound units are to be regarded separately as standard. The values stated in each system may not be exact equivalents; therefore, each system shall be used independently of the other. Combining values from the two systems may result in nonconformance with the standard. Reporting of test results in units other than SI shall not be regarded as nonconformance with this standard.  
1.4 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice D6026.  
1.4.1 The procedures used to specify how data are collected/recorded or calculated, in this standard are regarded as the industry standard. In addition, they are representative of the significant digits that generally should be retained. The procedures used do not consider material variation, purpose for obtaining the data, special purpose studies, or any considerations for the user’s objectives; and it is common practice to increase or reduce significant digits of reported data to be commensurate with these considerations. It is beyond the scope of this standard to consider significant digits used in analytical methods for engineering design  
1.5 This practice offers a set of instructions for performing one or more specific operations. This document cannot replace education or experience and...

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ASTM
ASTM D6028/D6028M-20(Practice)
Standard Practice for (Analytical Procedure) Determining Hydraulic Properties of a Confined Aquifer Taking into Consideration Storage of Water in Leaky Confining Beds by Modified Hantush Method

SIGNIFICANCE AND USE
5.1 Assumptions:  
5.1.1 The control well discharges at a constant rate, Q.  
5.1.2 The control well is of infinitesimal diameter and fully penetrates the aquifer.  
5.1.3 The aquifer is homogeneous, isotropic, and areally extensive.
Note 1: Slug and pumping tests implicitly assume a porous medium. Fractured rock and carbonate settings may not provide meaningful data and information.  
5.1.4 The aquifer remains saturated (that is, water level does not decline below the top of the aquifer).  
5.1.5 The aquifer is overlain or underlain, or both, everywhere by confining beds individually having uniform hydraulic conductivities, specific storages, and thicknesses. The confining beds are bounded on the distal sides by one of the cases shown in Fig. 1.  
5.1.6 Flow in the aquifer is two-dimensional and radial in the horizontal plane.  
5.2 The geometry of the well and aquifer system is shown in Fig. 1.  
5.3 Implications of Assumptions:  
5.3.1 Paragraph 5.1.1 indicates that the discharge from the control well is at a constant rate. Paragraph 8.1 of Test Method D4050 discusses the variation from a strictly constant rate that is acceptable. A continuous trend in the change of the discharge rate could result in misinterpretation of the water-level change data unless taken into consideration.
Note 2: The quality of the result produced by this standard is dependent on the competence of the personnel performing it, and the suitability of the equipment and facilities used. Agencies that meet the criteria of Practice D3740 are generally considered capable of competent and objective testing/sampling/inspection/etc. Users of this standard are cautioned that compliance with Practice D3740 does not in itself assure reliable results. Reliable results depend on many factors; Practice D3740 provides a means of evaluating some of those factors.  
5.3.2 The leaky confining bed problem considered by the modified Hantush method requires that the control well has an infinite...
SCOPE
1.1 This practice covers an analytical procedure for determining the transmissivity and storage coefficient of a confined aquifer taking into consideration the change in storage of water in overlying or underlying confining beds, or both. This practice is used to analyze water-level or head data collected from one or more observation wells or piezometers during the pumping of water from a control well at a constant rate. With appropriate changes in sign, this practice also can be used to analyze the effects of injecting water into a control well at a constant rate.  
1.2 This analytical procedure is used in conjunction with Test Method D4050.  
1.3 Limitations—The valid use of the modified Hantush method (1)2 is limited to the determination of hydraulic properties for aquifers in hydrogeologic settings with reasonable correspondence to the assumptions of the Hantush-Jacob method (Practice D6029/D6029M) with the exception that in this case the gain or loss of water in storage in the confining beds is taken into consideration (see 5.1). All possible combinations of impermeable beds and source beds (for example, beds in which the head remains uniform) are considered on the distal side of the leaky beds that confine the aquifer of interest (see Fig. 1).
FIG. 1 Cross Sections Through Discharging Wells in Leaky Aquifers with Storage of Water in the Confining Beds, Illustrating Three Different Cases of Boundary Conditions (from Reed (2) )  
1.4 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice D6026.  
1.4.1 The procedures used to specify how data are collected/recorded and calculated in the standard are regarded as the industry standard. In addition, they are representative of the significant digits that generally should be retained. The procedures used do not consider material variation, purpose for obtaining the data, special purpose studies,...

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ASTM
ASTM D5850-20(Practice)
Standard Practice for (Analytical Procedure) Determining Transmissivity, Storage Coefficient, and Anisotropy Ratio from a Network of Partially Penetrating Wells

SIGNIFICANCE AND USE
5.1 This practice is one of several available for determining vertical anisotropy ratio. Among other available methods are Weeks ((5); see Practice D5473/D5473M), that relies on distance-drawdown data, and Way and McKee (6), that utilizes time-drawdown data. An important restriction of the Weeks distance-drawdown method is that the observation wells need to have identical construction (screened intervals) and two or more of the observation wells need to be located at a distance from the pumped well beyond the effects of partial penetration. The procedure described in this practice general distance-drawdown method, in that it works in theory for most observation well configurations incorporating three or more wells, provided some of the wells are within the zone where flow is affected by partial penetration.  
5.2 Assumptions:  
5.2.1 Control well discharges at a constant rate, Q.  
5.2.2 Control well is of infinitesimal diameter and partially penetrates the aquifer.  
5.2.3 Data are obtained from a number of partially penetrating observation wells, some screened at elevations similar to that in the pumped well and some screened at different elevations.  
5.2.4 The aquifer is confined, homogeneous and areally extensive. The aquifer may be anisotropic, and, if so, the directions of maximum and minimum hydraulic conductivity are horizontal and vertical, respectively.  
5.2.5 Discharge from the well is derived exclusively from storage in the aquifer.  
5.3 Calculation Requirements—Application of this method is computationally intensive. The function, fs, shown in (Eq 4) should be evaluated numerous times using arbitrary input parameters. It is not practical to use existing, somewhat limited, tables of values for fs and, because this equation is rather formidable, it may not be easily tractable by hand. Because of this, it is assumed the practitioner using this will have available a computerized procedure for evaluating the function fs. This can be accomplished u...
SCOPE
1.1 This practice covers an analytical procedure for determining the transmissivity, storage coefficient, and ratio of vertical to horizontal hydraulic conductivity of a confined aquifer using observation well drawdown measurements from a constant-rate pumping test. This practice uses data from a minimum of four partially penetrating, recommended to be positioned observation wells around a partially penetrating control well.  
1.2 The analytical procedure is used in conjunction with the field procedure in Test Method D4050.  
1.3 Limitations—The limitations of the technique for determination of the horizontal and vertical hydraulic conductivity of aquifers are primarily related to the correspondence between the field situation and the simplifying assumption of this practice.  
1.4 Units—The values stated in inch-pound units are to be regarded as the standard. The SI units given in parentheses are mathematical conversions, which are provided for information purposes only and are not considered standard. The reporting of results in units other than inch-pound shall not be regarded as nonconformance with this standard.  
1.5 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice D6026, unless superseded by this standard.  
1.6 The procedures used to specify how data are collected/recorded or calculated in this standard are regarded as the industry standard. In addition, they are representative of the significant digits that generally should be retained. The procedures used do not consider material variation, purpose for obtaining the data, special purpose studies, or any considerations for the user’s objective; and it is common practice to increase or reduce the significant digits of reported data to be commensurate with these considerations. It is beyond the scope of this standard to consider significant digits used in analysis method or engineeri...

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ASTM
ASTM D6029/D6029M-20(Practice)
Standard Practice for (Analytical Procedures) Determining Hydraulic Properties of a Confined Aquifer and a Leaky Confining Bed with Negligible Storage by the Hantush-Jacob Method

SIGNIFICANCE AND USE
5.1 Assumptions:  
5.1.1 The control well discharges at a constant rate, Q.  
5.1.2 The control well is of infinitesimal diameter and fully penetrates the aquifer.  
5.1.3 The aquifer is homogeneous, isotropic, and areally extensive.
Note 2: Slug and pumping tests implicitly assume a porous medium. Fractured rock and carbonate settings may not provide meaningful data and information.  
5.1.4 The aquifer remains saturated (that is, water level does not decline below the top of the aquifer).  
5.1.5 The aquifer is overlain, or underlain, everywhere by a confining bed having a uniform hydraulic conductivity and thickness. It is assumed that there is no change of water storage in this confining bed and that the hydraulic gradient across this bed changes instantaneously with a change in head in the aquifer. This confining bed is bounded on the distal side by a uniform head source where the head does not change with time.  
5.1.6 The other confining bed is impermeable.  
5.1.7 Leakage into the aquifer is vertical and proportional to the drawdown, and flow in the aquifer is strictly horizontal.  
5.1.8 Flow in the aquifer is two-dimensional and radial in the horizontal plane.  
5.2 The geometry of the well and aquifer system is shown in Fig. 1.  
5.3 Implications of Assumptions:  
5.3.1 Paragraph 5.1.1 indicates that the discharge from the control well is at a constant rate. Section 8.1 of Test Method D4050 discusses the variation from a strictly constant rate that is acceptable. A continuous trend in the change of the discharge rate could result in misinterpretation of the water-level change data unless taken into consideration.  
5.3.2 The leaky confining bed problem considered by the Hantush-Jacob solution requires that the control well has an infinitesimal diameter and has no storage. Abdul Khader and Ramadurgaiah (5) developed graphs of a solution for the drawdowns in a large-diameter control well discharging at a constant rate from an aquifer confined...
SCOPE
1.1 This practice covers an analytical procedure for determining the transmissivity and storage coefficient of a confined aquifer and the leakance value of an overlying or underlying confining bed for the case where there is negligible change of water in storage in a confining bed. This practice is used to analyze water-level or head data collected from one or more observation wells or piezometers during the pumping of water from a control well at a constant rate. With appropriate changes in sign, this practice also can be used to analyze the effects of injecting water into a control well at a constant rate.  
1.2 This analytical procedure is used in conjunction with Test Method D4050.  
1.3 Limitations—The valid use of the Hantush-Jacob method is limited to the determination of hydraulic properties for aquifers in hydrogeologic settings with reasonable correspondence to the assumptions of the Theis nonequilibrium method (Practice D4106) with the exception that in this case the aquifer is overlain, or underlain, everywhere by a confining bed having a uniform hydraulic conductivity and thickness, and in which the gain or loss of water in storage is assumed to be negligible, and that bed, in turn, is bounded on the distal side by a zone in which the head remains constant. The hydraulic conductivity of the other bed confining the aquifer is so small that it is assumed to be impermeable (see Fig. 1).
FIG. 1 Cross Section Through a Discharging Well in a Leaky Aquifer (from Reed (1)3). The Confining and Impermeable Bed Locations Can Be Interchanged  
1.4 Units—The values stated in either SI units or inch-pound units are to be regarded separately as standard. The values stated in each system may not be exact equivalents; therefore, each system shall be used independently of the other. Combining values from the two systems may result in nonconformance with the standard. Reporting of results in units other than SI shall not...

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