On Simulation and Analysis of Variable‐Rate Pumping Tests

Mishra, P. K.; Vessilinov, Velimir V.; Gupta, H. V.

doi:10.1111/j.1745-6584.2012.00961.x

Cited by 28 publications

(30 citation statements)

References 15 publications

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“…Mishra et al () argued that step approximations may not be appropriate for smoothly varying flow rates and proposed a Laplace transform solution for timewise linear flow rate. Equation can also be easily integrated in this case.…”

Section: Methodsmentioning

confidence: 99%

“…In the case of Birsoy and Summers (1980), their choice made sense because they were seeking an approximation of drawdown during pumping, but it is somewhat less accurate if Q 0 is indeed small and zero after t cQ . Mishra et al (2013) argued that step approximations may not be appropriate for smoothly varying flow rates and proposed a Laplace transform solution for timewise linear flow rate. Equation (10) can also be easily integrated in this case.…”

Section: 1029/2018wr022684mentioning

confidence: 99%

See 1 more Smart Citation

Generalizing Agarwal's Method for the Interpretation of Recovery Tests Under Non‐Ideal Conditions

Trabucchi

Carrera

Fernàndez-García

2018

Water Resources Research

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Pumping tests are performed during aquifer characterization to gain conceptual understanding about the system through diagnostic plots and to estimate hydraulic properties. Recovery tests consist of measuring head response in observation and/or pumping wells after pumping termination. They are especially useful when the pumping rate cannot be accurately controlled. They have been traditionally interpreted using Theis' recovery method, which yields robust estimates of effective transmissivity but does not provide information about the conceptual model. Agarwal proposed a method that has become standard in the oil industry, to obtain both early and late time reservoir responses to pumping from recovery data. However, the validity of the method has only been tested to a limited extent. In this work, we analyze Agarwal's method in terms of both drawdowns and log derivatives for non‐ideal conditions: leaky aquifer, presence of boundaries, and one‐dimensional flow. Our results show that Agarwal's method provides excellent recovery plots (i.e., the drawdown curve that would be obtained during pumping) and parameter estimates for nearly all aquifer conditions, provided that a constant pumping rate is used and the log derivative at the end of pumping is constant, which is too limiting for groundwater hydrology practice, where observation wells are usually monitored. We generalize Agarwal's method by (1) deriving an improved equivalent time for time‐dependent pumping rate and (2) proposing to recover drawdown curves by extrapolating the pumping phase drawdowns. These yield excellent diagnostic plots, thus facilitating the conceptual model analysis for a broad range of conditions.

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Section: Methodsmentioning

confidence: 99%

Section: 1029/2018wr022684mentioning

confidence: 99%

Generalizing Agarwal's Method for the Interpretation of Recovery Tests Under Non‐Ideal Conditions

Trabucchi

Carrera

Fernàndez-García

2018

Water Resources Research

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“…For example, a step function on at

t_{D} = t_{D 0}

{\bar{f}}_{t} = e^{- t_{D 0} s} / s

(with the typical case of

{\bar{f}}_{t} = 1 / s

for

t_{D 0} = 0

), and a pulse function during

t_{D 0} \leq t_{D} \leq t_{D 1}

{\bar{f}}_{f} = true(e^{- t_{D 0} s} - e^{- t_{D 1} s} true) / s

. The temporal behavior of an arbitrary flow rate, Q ( t ), or downhole pressure,

Δ p (t)

, is readily approximated using piecewise constant or linear behavior [e.g., Streltsova , ; Mishra et al ., ]. For nearly constant or monotonically declining specified pressures and flow rates, the numerical inverse Laplace transform algorithm converges quickly (e.g., 21 Laplace‐space function evaluations for each time is typical).…”

Section: Solutionsmentioning

confidence: 99%

Multiporosity flow in fractured low‐permeability rocks

Kuhlman

Malama

Heath

2015

Water Resources Research

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A multiporosity extension of classical double and triple-porosity fractured rock flow models for slightly compressible fluids is presented. The multiporosity model is an adaptation of the multirate solute transport model of Haggerty and Gorelick (1995) to viscous flow in fractured rock reservoirs. It is a generalization of both pseudo steady state and transient interporosity flow double-porosity models. The model includes a fracture continuum and an overlapping distribution of multiple rock matrix continua, whose fracture-matrix exchange coefficients are specified through a discrete probability mass function. Semianalytical cylindrically symmetric solutions to the multiporosity mathematical model are developed using the Laplace transform to illustrate its behavior. The multiporosity model presented here is conceptually simple, yet flexible enough to simulate common conceptualizations of double and triple-porosity flow. This combination of generality and simplicity makes the multiporosity model a good choice for flow modelling in lowpermeability fractured rocks.

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“…Zhang (2013) applies Theis' method and proposes a new type of curve for the case of variable discharge, validating the method with a numerical model, although it requires several measurements of drawdowns in different points at varying distances from the pumping point. Mishra et al (2013) consider a sinusoidal variation of the discharge.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Analytical Methods to Study Aquifer Properties with Pumping Tests in Coastal Aquifers with Numerical Modelling (Motril-Salobreña Aquifer)

Calvache

Sánchez-Úbeda

Duque

et al. 2015

Water Resour Manage

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Two pumping tests were performed in the unconfined Motril-Salobreña detrital aquifer in a 250 m-deep well 300 m from the coastline containing both freshwater and saltwater. It is an artesian well as it is in the discharge zone of this coastal aquifer. The two observation wells where the drawdowns are measured record the influence of tidal fluctuations, and the well lithological columns reveal high vertical heterogeneity in the aquifer. The Theis and Cooper-Jacob approaches give average transmissivity (T) and storage coefficient (S) values of 1460 m 2 /d and 0.027, respectively. Other analytical solutions, modified to be more accurate in the boundary conditions found in coastal aquifers, provide similar T values to those found with the Theis and Cooper-Jacob methods, but give very different S values or could not estimate them. Numerical modelling in a synthetic model was applied to analyse the sensitivity of the Theis and Cooper-Jacob approaches to the usual boundary conditions in coastal aquifers. The T and S values calculated from the numerical modelling drawdowns indicate that the regional flow, variable pumping flows, and tidal effect produce an error of under 10 % compared to results obtained with classic methods. Fluids of different density (freshwater and saltwater) cause an error of 20 % in estimating T and of over 100 % in calculating S. The factor most affecting T and S results in the pumping test interpretation is vertical heterogeneity in sediments, which can produce errors of over 100 % in both parameters.

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On Simulation and Analysis of Variable‐Rate Pumping Tests

Cited by 28 publications

References 15 publications

Generalizing Agarwal's Method for the Interpretation of Recovery Tests Under Non‐Ideal Conditions

Generalizing Agarwal's Method for the Interpretation of Recovery Tests Under Non‐Ideal Conditions

Multiporosity flow in fractured low‐permeability rocks

Evaluation of Analytical Methods to Study Aquifer Properties with Pumping Tests in Coastal Aquifers with Numerical Modelling (Motril-Salobreña Aquifer)

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