scholarly journals Stochastic analysis of steady-state unsaturated flow in heterogeneous media: Comparison of the Brooks-Corey and Gardner-Russo Models

1998 ◽  
Vol 34 (6) ◽  
pp. 1437-1449 ◽  
Author(s):  
Dongxiao Zhang ◽  
T. C. Wallstrom ◽  
C. L. Winter
Keyword(s):  
Steady State ◽  
Stochastic Analysis ◽  
Heterogeneous Media ◽  
Unsaturated Flow ◽  
Media Comparison

scholarly journals A stochastic analysis of steady state two-phase flow in heterogeneous media

2005 ◽  
Vol 41 (1) ◽  
Author(s):  
Mingjie Chen ◽  
Dongxiao Zhang ◽  
Arturo A. Keller ◽  
Zhiming Lu
Keyword(s):  
Steady State ◽  
Stochastic Analysis ◽  
Heterogeneous Media ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase

scholarly journals Technical note: Analytical drawdown solution for steady-state pumping tests in two-dimensional isotropic heterogeneous aquifers

2016 ◽  
Vol 20 (5) ◽  
pp. 1655-1667 ◽  
Author(s):  
Alraune Zech ◽  
Sabine Attinger
Keyword(s):  
Steady State ◽  
Correlation Length ◽  
Heterogeneous Media ◽  
Radial Distance ◽  
Pumping Test ◽  
Two Dimensional ◽  
Aquifer Heterogeneity ◽  
Pumping Tests ◽  
Flow Solution ◽  
Ensemble Mean

Abstract. A new method is presented which allows interpreting steady-state pumping tests in heterogeneous isotropic transmissivity fields. In contrast to mean uniform flow, pumping test drawdowns in heterogeneous media cannot be described by a single effective or equivalent value of hydraulic transmissivity. An effective description of transmissivity is required, being a function of the radial distance to the well and including the parameters of log-transmissivity: mean, variance, and correlation length. Such a model is provided by the upscaling procedure radial coarse graining, which describes the transition of near-well to far-field transmissivity effectively. Based on this approach, an analytical solution for a steady-state pumping test drawdown is deduced. The so-called effective well flow solution is derived for two cases: the ensemble mean of pumping tests and the drawdown within an individual heterogeneous transmissivity field. The analytical form of the solution allows inversely estimating the parameters of aquifer heterogeneity. For comparison with the effective well flow solution, virtual pumping tests are performed and analysed for both cases, the ensemble mean drawdown and pumping tests at individual transmissivity fields. Interpretation of ensemble mean drawdowns showed proof of the upscaling method. The effective well flow solution reproduces the drawdown for two-dimensional pumping tests in heterogeneous media in contrast to Thiem's solution for homogeneous media. Multiple pumping tests conducted at different locations within an individual transmissivity field are analysed, making use of the effective well flow solution to show that all statistical parameters of aquifer heterogeneity can be inferred under field conditions. Thus, the presented method is a promising tool with which to estimate parameters of aquifer heterogeneity, in particular variance and horizontal correlation length of log-transmissivity fields from steady-state pumping test measurements.

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