Numerical evaluation of pumping well transmissivity estimates in laterally heterogeneous formations

Numerical evaluation of volumetric weighted mean transmissivity estimates in laterally heterogeneous aquifers

“…Early-time was represented by the first 17 data points and late-time was represented by the last eight data points for Model 2. The slope changes in the drawdown curve from early-to-middle time are indicative of the volumetric evolution of the cone within the heterogeneities prior to establishment of steady-shape conditions, and suggest that the early-time drawdown data were affected by a transition period between different types of averaging (Tumlinson et al, 2006). Comparison of this sinuous shape of early-to-late drawdown data with the Cooper-Jacob straight-line match to the late-time data suggests strongly that variable averaging within the cone of depression (shown in Fig.…”

“…They concluded that T approaches, but does not equal, the geometric mean of the values within the area between the pumping well and observation well; they also reported that S values approach the arithmetic mean within this area. Tumlinson et al (2006) showed that early-time drawdown data for a single pumping well in a heterogeneous aquifer reflect rapidly changing volumetric, weighted mean transmissivity (VWMT) values within specific portions of the cone of depression. They also reported that late-time drawdown data that reflect stabilized conditions yield spatially averaged VWMT values within the entire cone of depression.…”

“…Therefore, the T/S and volume of each heterogeneity control the percentage of the total cone of depression, by volume that occurs within that heterogeneity for a particular duration of pumping (Osiensky et al, 2000;Tumlinson et al, 2006). For this analysis, the term ''volume portion'' is used in the same manner as Osiensky et al (2000) and Tumlinson et al (2006), to define the percentage of the measurable total volume of the cone of depression that is contained within a definable heterogeneity (block heterogeneity) (Fig.…”

“…Eventually the weighting factor (w i ) will stabilize along with the cone as steady-shape conditions are approached. The weighting scheme used to average the volume portions is modified after the method described by Osiensky et al (2000) and Tumlinson et al (2006) which weights K as a function of volume portions as follows:…”

Particle Filters to Estimate Properties of Confined Aquifers

“…Lebbe and Breuck (1995) used inverse numerical modeling to estimate aquifer parameters along with factors that materially affect the accuracy of the estimates themselves. Tumlinson et al (2006) used numerical evaluations to develop estimates of aquifer parameters in laterally heterogeneous confined aquifers. Trinchero et al (2008) have studied pumping tests in leaky-confined aquifers, where the solution reverts to a confined aquifer curve if leakance of the confining unit is very small.…”