Logarithmic sensitivities and plausible relative errors are studied in a simple no-crossflow model of a transient flowmeter
test (TFMT). This model is identical to the model of a constant-rate pumping test conducted on a fully penetrating well with
wellbore storage, surrounded by a thick skin zone, and situated in a homogeneous confined aquifer. The sensitivities of wellbore
drawdown and wellface flowrate to aquifer and skin parameters are independent of the pumping rate. However, the plausible
relative errors in the aquifer and skin parameters estimated from drawdown and wellface flowrate data can be proportionally
decreased by increasing the pumping rate. The plausible relative errors vary by many orders of magnitude from the beginning
of the TFMT. The practically important flowrate and drawdown measurements in this test, for which the plausible relative errors
vary by less than one order of magnitude from the minimum plausible relative errors, can begin approximately when the dimensionless
wellface flowrate exceeds qD=q/Q≈0.4. During most of this stage of the test, the plausible relative errors in aquifer hydraulic conductivity (Ka) are generally an order of magnitude smaller than those in aquifer specific storativity. The plausible relative errors in
the skin hydraulic conductivity (Ks) are generally larger than the plausible relative errors in the aquifer specific storativity when the thick skin is normal
(Ks>Ka) and smaller when the thick skin is damaged (Ks<Ka). The specific storativity of the skin zone would be so biased that one should not even attempt to estimate it from the TFMT.
We acknowledge Wiebe H. van der Molen for recommending the De Hoog algorithm and sharing his code. This research was partially
supported by the US Geological Survey, USGS Agreement #1434-HQ-96-GR-02689 and North Carolina Water Resources Research Institute,
WRRI Project #70165. 相似文献
We present a nonlinear stochastic inverse algorithm that allows conditioning estimates of transient hydraulic heads, fluxes and their associated uncertainty on information about hydraulic conductivity (K) and hydraulic head (h ) data collected in a randomly heterogeneous confined aquifer. Our algorithm is based on Laplace-transformed recursive finite-element approximations of exact nonlocal first and second conditional stochastic moment equations of transient flow. It makes it possible to estimate jointly spatial variations in natural log-conductivity (Y=lnK), the parameters of its underlying variogram, and the variance–covariance of these estimates. Log-conductivity is parameterized geostatistically based on measured values at discrete locations and unknown values at discrete “pilot points”. Whereas prior values of Y at pilot point are obtained by generalized kriging, posterior estimates at pilot points are obtained through a maximum likelihood fit of computed and measured transient heads. These posterior estimates are then projected onto the computational grid by kriging. Optionally, the maximum likelihood function may include a regularization term reflecting prior information about Y. The relative weight assigned to this term is evaluated separately from other model parameters to avoid bias and instability. We illustrate and explore our algorithm by means of a synthetic example involving a pumping well. We find that whereas Y and h can be reproduced quite well with parameters estimated on the basis of zero-order mean flow equations, all model quality criteria identify the second-order results as being superior to zero-order results. Identifying the weight of the regularization term and variogram parameters can be done with much lesser ambiguity based on second- than on zero-order results. A second-order model is required to compute predictive error variances of hydraulic head (and flux) a posteriori. Conditioning the inversion jointly on conductivity and hydraulic head data results in lesser predictive uncertainty than conditioning on conductivity or head data alone. 相似文献
This paper has two main purposes. One is to present and analyse soil and structural vibration data obtained experimentally during certification testing of the high-speed train line between Córdoba and Málaga (Spain) that was opened on December 2007. The second is to show the capabilities of a three-dimensional boundary element method (BEM)/finite element method (FEM) numerical approach for the analysis of train induced vibrations. The model can represent local soil conditions, discontinuities such as underpasses, as well as structures placed next to the rail track. Vibrations in those structures can be computed taking into account, in a rigorous way, dynamic soil–structure interaction and local soil properties. Experimental and numerical results at several points near the track are compared. Results for an overhead contact support structure are also evaluated. The comparison of numerically predicted and recorded results shows that the model is reliable for predicting the amplitude of vibrations produced in the soil and nearby structures by high-speed trains. 相似文献