Re: Geostatistics Gs 9.0 Crack | Tested
Dwaine Hawke
Savioli, G. B., Falcigno, E. D., Bidner, M. S., and L. W. Lake. "Applications of Simulated Annealing on Actual but Atypical Permeability Data." Paper presented at the International Petroleum Conference and Exhibition of Mexico, Villahermosa, Mexico, March 1996. doi: -MS
The use of geostatistics is becoming recognized as a standard means of representing reservoir heterogeneity, Geostatistics has enjoyed an extensive use and a fairly well developed theoretical base. This is a little less true of simulated annealing (SA), the form of geostatistics tested here, but it is also a mature technology.
Yet there remains a need to exercise these procedures under actual conditions of nonuniformly sampled data, non-Gaussian distributions and truncated data sets. Providing insights into how to deal with these nonidealities is the objective of this work,
We find that SA estimates are improved when the original data sets are power-transformed. However, SA estimates tend to deviate from the input cumulative distribution function (CDF) because of excessive rejections. This deviation can be corrected by including the CDF into the SA objective function.
Aquitards are common hydrogeological features in the subsurface. Typically, pumping tests are used to parameterize the hydraulic conductivity of heterogeneous aquitards. However, they do not take spatial variability and uncertainty into account. Alternatively, core-scale measurements of hydraulic conductivity are used in geostatistical upscaling methods, for which their correlation lengths are needed, but this information is extremely difficult to obtain. This study investigates whether a pumping test can be used to obtain the correlation lengths needed for geostatistical upscaling and account for the uncertainty about heterogeneous aquitard conductivity. Random realizations are generated from core-scale data with varying correlation lengths and inserted into a groundwater flow model which simulates the outcome of an actual pumping test. The realizations yielded a better fit to the pumping test data than the traditional pumping test result, assuming homogeneous layers are selected. Ranges of horizontal and vertical correlation lengths that fit the pumping-test well are found. However, considerable uncertainty regarding the correlation lengths remains, which should be considered when parameterizing a regional groundwater flow model.
Los acuitardos son componentes hidrogeolgicos frecuentes en el subsuelo. Normalmente, los ensayos de bombeo se utilizan para parametrizar la conductividad hidrulica de acuitardos heterogneos. Sin embargo, no tienen en cuenta la variabilidad espacial ni la incertidumbre. Alternativamente, las mediciones de la conductividad hidrulica a escala de los testigos se utilizan en los mtodos de escalado geoestadstico, para los que se necesitan sus longitudes de correlacin, pero esta informacin es extremadamente difcil de obtener. Este estudio investiga si se puede utilizar un ensayo de bombeo para obtener las longitudes de correlacin necesarias para el escalado geoestadstico y tener en cuenta la incertidumbre sobre la conductividad heterognea del acuitardo. Se generan realizaciones aleatorias a partir de datos a escala de testigos con longitudes de correlacin variables y se insertan en un modelo de flujo de aguas subterrneas que simula el resultado de un ensayo de bombeo real. Se seleccionan las realizaciones que se ajustan mejor a los datos de los ensayos de bombeo que el resultado tradicional suponiendo capas homogneas. Se encuentran rangos de longitudes de correlacin horizontales y verticales que se ajustan al pozo de ensayo de bombeo. Sin embargo, sigue existiendo una incertidumbre considerable en cuanto a las longitudes de correlacin, que debe tenerse en cuenta a la hora de parametrizar un modelo regional de flujo de aguas subterrneas.
Aquitardos so feies hidrogeolgicas comuns na subsuperfcie. Tipicamente, testes de bombeamento so utilizados para parametrizar a condutividade hidrulica de aquitardos heterogneos. Contudo, os mesmos no levam a variabilidade espacial e incertezas e considerao. Alternati-vamente, medies em escala de testemunho da condutividade hidrulica so utilizados nos mtodos geoestatsticos de larga escala, para os quais as correlaes de comprimento so necessrias, mas esta informao extremamente difcil de se obter. Este estudo investiga se um teste de bombeamento pode ser utilizado para obter a correlao de comprimento necessria para a geoestastica de larga escala e explicar a incerteza sobre a condutividade heterognea dos aquitardos. Realizaes aleatrias foram geradas a partir de dados em escala de testemunho com variadas correlaes de comprimentos e inseridos em um modelo de fluxo de gua subterrnea que simula o resultado de um teste de bombeamento real. As realizaes que produziram os melhores ajustes com os dados do teste de bombeamento em comparao com o resultado do teste de bombeamento tradicional, assumindo camadas homogneas, foram selecionadas. Encontraram-se faixas de correlaes de comprimentos horizontais e verticais que tiveram bons ajustes no teste de bombeamento. Entretanto, uma incerteza considervel com relao as correlaes de comprimentos permanecem, que deve ser considerado ao parametrizar um modelo de fluxo da gua subterrnea regional.
Aquitards are important hydrogeological features, as they play a key role in groundwater resource assessment (Gurwin and Lubczynski 2005), contamination transport (Ponzini et al. 1989), land subsidence (Zhuang et al. 2017), salinization (e.g. Van et al. 2022) subsurface energy storage (Sommer et al. 2015) and radioactive waste disposal (Hendry et al. 2015). Although the importance of aquitards is widely recognized (Hart et al. 2006; Keller et al. 1989), many stochastic evaluations of hydrogeological field studies focus on the characterization of aquifers and neglect aquitards (Fogg and Zhang 2016). This study aims to improve the stochastic parameterization of aquitards specifically.
A large amount of data is needed to derive semivariograms (Weerts and Bierkens 1993) and accurate probability density functions (Khan and Deutsch 2016). If this is not available, estimates have to be used based on expert geological knowledge. However, inaccurate semivariograms, and in particular semivariogram ranges or correlation lengths, result in inaccurate block-scale hydraulic conductivity values. This is especially an issue with aquitards, as the core-scale hydraulic conductivity values of aquitard material, such as clay and peat, can vary several orders of magnitude (Neuzil 1994).
The objective of this study is to combine pumping tests and geostatistical upscaling to investigate whether pumping test observations can be used to obtain information about the spatial correlation of the lithology within aquitards. The procedure can be used to inversely estimate aquitard geostatistics. The paper is organized as follows. In the method section, the pumping test setup and the geological architecture of aquitards and aquifers at the site are described. Next, the core-scale conductivity data deemed representative of the aquitard under study, the groundwater flow model used and the stochastic method to estimate unknown correlation lengths of the aquitard are introduced. Following, the results are presented, which are then discussed in detail. The paper closes with a summary and conclusions.
A pumping test was performed at a site in Schouwen-Duiveland, province of Zeeland, in the southwestern Netherlands (Figs. 1 and 2). Three aquifers and three aquitards are present at this location. A schematic profile of the geology and lithology at the test location is shown in Fig. 3. For the pumping test, one extraction well and four infiltration wells were installed in the second aquifer that lies directly below the aquitard under study (aquitard 2; Fig. 2). The wells were fully penetrating this aquifer. A total of 20 piezometers were installed in the first, second and third aquifers. Five pumping tests were performed with varying configurations concerning discharges and distribution of extracted water over infiltration wells. The discharges during the pumping periods are listed in Table 1.
Two groundwater models were created for evaluating the pumping test using MODFLOW 6 (Langevin et al. 2017) with FloPy (Bakker et al. 2016). The first, a reference model, consists of five layers with homogeneous hydraulic conductivity values; the second model is set up with a heterogeneous second aquitard, consisting of multiple layers.
where Kcell is the resulting cell hydraulic conductivity, Kg is the geometric mean, and σY2 is the variance of the logarithm of the core-scale hydraulic conductivity distribution. This formula assumes the hydraulic conductivity variogram within the cell to be isotropic. Any anisotropy will follow from different horizontal and vertical correlation lengths at the scale of multiple cells and not from within the cells.
The performance of the simulated head distribution for each run of the heterogeneous aquifer model is evaluated and ranked according to the RMSE (Eq. 1) between the observed heads of the pumping test and each heterogeneous model realization.
Only the realizations with an RMSE lower than the RMSE of the reference model are evaluated. These realizations account for spatial variability and its uncertainty while outperforming the homogeneous model.
Number of realizations that perform better than the homogeneous model (in terms of RMSE) for each combination of horizontal and vertical correlation length. The size of the dots indicates the number, while the colour indicates the mean RMSE of these realizations
The representative aquitard conductivities K of the 209 best fitting realizations are calculated through two upscaling schemes. First, synthetic pumping tests are conducted on the heterogeneous fields and the corresponding representative conductivity for each realization identified. The second way is to run a flow simulation on each realization with a spatially uniform head distribution across the aquitard and identify the corresponding mean conductivity. The resulting frequency distributions of representative K values for the 209 realizations are shown in Fig. 7.
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