The objective of this study is to demonstrate the ability of riverstage tomography to estimate 2-D spatial distribution of hydraulic diffusivity (D) of Zhuoshui River alluvial fan, Taiwan, using groundwater level data from 65 wells and stream stage data from 5 gauging stations. In order to accomplish this objective, wavelet analysis is first conducted to investigate the temporal characteristics of groundwater level, precipitation, and stream stage. The results of the analysis show that variations of groundwater level and stream stage are highly correlated over seasonal and annual periods while that between precipitation is less significant. Subsequently, spatial cross-correlation between seasonal variations of groundwater level and riverstage data is analyzed. It is found that the correlation contour map reflects the pattern of sediment distribution of the fan. This finding is further substantiated by the cross-correlation analysis using both noisy and noise-free groundwater and riverstage data of a synthetic aquifer, where aquifer heterogeneity is known exactly. The ability of riverstage tomography is then tested with these synthetic data sets to estimate D distribution. Finally, the riverstage tomography is applied to the alluvial fan. The results of the application reveal that the apex and southeast of the alluvial fan are regions with relatively high D and the D values gradually decrease toward the shoreline of the fan. In addition, D at northern alluvial fan is slightly larger than that at southern. These findings are consistent with the geologic evolution of this alluvial fan. (C) 2017 Elsevier B.V. All rights reserved.

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[pt] A Equação da Difusividade Hidráulica Não-Linear (EDHN) modela o escoamento monofásico de fluidos em meios porosos levando em conta a variação das propriedades da rocha e do fluido presente no interior de seus poros. Normalmente, a solução adimensional da linha-fonte pD(rD, tD) para escoamento de líquidos é encontrada por meio do uso da transformada de Laplace ou transformação de Boltzmann, o qual, o perfil transiente de pressões em coordenadas cartesianas é descrito pela função erro complementar erfc(xD, yD, tD) e, em coordenadas cilíndricas pela função integral exponencial Ei(rD, tD). Este trabalho propõe a solução analítica pelo método de expansão assíntotica de primeira ordem em séries, para solução de alguns problemas de escoamento de petróleo em meios porosos com permeabilidade dependente da pressão de poros e termo fonte. A solução geral será implementada no software Matlab (marca registrada) e a calibração do modelo matemático será realizada comparandose a solução obtida neste trabalho com a solução calculada por meio de um simulador de fluxo óleo em meios porosos denominado IMEX (marca registrada) , amplamente usado na indústria de petróleo e em pesquisas científicas e que usa o método de diferenças finitas. A solução geral da equação diferencial é dada pela soma da solução para escoamento de líquidos com permeabilidade constante e o termo de primeira ordem da expansão assintótica, composto pela não linearidade devido à variação de permeabilidade. O efeito da variação instantânea de permeabilidade em função da pressão de poros é claramente demonstrado nos gráficos diagnósticos e especializados apresentados. / [en] The Nonlinear Hydraulic Diffusivity Equation (NHDE) models the singlephase flow of fluids in porous media considering the variation in the properties of the rock and the fluid present inside its pores. Normally, the dimensionless linear solution for the flow of oil is performed using the Laplace and Fourier transform or Boltzmann transformation and provides the unsteady pressure profile in Cartesian coordinates given by complementary error function erfc(xD, yD, tD) and in cylindrical coordinates described by the exponential integral function Ei(rD, tD). This work develops a new analytical model based on an integro-differential solution to predict the formation mechanical damage caused by the permeability loss during the well-reservoir life-cycle for several oil flow problems. The appropriate Green s function (GF) to solve NHDE for each well-reservoir setting approached in this thesis is used. The general solution is implemented in the Matlab (trademark) and the mathematical model calibration will be carried out by comparing the solution obtained in this work to the porous media finite difference oil flow simulator named IMEX (trademark). The general solution of the NHDE is computed by the sum of the linear solution (constant permeability) and the first order term of the asymptotic series expansion, composed of the nonlinear effect of the permeability loss. The instantaneous permeability loss effect is clearly noticed in the diagnostic and specialized plots.