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Variability Response Function for Sudden Change in Reservoir Level with Random Hydraulic Conductivity

The concept of variability response function based on the weighted integral method is extended to problem of sudden change in reservoir problem. The hydraulic conductivity is considered to be two-dimensional (in one-dimensional space-time domain), homogenous, stochastic field. The stochastic element conductivity matrix is decomposed into deterministic part and stochastic part of element conductivity matrix. The stochastic part of element conductivity matrix is expressed as linear function of the random variables (weighted integrals) with zero-mean property. The concept of the variability response function is used to compute the upper bound of the response variability (response reservoir level). The first and second moment of stochastic hydraulic conductivity are used as input quantities for the description of the random property. The response reservoir level is calculated using first-order Taylor expansion approximation of the variability response function. The variability of the response reservoir level is represented in terms of the second moment of the response reservoir level and related coefficient of variation. The k-time-step-randomness method is introduced to reduce the computational effort. The algorithm for calculation with variability of the response reservoir level from just last k time steps is given. Numerical example is provided for different values of k. Calculated results with less computational effort are compared with results calculated with complete random history.

Reservoir Level; Sudden change; Uncertain hydraulic conductivity; Weighted integral method; Response variability

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