On the stochastic simulation procedure of estimating critical hydraulic gradient for gas storage in unlined rock caverns

We investigated some aspects of spatial variability and their effect on critical hydraulic gradient which is essential for gas containment of underground storage caverns. Monte Carlo technique can be effectively applied to obtain an approximate solution to the two-dimensional steady flow of a stochastically defined nonuniform medium. For the stochastic simulation we generated hydraulic conductivity field on the selected grid resolution using HYDRO_GEN with estimated (based on actual data) ln-K statistics with mean, variance, anisotropic integral scales. In this study, among various covariance functions, a Gaussian covariance function (GCF) was used. To find the critical value of the hydraulic gradient, probability density functions (PDFs) using 1000 outputs at an interested cell were developed. The results obtained in this study were compared with previous results for an exponential covariance function (ECF). It was found that in a stationary ln K field the uncertainty of hydraulic head and gradient depend not only on the variance and integral scale of the In K field but also on the shape of its covariance function. From these results we can conclude that the critical range of hydraulic gradient is significantly affected by the type of covariance function. Thus, when critical hydraulic gradient is to be determined one should consider shape of covariance function as well as statistical parameters such as mean, variance and correlation scale.