Using sequential self-calibration method to estimate a correlation length of a log-conductivity field conditioned upon a tracer test and limited measured data

Abstract

A gradient-based inverse method, the sequential self-calibrated method (SSC), has been developed to identify a parameter for the statistical distribution function of a conductivity field, a correlation length. The identification is based on a tracer test data and some conductivity measurements. Correlation length is an important parameter for geostatistical description of a conductivity distribution. It is generally difficult to obtain from limited field measurements, especially in the horizontal direction, because the measurement in this direction is generally limited and sparsely populated. When the SSC method is used to estimate conductivity statistical distribution conditioned upon tracer test data, the closer the chosen correlation length to the real value, the faster the convergence rate, which is the basis of the identification method proposed in this study. The study results indicate the correlation length can be well determined by the tracer data and some conductivity measurements. In comparison with the identification of correlation length with only conductivity measurement, with tracer test data, much less measurement is required.