Efficient high-dimensional characterization of conductivity in a sand box using massive MRI-imaged concentration data

Abstract:

Characterizing subsurface properties, particularly hydraulic conductivity, is crucial for reliable and cost-effective groundwater supply management, contaminant remediation, and emerging deep subsurface activities such as geologic carbon storage and unconventional resources recovery. With recent advances in sensor technology, a large volume of hydro-geophysical and chemical data can be obtained to achieve high-resolution images of subsurface properties, which can be used for accurate subsurface flow and reactive transport predictions. However, subsurface characterization with a plethora of information requires high, often prohibitive, computational costs associated with "big data" processing and large-scale numerical simulations. As a result, traditional inversion techniques are not well–suited for problems that require coupled multi-physics simulation models with massive data.

In this work, we apply a scalable inversion method called Principal Component Geostatistical Approach (PCGA) for characterizing heterogeneous hydraulic conductivity (K) distribution in a 3-D sand box. The PCGA is a Jacobian-free geostatistical inversion approach that uses the leading principal components of the prior information to reduce computational costs, sometimes dramatically, and can be easily linked with any simulation software. Sequential images of transient tracer concentrations in the sand box were obtained using magnetic resonance imaging (MRI) technique, resulting in 6 million tracer-concentration data [Yoon et. al., 2008]. Since each individual tracer observation has little information on the K distribution, the dimension of the data was reduced using temporal moments and discrete cosine transform (DCT). Consequently, 100,000 unknown K values consistent with the scale of MRI data (at a scale of 0.25^3 cm^3) were estimated by matching temporal moments and DCT coefficients of the original tracer data. Estimated K fields are close to the true K field, and even small-scale variability of the sand box was captured to highlight high K connectivity and contrasts between low and high K zones. Total number of 1,000 MODFLOW and MT3DMS simulations were required to obtain final estimates and corresponding estimation uncertainty, showing the efficiency and effectiveness of our method.