Estimation and simulation for geospatial porosity and permeability data

Reservoir simulation of (hbox {CO}_2) sequestration, energy recovery, and environmental contamination scenarios must be accompanied by uncertainty quantification. Typically this is done by stochastically modeling porosity and permeability fields, simulating realizations based on the model, and then numerically simulating flow and transport. The challenge is to generate simulated porosity and permeability fields with characteristics as similar as possible to those known of the reservoir under study. In this paper we focus on the first two steps above in analyzing a large 3-dimensional array of geospatial porosity data and using the results to produce simulated data with characteristics mimicking those of the original porosity observations. The spatial covariance is empirically approximated from horizontal cross sections of the data via a kernel principle component analysis yielding dimension reduction. Simulations in three dimensions are produced by linking consecutive parallel cross sections via conditioning on a small subarray of the data. The conditional simulations effectively reproduce observed channeling, an important large scale feature of interest in the sub-surface relevant to transport of contaminates. The original porosity data is non-Gaussian and requires additional analysis and transformation to generate both porosity and permeability fields.