Optimal sensor configuration for parameter estimation in single-phase hydrocarbon reservoir

The selection of the sensor locations has a significant impact on the quality of estimated parameters in hydrocarbon reservoirs. They are distributed parameter systems modeled by partial differential equations, and in this context, the determination of the rock properties such as the porosity (ratio of the pore volume to the total volume) and permeability (a measure of the rock resistance to the fluid flow) is required based on limited number of sensors. In this work, we address the problem on where to locate the discrete measurements on single-phase hydrocarbon reservoirs such that the estimated parameters have minimal variance. For that, we have performed a low-dimensional parameterization of the large-scale parameter space of rock properties and have applied classical theory for experiment design and sensitivity analysis. We have derived the sensitivity equations with respect to the parameterization, and finally have found the measurement experiment that minimize the variance of the parameter estimates, which is optimal with respect a performance measure related to the Fisher information matrix.