Characterization of permeability and porosity from nanosensor observations

In this paper, we investigate the information content in “nanosensors” with limited functionality that might be injected into a reservoir or an aquifer to provide information on the spatial distribution of properties. The two types of sensors that we consider are sensors that can potentially measure pressure at various times during transport, and sensors can be located in space by perturbations in electrical, magnetic, or acoustic properties. The intent of the study is to determine the resolution of estimates of properties that can be obtained from various combinations of sensors, various frequencies of observations, and various specifications on sensor precision.Our goal is to investigate the resolution of model estimates for various types of measurements. For this, we compute linearized estimates of the sensitivity of the observations to the porosity and permeability assuming gaussian errors in the pressure and location observations. Because the flow is one-dimensional and incompressible, observations of location are sensitive to the porosity between the injection location and the sensor location, while the location of particles is sensitive to the effective permeability over the entire interval from injector to producer. When only the pressure is measured but the location of the sensor is unknown, as might be the situation for a threshold sensor, the pressure is sensitive to both permeability and porosity only in the region between the injector and sensor.In addition to the linearized sensitivity and resolution analyses, Markov chain Monte Carlo sampling is used to estimate the posterior pdf for model variables for realistic (non-Gaussian) likelihood models. For a Markov chain of length one million samples approximately 200–500 independent samples are generated for uncertainty and resolution assessment. Results from the MCMC analysis are not in conflict with the linearized analysis.

► Sensitivity of nanosensor observations.
► Resolution of estimates.
► Assimilation of Lagrangian sensors.