Optimal input experiment design and parameter estimation in core-scale pressure oscillation experiments

• Published in: Journal of hydrology (Amsterdam) 2016-03, Vol.534, p.534-552
• Main Authors: Potters, M.G., Mansoori, M., Bombois, X., Jansen, J.D., Van den Hof, P.M.J.
• Format: Article
• Language: English
• Subjects: Actuators; Estimation; Experiment Design; Inlet pressure; Mathematical models; Optimization; Outlets; Porous media; Pressure measurement; Pressure oscillations; Variance; Variance constraints
• ISSN: 0022-1694; 1879-2707
• DOI: 10.1016/j.jhydrol.2016.01.043

•Optimal actuator signals are designed that minimise experiment times.•An identifiability issue is revealed for an existing measurement methodology.•Parameter estimates are guaranteed to be of a minimal quality.•A new identification method delivers great experiment time reductions. This paper considers Pressure Oscillation (PO) experiments for which we find the minimum experiment time that guarantees user-imposed parameter variance upper bounds and honours actuator limits. The parameters permeability and porosity are estimated with a classical least-squares estimation method for which an expression of the covariance matrix of the estimates is calculated. This expression is used to tackle the optimization problem. We study the Dynamic Darcy Cell experiment set-up (Heller et al., 2002) and focus on data generation using square wave actuator signals, which, as we shall prove, deliver shorter experiment times than sinusoidal ones. Parameter identification is achieved using either inlet pressure/outlet pressure measurements (Heller et al., 2002) or actuator position/outlet pressure measurements, where the latter is a novel approach. The solution to the optimization problem reveals that for both measurement methods an optimal excitation frequency, an optimal inlet volume, and an optimal outlet volume exist. We find that under the same parameter variance bounds and actuator constraints, actuator position/outlet pressure measurements result in required experiment times that are a factor fourteen smaller compared to inlet pressure/outlet pressure measurements. This result is analysed in detail and we find that the dominant effect driving this difference originates from an identifiability problem when using inlet–outlet pressure measurements for joint estimation of permeability and porosity. We illustrate our results with numerical simulations, and show excellent agreement with theoretical expectations.