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

M.G. Potters, M. Mansoori, X. Bombois, J.D. Jansen, P.M.J. Van den Hof

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)

Abstract

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.

LanguageEnglish
Pages534-552
Number of pages19
JournalJournal of Hydrology
Volume534
DOIs
StatePublished - 1 Mar 2016

Fingerprint

oscillation
experiment
porosity
permeability
parameter estimation
measurement method
estimation method
matrix
parameter
simulation

Keywords

  • Estimation
  • Experiment Design
  • Porous media
  • Variance constraints

Cite this

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abstract = "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.",
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Optimal input experiment design and parameter estimation in core-scale pressure oscillation experiments. / Potters, M.G.; Mansoori, M.; Bombois, X.; Jansen, J.D.; Van den Hof, P.M.J.

In: Journal of Hydrology, Vol. 534, 01.03.2016, p. 534-552.

Research output: Contribution to journalArticleAcademicpeer-review

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