### 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.

Language | English |
---|---|

Pages | 534-552 |

Number of pages | 19 |

Journal | Journal of Hydrology |

Volume | 534 |

DOIs | |

State | Published - 1 Mar 2016 |

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### Keywords

- Estimation
- Experiment Design
- Porous media
- Variance constraints

### Cite this

*Journal of Hydrology*,

*534*, 534-552. DOI: 10.1016/j.jhydrol.2016.01.043

}

*Journal of Hydrology*, vol. 534, pp. 534-552. DOI: 10.1016/j.jhydrol.2016.01.043

**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.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Optimal input experiment design and parameter estimation in core-scale pressure oscillation experiments

AU - Potters,M.G.

AU - Mansoori,M.

AU - Bombois,X.

AU - Jansen,J.D.

AU - Van den Hof,P.M.J.

PY - 2016/3/1

Y1 - 2016/3/1

N2 - 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.

AB - 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.

KW - Estimation

KW - Experiment Design

KW - Porous media

KW - Variance constraints

UR - http://www.scopus.com/inward/record.url?scp=84956689439&partnerID=8YFLogxK

U2 - 10.1016/j.jhydrol.2016.01.043

DO - 10.1016/j.jhydrol.2016.01.043

M3 - Article

VL - 534

SP - 534

EP - 552

JO - Journal of Hydrology

T2 - Journal of Hydrology

JF - Journal of Hydrology

SN - 0022-1694

ER -