Kjetil Folgerø

Measurement models that have a chemical composition as one of the arguments require special attention when used with the law of propagation of uncertainty from the Guide to the expression of uncertainty in measurement. The constraint that the amount fractions in a composition add exactly to unity not only affects the covariance matrix associated with the composition, but also impacts the differentiation of the measurement model to obtain the expressions and values of the sensitivity coefficients. Differentiating the measurement model with respect to each variable individually is not possible as it involves evaluating the model for infeasible inputs, leading to an undefined output. In this work, a numerical method for constrained partial differentiation is presented, enabling the use of the law of propagation of uncertainty for measurement models with compositions as one of their arguments. The numerical method enables treating the measurement model as a black box and using it with measurement models in the form of an algorithm. The numerical method is demonstrated by showing how the uncertainty associated with composition, temperature and pressure can be propagated through an equation of state, in this case, the GERG-2008 equation of state. It is shown that this differentiation can be completed in a few simple steps, requiring only a valid implementation of the measurement model that provides an output value for given input quantities. The numerical differentiation method applies in principle to all differentiable functions of a composition.

Measurement models that have a chemical composition as one of the arguments require special attention when used with the law of propagation of uncertainty from the Guide to the expression of uncertainty in measurement. The constraint that the amount fractions in a composition add exactly to unity does not only affect the covariance matrix associated with the composition, but also impacts the differentiation of the measurement model to obtain the expressions and values of the sensitivity coefficients. Differentiating the measurement model with respect to each variable individually is not possible as it involves evaluating the model for infeasible inputs, leading to an undefined output. In this work, a numerical method for constrained partial derivatives is presented, enabling using the law of propagation of uncertainty for measurement models with compositions as one of their arguments. The numerical method enables treating the measurement model as a black box and using it with measurement models in the form an algorithm. The numerical method is demonstrated by showing how the uncertainty associated with composition, temperature and pressure can be propagated through an equation of state, in this case the GERG-2008 equation of state. It is shown that this propagation can be done in a few simple steps, requiring only a valid implementation of the measurement model that provides an output value for given input quantities. The numerical differentiation method applies in principle to all differentiable functions of a composition.

The total quantity and energy delivered through a gas grid is calculated using simple formulæ that sum the increments measured at regular time intervals. These calculations are described in international standards (e.g., ISO 15112 and EN 1776) and guidelines (e.g., OIML R140). These guidelines recommend that the associated measurement uncertainty is evaluated assuming the measurement results to be mutually independent. This assumption leads to the underestimation of the measurement uncertainty. To address the growing concern among transmission and distribution system operators, the underlying assumptions of these uncertainty evaluations are revisited and reworked to be more adequate. The dependence of measurement results coming from, e.g., the same flow meter and gas chromatograph will be assessed for correlations, as well as other effects, such as the effect of the chosen mathematical approximation of the totalisation integral and fluctuations in the flow rate and gas quality. In this paper, an outline is given for improvements that can be implemented in the measurement models to render them more responsive to the error structure of the measurement data, temporal effects in these data, and the fluctuations in the gas quality and gas quantity. By impact assessment using a simple scenario involving the injection of (renewable) hydrogen into a natural gas grid, it is shown that these improvements lead to a substantive difference. This preliminary work demonstrates that correlations occur both in the instrumental measurement uncertainty and due to temporal effects in the gas grid. To obtain a fit-for-purpose uncertainty budget for custody transfer and grid balancing, it is key to enhance the current models and standards accordingly.

The total quantity and energy delivered through a gas grid is calculated using simple formulas that sum the increments measured at regular time intervals. These calculations are described in international standards (e.g., ISO 15112 and EN 1776) and guidelines (e.g., OIML R140). Currently, in the evaluation of the associated measurement uncertainty, the measurement results that enter into the calculation are assumed to be mutually independent. This assumption leads to underrating of the measurement uncertainty. There is a growing concern among transmission and distribution system operators that this assumption and the obtained values for the measurement uncertainty are not fit for purpose when fluctuations in gas quantity and quality increase, which occurs when injecting renewable energy gases such as hydrogen and biomethane. In a project in the European Partnership for Metrology programme, "Metrology for the hydrogen supply chain", the underlying assumptions of these uncertainty evaluations are revisited and reworked to be more adequate. The dependence of measurement results coming from, e.g., the same flow meter and gas chromatograph will be assessed for correlations, as well as other effects, such as the effect of the chosen mathematical approximation of the totalisation integral, and fluctuations in flow rate and gas quality. % The poster presentation gives an impression of the models being developed, the first findings and the magnitudes of the effects concerned. In this paper, an outline is given for the improvements that can be made in the measurement models to make them more responsive to the error structure of the measurement data, temporal effects in these data, and the fluctuations in gas quality and gas quantity.

This paper presents a method to simultaneously determine the thickness and permittivity of thin layers from multi-frequency reflection coefficient measurements using an open-ended coaxial probe. This is achieved by exploiting that the probe becomes radiating at frequencies higher than the probe’s typical operating range. Permittivity information is extracted from measurements in the typical frequency range, whereas thickness information is obtained from high frequency measurements by exploiting resonances that occur when the radiated waves are reflected at the layer boundary. A finite element model of the measurement set-up is made in COMSOL Multiphysics^TM, and a matrix of simulations spanning the relevant layer thicknesses and permittivity range is generated. The measured permittivity spectra of unknown samples are compared to the simulation matrix to estimate layer thickness and permittivity. The method is verified by measurements of water–ethanol mixtures. An application example where the water fraction and layer thickness of a gas hydrate deposition layer is estimated from permittivity measurements in a multiphase flow loop is also presented.