Characterization of energy gases by ultrasound : theory and experiments

The long-term goal with the research presented in this thesis has been to develop an ultrasonic sensor capable of measuring the energy content of energy gases such as natural- and biogas. The energy content can be calculated if the concentration of each constituent of a gas mixture is known. The acoustic properties of a gas mixture are dependent on its composition and by measuring, for example, the speed of sound it is possible to draw conclusions about the composition of the gas mixture. This feature could for instance be built into an ultrasonic flow meter. Natural gas manufactured from a single well is usually very consistent in its composition. However, the gas composition might vary between different wells and therefore also the energy content of the gas. This has the consequence that the quality of a gas might fluctuate if gases from different sources are mixed together. Therefore, the energy content of the gas mixture needs to be monitored in order to assure the quality of the gas. The physical principal that makes ultrasound suitable for gas measurements is called molecular relaxation. At certain frequencies this is the dominating source of acoustic attenuation and dispersion in gases. The frequency region at which the relaxation occurs differs between gases. This feature makes it possible to extract information about the composition of a gas from an ultrasonic pulse that has propagated through the gas. In a gas the molecules are constantly in motion. The molecules have also rotational and vibrational energy levels excited and the temperature determines the equilibrium between external and internal motion. An ultrasonic pulse transmitted trough the gas disturbs the equilibrium between the external and internal modes. This is due to the fact that a pressure pulse locally increases the velocity of the gas molecules, which is equivalent to an increase in temperature. This generates a flow of energy from the translational mode to the internal modes and the pulse is therefore attenuated. In order to design an ultrasonic energy meter there is number of problems that has to be considered. The frequency region where the relaxation effect is dominant has to be determined in order to maximize the variation of measured parameters as function of gas composition. These frequency regions can be found from theoretical predictions or by performing experiments. Many external factors will affect the performance of an energy meter situated \textit{in-situ}. It is important to be able to differ between effects generated by actual variations in gas composition from variations generated by other factors, for example, temperature variations and contamination in the flow. Before an energy meter can be manufactured, simulations has to be done \textit{a priori} in order to design the meter. Such a simulation must consider the electronics of the measurement system and the physics of the acoustic wave propagation through the gas. Much of the useful information wanted is found as variations in the frequency spectra of speed and attenuation of sound. Hence, the ability to measure the frequency dependent speed and attenuation accurate from pulses must be mastered. Further more, ultrasonic pulses are attenuated rapidly in many gases. Therefore, the signal-to-noise ratio can be very low. Is it still possible to extract the useful information even for such pulses? In the thesis different problems concerning gas measurements and modeling is addressed. The research has resulted in a model for temperature dependency of the speed of sound in gases. The model that is applicable to ideal gases has been derived by statistical thermodynamics. Measurement results of the frequency dependency of acoustic properties of gases are presented. Diffraction effects present in the ultrasonic measurement system have been simulated with equivalent circuits. It is shown how pulse shape distortions between pulses that have traveled through different samples of gas can be used as a mean for statistical gas classification. A method for calculating the speed of sound from noisy measurements has been derived. The thesis consists of two parts. The second part contains seven papers that describe the research. The first part serves as an introduction, and a survey, to some of the research problems described in Part II.Godkänd; 2004; 20061026 (haneit

Investigating the feasibility of using principal component analysis for ultrasonic classification of gas mixtures

On-line measurement of the energy content of natural gas is of interest for both industry and customers, since the energy content determines its monetary value. Experiments with pulsed ultrasound show that, in addition to changes in speed of sound and acoustic attenuation, there is also a change in the shape of the sound waveform. In this paper, we investigate the feasibility of using principal component analysis (PCA) to quantify this change in pulse shape. The principle is evaluated for pure oxygen, pure ethane, and mixtures of the two, for different pressures. The results show that by using PCA, it is possible to distinguish between pulses that have propagated through oxygen from pulses in ethane and mixtures of the two.Godkänd; 2003; 20061005 (ysko

Ultrasonic measurements of molecular relaxation in ethane and carbon monoxide

This paper describes how molecular relaxation can be measured using ultrasound. The velocity and absorption of sound varies with frequency due to molecular relaxation. By measuring these variation the relaxation strength and the effective relaxation time for singular relaxations can be calculated. This paper describes initial measurements performed in order to survey the sound properties in gases both experimentally and theoretically.Godkänd; 2002; 20061031 (ysko)</p

A simple scattering model for measuring particle mass fractions in multiphase flows

In this paper we present a simple theoretical model of how pulsed ultrasound is attenuated by the particles in a solid/liquid flow. The theoretical model is then used to predict the attenuation of sound, given the mass fraction, the density, and the size distribution of the solid particles. The model is verified experimentally for suspensions of 0–10% (by mass) Dolomite ((Ca,Mg)CO3) particles and water. The experimental results show that the attenuation of sound due to particles varies linearly with mass fraction, and that the proposed theoretical model can be used to predict this attenuation. In all experiments the transmitter and receiver array were clamped onto the pipe wall, thus providing a completely non-invasive and non-intrusive measurement technique.Validerad; 2002; 20061005 (ysko

Ultrasonic measurement of molar fractions in gas mixtures by orthogonal signal correction

Within Sweden and the EU, an increased use of biogas and natural gas is encouraged. To support more effective manufacturing, distribution, and consumption of energy gases, new methods for the measurement of the calorimetric value or the gas composition are needed. In this paper, we present a method to quantify variation in ultrasound pulse shape, caused by interaction effects between the constituents of a two-component gas mixture. The method is based on a combination of principal component analysis and orthogonal signal correction. Experiments on mixtures of oxygen and ethane show that the extracted information correlates well with the molar fraction of ethane in the mixture.Validerad; 2004; 20060925 (ysko

Incorporation of diffraction effects in simulations of ultrasonic systems using PSpice models

The use of PSpice models for piezoelectric devices and ultrasonic transmission media is of major importance in the design of electronics for ultrasonic systems. Today, these models include viscoelastic loss but disregard loss due to diffraction, i.e. beam spreading. This paper presents a method to include diffraction loss in PSpice simulations of ultrasonic systems. The conductive loss in the transmission line, that models the propagation media of the ultrasound pulse, is used to model the loss due to diffraction. Parameter variations for the piezoelectric device can affect the result greatly. Thus, a sensitivity analysis for the simulation model is presented. Measurements and simulations have been performed using a pulse echo system in water. Maximum distance to the reflector was 200 mm. The piezoelectric devices used were PZ-27 crystals with diameters 6 mm and 12 mm, with a center frequency of 4 MHz. Results show that the simulated amplitude of the echo follows measured values well in both near and far fields, with an offset of about 10%Godkänd; 2001; 20061101 (ysko)</p

A noise-tolerant group delay estimator applied to dispersion measurement in gases

In this paper we present a model-based group velocity estimator, that can be used to measure speed of sound in ultrasonic pulse-echo systems as a function of ultrasound frequency. The estimation of group velocities involves numerical differentiation of the phase difference. In the presence of noise, this becomes numerically unstable. The model-based approach presented herein, shows better tolerance to experimental noise. The performance of the estimator is evaluated with simulations as function of pulse bandwidth and SNR. Finally, the estimator applied to real data and compared with other methods for measuring speed of sound in Ethane and Oxygen.Godkänd; 2003; 20061005 (ysko)</p

Simulation of absolute amplitudes of ultrasound signals using equivalent circuits

Equivalent circuits for piezoelectric devices and ultrasonic transmission media can be used to cosimulate electronics and ultrasound parts in simulators originally intended for electronics. To achieve efficient systemlevel optimization, it is important to simulate correct, absolute amplitude of the ultrasound signal in the system, as this determines the requirements on the electronics regarding dynamic range, circuit noise, and power consumption.This paper presents methods to achieve correct, absolute amplitude of an ultrasound signal in a simulation of a pulse-echo system using equivalent circuits. This is achieved by taking into consideration loss due to diffraction and the effect of the cable that connects the electronics and the piezoelectric transducer. The conductive loss in the transmission line that models the propagation media of the ultrasound pulse is used to model the loss due to diffraction.Results show that the simulated amplitude of the echo follows measured values well in both near and far fields, with an offset of about 10%. The use of a coaxial cable introduces inductance and capacitance that affect the amplitude of a received echo. Amplitude variations of 60% were observed when the cable length was varied between 0.07 m and 2.3 m, with simulations predicting similar variations. The high precision in the achieved results show that electronic design and system optimization can rely on system simulations alone. This will simplify the development of integrated electronics aimed at ultrasound systems.Validerad; 2007; 20070318 (jerker