Characterization of energy gases by ultrasound theory and experiments

Abstract: 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 physicalprincipal 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 extit{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 extit{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 ofspeed 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 calculatingthe 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.