# Each-Phase Metering with Gas-Liquid Stratified Flow Based on the Multi-Frequency Coriolis Principle
## 1 Introduction  
The crude oil collection technology at the wellhead has developed rapidly. However, wellhead output metering is faced with problems of low measurement accuracy, short maintenance period, and human interference. In the oil field, wellhead output metering methods are usually divided into separation and non-separation, of which separation includes separation completely and partially. Three-phase separated metering adopts a horizontal three-phase separator, whose shortcomings are poor real-time performance, significant single-well measurement errors, and high maintenance costs. The dynamometer card method [1] for the rod pumped well as a non-separation metering method can achieve continuous measurement and real-time monitoring and simplify measurement process, however it is only applicable to low gas-containing pumping wells and only measures liquid phase flow. In recent years, multiphase flow meters (MPFMs) as non-separation metering methods are highlyrequired in either pipelines or well output metering, and remain a viable solution compared to test separators as they are less bulky, cheaper, more accurate, and allow real-time measurement [2]. However, the complex and variable flow patterns will reduce the reliability and accuracy of MPFMs [3]. The production fluid flows through the oil pipeline, which is usually a three-phase flow of oil, gas, and water with low gas content and high water cut. Given the densities of oil, gas, and water, it is necessary to treat oil and water as single-phase liquid to calculate the phase-separation flow of gas and liquid. The measured fluid has three unknown independent variables: liquid flow, gas flow, and volume void fraction (or cross-section void fraction), which need to be solved by at least three simultaneous equations. This subject is to use three equations to address the situation of three independent variables, thereby improving the accuracy of each-phase metering in gas-liquid two-phase flow. Many MPFMs commonly employ a combination of two or more measurement technologies, for example, differential pressure using Venturi, orifice [4] or V-cone [5], ultrasonic meter, gamma ray densitometry, microwave technology, capacitance, etc. [2]. Coriolis flowmeters can simultaneously measure parameters such as fluid density and mass flow compared with other flowmeters, which have the advantage of multi-parameter output. Gas is mixed into the liquid phase as interference. It has been found from research and field application that the bubble effect and resonance effect (increased fluid compressibility) caused by the presence of gas, which will seriously affect the accuracy of the Coriolis flowmeter measurement results, and even vibration stops [6]. Therefore, it is a feasible metering method to add at least one additional independent parameter (or an equation) to the existing two independent variables of a single-frequency Coriolis flowmeter to make the measurement equation have a unique solution. To this end, many scholars have explored the application of Coriolis flowmeters in gas-containing fluids through theoretical analysis, experimental research, and model building to improve the measurement accuracy of Coriolis flowmeters further. [PERSON] and [PERSON] [7] thoroughly discussed the theoretical work on the compressibility effect and derived the relevant formulas of density and mass flow measurement errors. [PERSON] [8] proposed a lumped parameter aeroelastic model to improve the measurement accuracy by measuring the sound velocity, but this method is only suitable for ideal uniform bubble flow. [PERSON] et al. [9] elaborated in detail that the neural network trained by the multi-layer perceptron (MLP) technology can obtain the internal parameters of the sensor (such as the apparent values of density, damping, mass flow) and correct the errors. [PERSON] and [PERSON] [10] described the technique of applying a viscosity correction factor to correct measurement errors caused by bubble effects. [PERSON] et al.