A Software Technique for Flow-Rate Measurement in Horizontal Two-Phase Flow

Abstract

Summary This paper presents a software technique for measuring individual phase flow rates in two-phase flow. The technique is based on the extraction, classification, and identification of stochastic features from turbulent pressure and void-fraction waveforms. Experiments in a horizontal air/water loop showed that a set of stochastic features is uniquely related to the individual phase flow rates. The software flowmeter is calibrated in situ by compilation of feature sets related to individual phase flow rates in a data base. On-line flow-rate measurement is made by a pattern recognition technique that identifies the best match to the measured feature vector from the calibration data base. Introduction In the current practice for testing multiphase well and pipe flow, a test separator separates different fluid phases, which are then metered in their respective single-phase flowlines by any single-phase flow measurement device. This approach suffers from inaccuracy and high cost. The requirements for a multiphase meter include an accuracy of ±5% for reservoir management and ±0.5% for fiscal measurement, a small footprint, minimum length upstream and downstream of the meter, a sampling frequency of at least 10Hz, design pressure up to 35 MPa, and a pressure drop of not more than 100 kPa across the meter. Finally, the meter should be easy to install and maintain.1 The software-based multiphase metering technique (called ESMER) reported in this paper appears to offer an accuracy suitable for testing and to meet the design criteria for an oilfield on-line multiphase flowmeter (Fig. 1). Theoretical Background Stochastic Features. A number of researchers2–11 used stochastic methods to analyze pressure and void-fraction waveforms to discriminate between different flow regimes. We have extended the stochastic treatment of the turbulent pressure and void-fraction waveforms by applying signal analysis methods, such as voice recognition, used in other disciplines. These methods have enabled us to derive "stochastic features" that characterize flow regimes with a greater degree of sensitivity and reproducibility than previously available. The stochastic features can be separated into two groups, the amplitude- and frequency-domain features. The amplitude-domain features include the probability density function, standard deviation, coefficient of skewness, and kurtosis. The frequency-domain features, widely used in voice and speaker recognition research, include the linear prediction coefficients.12,13 Feature Vector. A set of stochastic features derived from a waveform is called the "feature vector" of the waveform. We can also visualize the waveform as a distinct "object" by translating its feature vector to "feature space," as shown in Fig. 2. We use "waveform" to mean any signal that can be obtained from any sensor or combination of sensors that responds to the turbulent hydrodynamics of the flow, such as pressure, differential pressure, and void-fraction sensors. Flow-Regime Maps. Many studies propose generalized multiphase flow-regime maps on the basis of empirical/visual observations14–16 and/or mechanistic force balances.1 Flow-Regime/Rate-Identification Grid. The superficial-velocity flow-regime map is used in this study. This map is overlain by a grid, and we propose that each grid cell has a unique hydrodynamic waveform that can be modeled by its feature vector. Grid cells can be refined, depending on the variation of the feature vector between adjacent cells. This variation must be greater than the variation of the feature vector within a given grid cell in consecutive measurements (under conditions of constant superficial velocity). F-Ratio. An objective scale, the F-ratio, can be established to test the sensitivity of the feature vector to distinguish between neighboring cells. Atal19 first used the F-ratio in speaker recognition. It was defined as: Equation 1 where x=time dependent quantity observed, < >i = average over speakers, < >a = average over different blocks of one speaker, xi=<xi> a, a=block of observation, and µ=<xi>i, The higher the F-ratio, the greater the chances of speaker identification. ESMER's two-phase grid nodes are analogous with speakers; i.e., ESMER identifies grid nodes by the same techniques used to identify speakers. Speaker recognition techniques "train" the recognition system on the digitized waveforms of the voices or utterances of the speakers. ESMER trains (calibrates) the recognition system on the digitized waveforms of the turbulent hydrodynamic signals. The capabilities of the pattern recognition algorithms notwithstanding, the higher the F-ratio, the greater the refinement of the grid cells; i.e., the greater the sensitivity of the technique to flow-regime or flow-rate identification. At its coarsest, ESMER is capable of identifying flow regimes. Beyond a certain threshold, grid-cell identification can be related directly to individual phase flow rates. The strength of the F-ratio is expected to depend on a number of factors, such as sensor selection, number of calibration points, stochastic features derived from the flow, flowline geometry (up and downstream conditions, diameter, and orientation), and fluid physical properties. Calibration. ESMER must be calibrated in situ by extraction of feature vectors at a number of grid cells. Contour mapping techniques are used to interpolate/extrapolate the measurements to the entire grid-cell domain. The adequacy of the calibration points can be determined through observation of (1) the variance of the contour map with additional data (Fig. 3) or (2) the change in F-ratio with additional gridpoints. Stochastic Features. A number of researchers2–11 used stochastic methods to analyze pressure and void-fraction waveforms to discriminate between different flow regimes. We have extended the stochastic treatment of the turbulent pressure and void-fraction waveforms by applying signal analysis methods, such as voice recognition, used in other disciplines. These methods have enabled us to derive "stochastic features" that characterize flow regimes with a greater degree of sensitivity and reproducibility than previously available. The stochastic features can be separated into two groups, the amplitude- and frequency-domain features. The amplitude-domain features include the probability density function, standard deviation, coefficient of skewness, and kurtosis. The frequency-domain features, widely used in voice and speaker recognition research, include the linear prediction coefficients.12,13 Feature Vector. A set of stochastic features derived from a waveform is called the "feature vector" of the waveform. We can also visualize the waveform as a distinct "object" by translating its feature vector to "feature space," as shown in Fig. 2. We use "waveform" to mean any signal that can be obtained from any sensor or combination of sensors that responds to the turbulent hydrodynamics of the flow, such as pressure, differential pressure, and void-fraction sensors. Flow-Regime Maps. Many studies propose generalized multiphase flow-regime maps on the basis of empirical/visual observations14–16 and/or mechanistic force balances.1 Flow-Regime/Rate-Identification Grid. The superficial-velocity flow-regime map is used in this study. This map is overlain by a grid, and we propose that each grid cell has a unique hydrodynamic waveform that can be modeled by its feature vector. Grid cells can be refined, depending on the variation of the feature vector between adjacent cells. This variation must be greater than the variation of the feature vector within a given grid cell in consecutive measurements (under conditions of constant superficial velocity). F-Ratio. An objective scale, the F-ratio, can be established to test the sensitivity of the feature vector to distinguish between neighboring cells. Atal19 first used the F-ratio in speaker recognition. It was defined as: Equation 1 where x=time dependent quantity observed, < >i = average over speakers, < >a = average over different blocks of one speaker, xi=<xi> a, a=block of observation, and µ=<xi>i, The higher the F-ratio, the greater the chances of speaker identification. ESMER's two-phase grid nodes are analogous with speakers; i.e., ESMER identifies grid nodes by the same techniques used to identify speakers. Speaker recognition techniques "train" the recognition system on the digitized waveforms of the voices or utterances of the speakers. ESMER trains (calibrates) the recognition system on the digitized waveforms of the turbulent hydrodynamic signals. The capabilities of the pattern recognition algorithms notwithstanding, the higher the F-ratio, the greater the refinement of the grid cells; i.e., the greater the sensitivity of the technique to flow-regime or flow-rate identification. At its coarsest, ESMER is capable of identifying flow regimes. Beyond a certain threshold, grid-cell identification can be related directly to individual phase flow rates. The strength of the F-ratio is expected to depend on a number of factors, such as sensor selection, number of calibration points, stochastic features derived from the flow, flowline geometry (up and downstream conditions, diameter, and orientation), and fluid physical properties. Calibration. ESMER must be calibrated in situ by extraction of feature vectors at a number of grid cells. Contour mapping techniques are used to interpolate/extrapolate the measurements to the entire grid-cell domain. The adequacy of the calibration points can be determined through observation of (1) the variance of the contour map with additional data (Fig. 3) or (2) the change in F-ratio with additional gridpoints.