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Strain gauge type pressure sensors are widely used in different branches of industry to measure pressure from very low to very high (1400 Mpa) values. This article investigates a strain gauge type pressure sensor that uses silicon oil within its housing to transmit working pressure from the external environment to a sensing plate. An important failure mode arises from loss/leakage of the silicon oil, whereby a portion of the internal volume is replaced by gas, usually air. Coupled nonlinear governing equations have been derived and solved in both static and dynamical states to describe the behavior of the external membrane, the interface oil including pockets of gas, and the sensing plate. Nonlinear behavior arises from the plate and membrane midplane stretching, and of course the behavior of the gas. The resulting model describes how oil loss affects the sensor performance and changes the sensor output and pressure measurable range.

Signal processing is a fundamental component of almost any sensor-enabled system, with a wide range of applications across different scientific disciplines. Time series data, images, and video sequences comprise representative forms of signals that can be enhanced and analysed for information extraction and quantification. The recent advances in artificial intelligence and machine learning are shifting the research attention towards intelligent, data-driven, signal processing. This roadmap presents a critical overview of the state-of-the-art methods and applications aiming to highlight future challenges and research opportunities towards next generation measurement systems. It covers a broad spectrum of topics ranging from basic to industrial research, organized in concise thematic sections that reflect the trends and the impacts of current and future developments per research field. Furthermore, it offers guidance to researchers and funding agencies in identifying new prospects., 48 pages, https://iopscience.iop.org/article/10.1088/1361-6501/ac2dbd

The Prism is a new signal processing module which implements fully recursive, linear phase FIR filtering, so its computational cost is fixed irrespective of filter length. The Prism also has negligible design cost. Recent work has demonstrated how, using simple design rules, a chain of six Prisms can create a narrowband filter with arbitrary central frequency and bandwidth. In this paper, the technique is applied to spectral analysis of data, whereby a sequence of filters is applied to a data set to provide narrow frequency analysis, yielding accurate estimates of the frequencies and amplitudes of spectral peaks in the data. Although this time domain technique remains computationally expensive compared to the FFT, it can identify and reject spectral leakage, offering an alternative analysis for low amplitude and/or adjacent spectral peaks, including hidden tones, where FFT discrimination may be limited.

This paper presents new complex signal processing methods, Complex Bandpass Filtering (CBF), Complex Notch Filtering (CNF) and their combination (CBF-CNF), applied to the Coriolis Mass Flowmeter (CMFM). CBF, CNF and CBF-CNF can be utilized to suppress the negative frequency component of each sensor signal in order to produce the corresponding analytic form with reduced tracking delay. Further processing of the analytic form yields the amplitude, frequency, phase and phase difference of the sensor signals. In comparison with previously published methods, the new techniques offer short delay, high noise suppression, high accuracy and low computational cost. A reduced delay is useful in CMFM signal processing especially for maintaining flowtube oscillation in two/multi-phase flow conditions. The central frequency and the frequency range for the CBF, CNF and CBF-CNF methods are selectable so that they can be customized for different flowtube designs.

This paper introduces the Prism, a new type of signal processing block, as a contribution to the challenges of 21st Century metrology. The Prism is a fully recursive, dual output, FIR filter: the computational burden is low and independent of data window length. Prism design is trivial, so that networks of Prisms can be created, whether at design time or autonomously in real time, to carry out a range of metrological tasks. Prism-based trackers can generate sample-by-sample estimates of frequency, phase, and/or amplitude of a sinusoid. A simulation example of sensor validation demonstrates how Prism signal processing can be used to autonomously detect, track, and compensate for an undesired frequency component in a frequency-based sensor.

An earlier paper introduced a dataset of Coriolis meter mass flow and density errors, induced by the effects of two-phase (gas/liquid) flow, as a benchmark for which various error correction strategies might be developed. That paper further presented a series of error correction models based on neural nets. The current paper presents an alternative analysis of the same data set, using a support vector machine (SVM) approach. The analysis demonstrates that, for the benchmark data set, more accurate models are generated than those developed using neural nets. More specifically, it is found that a linear SVM model provides better performance than non-linear SVM. This improved performance may arise from over-fitting by both non-linear SVM and neural nets on this relatively small data set.

Prism signal processing is a new recursive FIR technique that facilitates the rapid tracking of sinusoidal signals, such as those used in a Coriolis Mass Flow Meter (CMFM). A Prism-based CMFM prototype has been developed using a commercial flowtube and a dual ARM processor-based transmitter, which is capable of generating flow measurement updates at 48 kHz. This has been applied in a feasibility study to the tracking of fast (e.g. 1.5 ms) injections of diesel fuel on a laboratory rig at engine speeds of up to 4000 rpm equivalent and at fuel pressures of up to 100 MPa. Due to the high level of vibration in the system, Prism-based notch filtering is used to suppress undesired modes of flowtube vibration in the sensor signal. Individual flow pulses can be detected by the system, but the relatively long period of oscillation of the flowtube compared to the fuel injection duration results in a spreading out over time of each flow pulse measurement. More precise measurement results may be obtained using a higher frequency resonant flowtube.

Prism Signal Processing is a new recursive FIR technique offering rapid filter design and calculation. It has previously been applied to Coriolis mass flow metering to generate fast (48 kHz) flow measurement updates, facilitating for the first time the direct mass flow measurement of individual fuel pulses injected into a laboratory diesel fuel injection test bench. In this paper we describe an augmented sensor signal filtering scheme which enables rapid tracking of the desired mode of flow tube vibration while notching out undesired modes. The new scheme is applied to a gasoline injection test bench where the vibrational interference is greater than for the previously described diesel system due to increased hydraulic shock. The paper presents experimental findings which illustrate the further challenges to be overcome in order to achieve the goal of traceable direct mass flow measurement of individual fuel injection pulses. For example, when a fuel pulse is shorter than the resonant period of the flow tube, the observed phase difference appears to show dependence on the instantaneous phase of the flow tube vibration.

— Two-phase (gas/liquid) flow is common in many industrial applications but its measurement remains challenging for Coriolis mass flow meters (CMFM), especially for high Gas Void Fraction (GVF). In this paper, we present experimental results applying previously developed complex signal processing techniques for tracking the rapidly changing sensor signals generated by two-phase flow. The techniques are implemented in a new System-on-Chip (SOC) prototype transmitter connected to a commercial Coriolis flow tube. Experiments have been carried out over a range of single phase and two-phase (water/air) flows. The signal tracking as well as mass flow rate and density measurement performance is compared with that of a laboratory version of a commercial Coriolis transmitter with two-phase flow capability. The results show that the complex bandpass algorithms, coupled with flowtube control algorithms, reduce the standard deviation of the mass flow measurement by a factor of 3 or more in 50% of the experiments undertaken. For the density measurement, the corresponding reduction in standard deviation is by a factor of 6.

A previously described Net Oil & Gas Skid (Henry et al., 2013) [1] combines a multiphase Coriolis mass flow meter with a water cut meter to generate on-line estimates of oil, water and gas flow rates, with an update rate of one second. This system has received approval from GOST, the Russian standards agency, for use in upstream oil and gas applications. The NOG system has been applied to well testing, where the output of an individual well is measured, typically over several hours. The conventional equipment used for this task is a test separator; however, a separator only provides the totalised flows of oil, water and gas over the test period. By contrast, the NOG system is able to provide time series of each flow rate, thus allowing more detailed characterisations of well behaviour. This paper draws on the results of several hundred well tests carried out in Russia to illustrate the different types of well behaviour observable using the Net Oil & Gas Skid.

For more than a decade there has been growing interest in the use of Coriolis mass flow metering applied to two-phase (gas/liquid) and multiphase (oil/water/gas) conditions. It is well-established that the mass flow and density measurements generated from multiphase flows are subject to large errors, and a variety of physical models and correction techniques have been proposed to explain and/or to compensate for these errors. One difficulty is the absence of a common basis for comparing correction techniques, because different flowtube designs and configurations, as well as liquid and gas properties, may result in quite different error curves. Furthermore, some researchers with interests in the modelling aspects of the field may not have suitable multiphase laboratory facilities to generate their own data sets. This paper offers a small data set that may be used by researchers as a benchmark i.e. a common data set for comparing correction techniques. The data set was collected at the UK National Flow Laboratory TUV-NEL, using air and a viscous oil, and provides experimental points over a wide flow range (8:1 turndown) and with Gas Volume Fraction (GVF) values up to 60%. As a first investigation using the benchmark data set, we consider how data sparsity (i.e. the flow rate and GVF spacing in the experimental grid) affects the accuracy of a correction model. A range of neural network models are evaluated, based on different subsets of the benchmark data set. The data set and some exemplary code are provided with the paper. Additional data sets are available on a web site created to support this initiative.

Our companion conference paper describes the requirement for flexible, self-validating instrumentation to support the goals of Industrial Cyber-Physical Systems. For high-value instruments such as Coriolis Mass Flow (CMF) meters, this entails more sophisticated signal processing techniques to provide additional sources of diagnostic and measurement data, particularly in dealing with common, but difficult real-world conditions such as two-phase (gas/liquid) flow. A novel Matrix Pencil Method (MPM) was described, adapted to monitor two modes of vibration for the CMF flowtube, and its performance evaluated in simulation. In this paper, we present results from applying the MPM technique to experimental data.

A key requirement for Industrial Cyber-Physical System (ICPS) instrumentation is measurement validation i.e. assessing measurement quality, including detecting and correcting for fault conditions. Coriolis Mass flow meters are used widely throughout industry, but commonly only for single-phase fluids, i.e. either liquids or gases, since accuracy is degraded by gas/liquid flows. The provision of robust measurement in non-ideal conditions is an increasingly important requirement. Here we propose that a modified Matrix Pencil Method is able to track the modes of flowtube vibration excited by gas/liquid flow, and show the results of applying the technique to numerically simulated data.

Trials have taken place to determine the response of a prototype Coriolis mass flowmeter to step changes in flow rate. The meter typically exhibits a delay of 16 ms, and tracks step changes well. Comparison with previously published results suggests that this performance represents an improvement over several types of current commercial flowmeters. The effect of a correction technique to reduce noise is demonstrated. This is considered valuable, even though it is responsible for 6 ms of the overall delay. A good dynamic response is important in process industry applications with short batch times. © 2003 Elsevier Science Ltd. All rights reserved.

Previous work has described the use of Coriolis mass flow metering for multiphase flows, with applications in the oil and gas industry. This paper describes the development and testing of a Coriolis two-phase flow metering solution for nitrogen/synthetic oil mixtures with viscosities ranging from 50 cSt to 500 cSt, and with Gas Volume Fractions (GVFs) ranging from 0% to 90%. Formal trials took place at the UK National Flow Laboratory. A single synthetic oil was used; its viscosity was adjusted by controlling temperature. The results show that Coriolis metering is well suited to high viscosity oil/gas mixtures: in the formalized trials, mass flow errors for gas were mostly within 5% and for liquid were mostly within 2.5%. Achieving this accuracy up to 90% GVF represents an advance on previous work, which has been limited to around 50% GVF for low viscosity oils in two-phase and three-phase mixtures.

Self-validation is a valuable tool for extending the operating range of sensing systems and making them more robust. Wireless sensor networks suffer many limitations meaning that their efficacy could be greatly improved by self-validation techniques. We present two independently developed data analysis techniques and demonstrate that they can be applied to a wireless sensor network. Using an acoustic ranging application we demonstrate an improvement of more than ten-fold in the uncertainty of a single measurement where multiple sensor readings are appropriately combined. We also demonstrate that of the two methods for determining a largest consistent subset one is more rigorous in dealing with correlation, and the other more suited to time-series data. © 2008 IOP Publishing Ltd.

Previous work has described the use of Coriolis mass flow metering for two-phase (gas/liquid) flow. As the Coriolis meter provides both mass flow and density measurements, it is possible to resolve the mass flows of the gas and liquid in a two-phase mixture if their respective densities are known. To apply Coriolis metering to a three-phase (oil/water/gas) mixture, an additional measurement is required. In the work described in this paper, a water cut meter is used to indicate what proportion of the liquid flow is water. This provides sufficient information to calculate the mass flows of the water, oil and gas components. This paper is believed to be the first to detail an implementation of three-phase flow metering using Coriolis technology where phase separation is not applied. Trials have taken place at the UK National Flow Standards Laboratory three-phase facility, on a commercial three-phase meter based on the Coriolis meter/water cut measurement principle. For the 50. mm metering system, the total liquid flow rate ranged from 2.4. kg/s up to 11. kg/s, the water cut ranged from 0% to 100%, and the gas volume fraction (GVF) from 0 to 50%. In a formally observed trial, 75 test points were taken at a temperature of approximately 40. °C and with a skid inlet pressure of approximately 350. kPa. Over 95% of the test results fell within the desired specification, defined as follows: the total (oil+water) liquid mass flow error should fall within ±2.5%, and the gas mass flow error within ±5.0%. The oil mass flow error limit is ±6.0% for water cuts less than 70%, while for water cuts between 70% and 95% the oil mass flow error limit is ±15.0%. These results demonstrate the potential for using Coriolis mass flow metering combined with water cut metering for three-phase (oil/water/gas) measurement. © 2013 Elsevier Ltd.

A review is given of the Second Edition of Professor Roger C. Baker's Flow Measurement Handbook, published in 2016 by Cambridge University Press.

Most two-phase applications for Coriolis mass flow metering are for low Gas Void Fraction (GVF) conditions, i.e. where the process fluid is essentially liquid with relatively low levels of entrained air or gas. There are particular challenges associated with metering wet gas, where the GVF exceeds 95%. Established wet gas metering techniques are typically based on a differential pressure-type device (for example an orifice plate or V-cone). It is well-known that such devices over-read compared to a dry gas calibration; equations to correct the reading are available if the degree of gas “wetness” is known. For Coriolis mass flow metering of wet gas, two approaches are described. The natural extension of the low GVF techniques is to map the observed mass flow and density readings onto estimates of the flow rates of the gas and liquid components. The alternative is to use the Coriolis meter to estimate the degree of gas “wetness” (e.g. the Lockhart-Martinelli number) and to apply a conventional correlation (e.g. Murdock or Chisholm) to a differential pressure flow reading. A prototype Coriolis-based wet gas meter is described, together with results from laboratory trials at CEESI in Colorado, and from extended field trials at BP's Wamsutter gas field in Wyoming.

The paper identifies the requirements for both a Coriolis flow-tube and the associated flow-transmitter, to achieve an ultra-fast dynamic response. A ‘new’ meter was assembled using a commercially available straight flow-tube, selected for its high drive (fundamental resonant) frequency of about 750 Hz (water-filled) and this was interfaced with a newly extended version of Oxford’s digital transmitter technology. This new transmitter gives measurement updates that are calculated every half drive-cycle, at 1.5 kHz, and are output via a high precision frequency pulse signal. Dynamic response tests in the laboratory and during a field trial have shown the ‘new’ meter to have a response time at least an order of magnitude faster than was reported previously [Clark C, Cheesewright R. Experimental determination of the dynamic response of Coriolis mass flow meters. Flow Measurement and Instrumentation 2006;17:39–47] from tests on the fastest response commercially available Coriolis meters. The ‘new’ meter shows a typical delay of 3.8 ms between a change in fluid flow rate and the corresponding change in the frequency output. Suggested further developments of the new transmitter technology indicate a route that could be followed to produce transmitters suitable for the newly emerging micro-machined Coriolis flow-tubes, which have fundamental resonant frequencies in the range 10–30 kHz.

The dynamic response of flow meters is significant in many applications, including fast control operations, e.g. short duration (less than 1 s) batch filling and for tracking the periodic flow fluctuations produced by positive displacement devices. The factors which determine Coriolis dynamic response have been elucidated. It has been shown that the meter flow tube response time cannot be less than the duration of one drive cycle of the tube vibration (i.e. reciprocal of drive frequency). This gives the potential of a response time of order 1 ms for the fastest currently available meters. However, the delay-time and update rates from the user output depend upon flow transmitter technology and design. Flow tube dynamic response has been investigated theoretically (simple straight tube), by finite element simulation (complex flow tube shapes) and experimentally. Commercially available meters were tested to determine the flow tube dynamic response to step changes in flow rate and the response to low frequency (compared with meter drive frequency) flow pulsations. Generally, dynamic flow events have been found to introduce contaminating signal components at one or more frequencies, other than that of the meter drive. The paper also presents details of the signal processing used to extract the required phase-difference and a method for reducing the contaminating signal noise. A new fast-response meter is currently being developed and some of the significant advances in the technology of a novel digital transmitter are described.

A new three-phase (oil/water/gas) flow metering system has been developed for use in the oil and gas industries, based on Coriolis mass flow metering. To obtain certification for use in the Russian oil and gas industries, trials have taken place at the UK and Russian national flow laboratories, NEL in Glasgow and VNIIR in Kazan, respectively. The metrology of three-phase flow is complex, and the uncertainty of each measurement varies dynamically with the operating point, as well as the metering technology, and other aspects. To a limited extent this is reflected in the error limits allowed in national standards, which may vary with operating point. For example, the GOST standard allows errors in the oil flow rate of ±6% for water cuts of less than 70%, which is increased to ±15% for water cuts between 70 and 95%. The provision of online uncertainty for each measurement, for example in accordance with the British Standard BS-7986, would be highly desirable, allowing the user to observe in real time variations in measurement quality. This paper will discuss how an online uncertainty assessment could be implemented in the Coriolis meter-based system.

The principle of injecting gases such as N2 and CO2 into oilfields to manage reservoir resources is well understood. The Yates Field — a mature site in West Texas — presented Kinder Morgan with particular difficulties, with the requirement to inject low pressure CO2 with flow control and measurement at the well-head. The low pressure and high ambient temperatures lead to almost continuous flashing, with gas void fractions (GVFs) estimated to range between 0% and 80%. A solar and wind powered station was designed around a two-phase capable Coriolis mass flow meter. As well as metering the flow, the station controls it using a modulating valve, based on the two-phase flow measurement. A wireless communication system maintains contact with the central control. Some 20 stations have been operating successfully for four years, enabling effective reservoir management techniques.

The use of Coriolis mass flow metering for two-phase (gas/liquid) flow is an emerging theme of both academic research and industrial application. The key issues are maintaining flow-tube operation, and modelling and correcting for the errors induced in the mass flow and density measurements. Experimentally-derived data is used to illustrate that these errors vary most notably with gas void fraction (GVF) and liquid flow rate, but other factors such as flow-tube geometry and orientation, and fluid properties such as viscosity are also influential. While undoubtedly a universal two-phase flow correction model is the ultimate research goal, there is currently no obvious candidate to explain the range of behaviours observed. This paper describes and demonstrates an empirical methodology that has proven effective in developing good correction models for a given choice of Coriolis flow-tube and flow mixture. A growing proportion of the world's oil reserves may be described as "heavy", implying high density and high viscosity. Of the various metering challenges heavy oil poses, one of the most significant is its ready entrainment of gas, and the difficulties entailed in separating gas from the oil. Accurate two-phase measurement of heavy oil is therefore an especially desirable technical goal. Trials were carried out at the National Engineering Laboratory (NEL), Scotland on a 75 mm flowmeter using a high viscosity oil. Flowrates from 1 kg/s to 10 kg/s were examined, with gas void fraction (GVF) up to 80%. The resulting models were tested online in a commercial Coriolis mass flow meter and demonstrated good performance for both steady and slugging two-phase flows, with the corrected measurements typically within 1%-5% of the nominal mass flow and density. Field trials in Venezuela have confirmed the performance of this two-phase solution. While research continues into the development of a generic two-phase correction, this case study demonstrates that the current state of the art can provide, for economically important fluids, tailored models with good two-phase flow performance. © 2006 Elsevier Ltd. All rights reserved.

This paper discusses Small Volume Provers (SVPs), used in the oil and gas industry to validate the performance of custody transfer meters. Recently Coriolis mass flow meters have been introduced for custody transfer; while these offer reduced maintenance requirements over traditional PD and turbine meters, proving Coriolis flow meters using SVP is challenging. This paper presents SVP results for a Coriolis meter which matches or exceeds the most stringent requirements for custody transfer. This is achieved in part by using a novel signal processing technique which reduces the dominant component of the measurement noise, associated with so-called Coriolis mode vibration, with negligible loss of dynamic response. © 2006 Elsevier Ltd. All rights reserved.

For many years it has been demonstrated that the use of digital technology, particularly embedded microprocessors, can improve flowmeter performance in various ways (e.g. temperature compensation, elimination of drift, generation of engineering units, diagnostics). A self-validating or SEVA sensor uses in-built processing power to generate generic metrics of measurement quality, based on on-line uncertainty. This uncertainty includes all factors effecting the on-line measurement, including diagnostics but also manufacturing aspects such as the components used and the characterisation procedure. This paper describes a prototype SEVA coriolis mass flow meter transmitter built primarily from digital components, which provides compensation for both faults and manufacturing limitations. A technique to compensate for drift and imbalance in the transmitter front-end circuitry is described in detail. The prototype has been developed using a hardware/software co-design approach in which virtually all aspects of instrument design are described in software, but which can be implemented flexibly in either hardware or software according to economic requirements. This approach offers manufacturers the opportunity of incorporating the latest components into their products rapidly in order to remain competitive.

Coriolis mass flow meters provide accurate measurement of single-phase flows, typically to 0.2%. However gas-liquid two-phase flow regimes may cause severe operating difficulties as well as measurement errors in these flow meters. As part of the Sensor Validation (SEVA) research at Oxford University a new fully digital coriolis transmitter has been developed which can operate with highly aerated fluids. This paper describes how a neural network has been used to correct the mass flow measurement for two-phase flow effects, based entirely on internally observed parameters, keeping errors to within 2%. The correction strategy has been successfully implemented on-line in the coriolis transmitter. As required by the SEVA philosophy, the quality of the corrected measurement is indicated by the on-line uncertainty provided with each measurement value. © 2001 Elsevier Science Ltd. All rights reserved.