WO2009030870A1 - Multi phase flow measurement system - Google Patents

Abstract

A method of measuring flow rate, comprising measuring a first flow rate of a disperse phase using a first flow measurement system; measuring a second flow rate of a continuous phase using a second flow measurement system,- and combining the first and second flow rates to obtain a total flow rate.

Description

MULTI PHASE FLOW MEASUREMENT SYSTEM

Field of the Invention

Embodiments of this invention relate to a flow measurement system.

Background to the Invention

Slurry is an essential mixture of solid and liquid, and its physical characteristics are dependent on many factors such as size and concentration distributions of solids in the liquid phase, size of the conduit, level of turbulence, temperature, and absolute (or apparent) viscosity of the carrier. The transport of solid-liquid slurries over short and medium distances via pipelines is very important in many industrial applications. Local solid hold-up is one of the most important hydrodynamic characteristics that is needed for the design, analysis and performance estimation of liquid-solid -two-phase flow and pipeline transportation systems.

Electromagnetic flow meters (EMF) have been successfully applied to measure mean velocities of single-phase liquid in various industries. Continuous efforts have been made to measure the characteristics of two-phase flow using electromagnetic flow meters, since such meters do not introduce a pressure drop and can provide a fast response to changes in the flow. Thus, there are many potential applications for electromagnetic flow meters in two-phase flow. However, due to the complexity of multiphase flow in solid slurry transportation, it is difficult to accurately measure solid concentration and flow rate using a conventional electromagnetic flow meter alone. Normally, a secondary sensor, e.g. gamma-ray density meter, has to be employed.

Electrical resistance tomography (ERT) has been used successfully in predicting solid concentration, disperse phase velocity and flow regimes in both vertical and horizontal flows (McKee et al, 1995; Williams et al, 1996; Mann and Wang, 1997; G.P. Lucas et al., 1999; Wang and Yin, 2001). However, ERT is unable to measure the flow rate of the continuous phase and in its current form has difficulties in presenting an absolute value. Current multiphase flow measurements are very limited and cannot accurately measure flow rates in all multiphase flows, particularly where the phase distributions and velocity profiles are highly complex and non- steady, such as inclined oil-water flows in which internal waves intermittently form and decay. Two most commonly used methods for measuring gas- water two-phase flow are based on γ-ray attenuation and electrical impedance techniques. In addition to these methods, there are a number of other techniques, which have been used or being developed for industrial applications [9]. These include microwave attenuation and phase shift, pulsed neutron activation (PNA) and nuclear magnetic resonance (NMR). In principle, dual-energy γ- ray attenuation methods are elegant, but in practice a number of difficulties have to be overcome. As with all radiation measurement methods, more intense source can be used to enhance both the temporal and spatial resolution with the expense of increase safety precautions [10]. The salinity of the seawater may cause problems in the use of γ-ray methods. Since salt has a high attenuation coefficient compared to that of water, a change in the salinity of the water phase could cause a significant error in the measured water fraction [11]. Both techniques of PNA and NMR are complex and expensive although they can produce accurate measurement with limitations of temporal resolution and environmental restriction. Therefore, almost no three-phase flowmeter is practically available to most industrial applications.

Since electrical impedance tomography (EIT) can detect local changes in conductivity, the technique is used to study the unsteady mixing or flow dynamics of liquid mixtures such as, gas-liquid and solid-liquid mixtures where the fluids have different conductivities [12,13]. EIT may, therefore, be suitable for numerous aqueous-based processes. Typical measurements of a solid- water swirling flow were taken from downstream of a swirling inducer, which demonstrated how detailed quantification of the flows was possible (see Figure Ia) [6]. Using sequences of images obtained from a dual-plane EIT flow sensor, the local flow velocity of the dispersed phase can be deduced based on pixel-pixel cross-correlation methods [14,15]. According to other workers [16], the minimum acquisition time, t, can be taken as twice the product of the minimum transit time of the fluid, τ, and the fractional velocity discrimination, k, given by k = t/2τ. If the distance between two sensing planes is d = 0.1m then τ = O.lm/lOms^"1 = 0.01s. If 1000 frames/s is achieved then t = 0.001s and then the velocity discrimination error, k, is 5%. Therefore, the speed of data collection plays a dominant role in the use of cross-correlation algorithm. Recent research has successfully developed a high . performance electrical impedance tomography (EIT) system, which can be operated at a speed of 1164 dual-frames/second with RMS error less than 0.8% [17,2,3]. This is a vital specification that has to be met for the use of the cross-collection method to enable measurement of flow velocities up to 10 m/s [15].

Another difficulty in the use of EIT for unsteady two-phase flow measurements is due to the coverage of electrodes by the large bubbles or stratified non-conductive phase, which will produce significant measurement error and even failure. An EIT system containing a conducting liner, flush mounted with the internal diameter of the pipe, demonstrated is well suited to stratified and unsteady flows (see Figure Ib) [18,5]. In such flow regimes, where the current from the electrodes of a conventional EIT system would be blocked, the presence of the conducting liner allows the current to find an alternative path through the multiphase flow enabling the distributions of the phases to be accurately imaged.

Using a 'best pixel correlation method' [19], a dual-plane EIT system was able to measure the mean local axial, radial and azimuthal velocities ( v_z , v_r , v_θ ) of the dispersed phase in air-in water and oil-in-water flows. In the work, significant non- axial components were present e.g. swirling flows. A two-phase flow meter comprising a dual-plane EIT system and a Venturi [1], which, in vertical, bubbly air- water flows, enabled the volumetric flow rates of each phase to be measured with an accuracy of better than 1% of reading [20]. Examples of comparisons between results obtained from the tomographic method and from a local probe measurements are given in Figure 2.

EIT measurements also have limitations. Due to the inherent feature of electric field inverse solution problem in EIT it has a poor spatial resolution, under-determination of reconstructed local conductivity or volume fraction and possibly large error and noise at its low sensitive region and electrode region, respectively. It only can obtain the disperse phase flow rate in a two-phase flow and also can not correctly measure the true flow rate of a stratified flow as no flowing signature inside such a stratified flow layer. Without an assistance of a secondary flow meter, it is almost impossible to measure flow rates of both phases in a two-phase flow [20], so do for three-phase flows.

It is an object of embodiments of the invention to at least mitigate one or more of the problems of the prior art.

Brief Description of the Drawings

Embodiments of the invention will now be described by way of example only, with reference to the accompanying drawings, in which:

Figure Ia shows solid volume fraction distribution at downstream positions of

L/D=3.0, 7.4, 17.7 and 23 for water flow velocities of 1, 1.5, 2.0 and 2.5 m/s (L/D: the ratio of downstream length to pipe diameter);

Figure Ib shows an overview (top) and inside view (bottom) of the single electrode ERT sensor;

Figure 2 shows comparison of radial, axial and azimuthal velocity components from ERT (black diamonds) and a local probe (open squares);

Figure 3 shows an integrated system;

Figure 4 shows a signal flow chart of the measurement system;

Figure 5 shows an integrated slurry sensing system;

Figure 6 shows an integrated slurry sensing system;

Figure 7 shows a block diagram of at least one measurement system; Figure 8 shows a schematic of a test flow loop;

Figure 9 shows a comparison of volumetric solids fractions obtained using the ERT system and ERM model;

Figure 10 shows flow rates obtained from EMF; and

Figure 11 shows axial solids volume fraction distribution obtained using the ERT system.

Detailed Description of Embodiments of the Invention

Embodiments of the invention combine readings from one or more electrical impedance tomography sensors with the principles of an electromagnetic flow meter (EMF). Embodiments of the invention are able to measure one or more of the in-site volumetric flow rate and mean volume fraction of solid phase and true total flow rate in water-solid two-phase flows, as well as to visualise complex flow patters and spatial distribution of particle size distribution.

For example, embodiments of the invention relate to a method of measuring flow rate, comprising measuring a first flow rate of a disperse phase (e.g. a solid) using an EIT or ERT system, measuring a second flow rate of a continuous phase (e.g. water) using an EMF system, and combining the first and second flow rates to obtain a total flow rate. Embodiments of the invention also relate to a corresponding apparatus for implementing methods according to embodiments of the invention. For example, apparatus comprises an EIT or ERT system for measuring the first flow rate, an EMF system for measuring the second flow rate and combining means for combining the first and second flow rates to obtain the total flow rate. Disperse phases may comprise, for example, a single phase such as a solid, or may comprise multiple phases such as gas and oil. Thus, for example, methods and/or apparatus according to embodiments of the invention may be used to measure flow rates of two- or three- phase flows. Methods described will extend the concept of EIT-based two-phase measurement to three-phase systems. The measurement principle of the proposed three-phase systems is based on the use of multi-modality sensors and multi-dimensional data fusion, where three independent flow measurement sub-systems and one sub-system of density metering are applied. For example of a gas, oil and water three-phase system, an EIT technique with dual conductive ring sensors is used to extract local volume fraction distribution (a ^s'° ) and flow rate (Q^g'° ) of disperse phases (e.g. gas & oil). The principle of electromagnetic flowmeter (EMF) is applied to measure the flow rate (Q^w) of continuous phase (e.g. water). The mean volume fraction (Λ^g'°) of gas and oil phases obtained using the EIT also can be used to correct the measurement obtained from the EMF. The concept of Venturi differential-pressure flowmeter (VDF) is adopted for the measurement of the incompressible liquids' flow rate (Q^w>0) (e.g. of oil & water). The gas correction factor and mean density of liquids can be obtained by an online density meter, for example, γ-ray density meter, or a flow weighing system (OFW).

The flow rate of disperse phases can be derived as

Q^ε-° = AY_Jaf-° -V₁ (!)

1 where A is the area of cross section of the EIT imaging area, v,- is the local velocity at pixel i, which is implemented using the cross-correlation method, Mis the total number of pixels over the cross section imaged by EIT.

The flow rate of the continuous phase can be derived as, g^» = A^{w ■} v'" = A ^■ Λ'" ^■ v¹" = A • (1 - A^g-°) ^■ v" = A - (I - Y αf°) •— (²) tf zBd where A^w is the effective water coverage area, v^w is the average water flow velocity, u is electric potential, z denote the EMF impedance¹, B is the magnetic flux density and d is the effective distance between the electrodes. The flow rate of liquid phases can be derived as,

er-∞ (3) where C is the compressible fluid correction factor and the function of Λ^g, E is the installation coefficient of VDF, g is the gravitational acceleration, AP is the differential press drop of VDF and p^w'° is the mean density of the two-phase liquids, which can be obtained from OFW directly.

Now, we can simply derive other two phases' and total flow rates as,

Q = Q^S'° + Q^W

In order to simplify the construction and enhance the performance of the measurement system, both conventional EIT, EMF and VDF flow measurement methods will be modified and then, with integrated together to one robotic, rigid multiphase flow measurement and imaging system. The use of a flow weighing system (OFW) can provide a 'clean' and accessible environment for flow engineer although the γ-ray density meter also can be used to obtain the mean density of incompressible liquids.

In the use of the Venturi differential pressure flowmeter two parameters have to be known, namely, the compressible fluid correction factor, C, in regard to the volume fraction of gas phase, Λ⁸, and the mean density of the mixed fluid, e.g. p^w'° of water and oil. An online density meter, e.g. γ-ray density meter or a flow weighing system (OFW) or measurement of flow head using two pressure sensors, can be used to obtain the two parameters. In case of using an online flow weighting sub-system for a horizontal pipeline flow, which is considered as a 'clean' and accessible environment, the weight of the three-phase flow, π in the OFW' s effective measurement volume, γ^0FW _i can be presented as,

_WOFW _{= v}om . _(Λ., . _{p W + A}o . _po _{+ A}s . _{pg )} (5) where Λ^w, Λ°, A^g and p^w, p°, //, are volume fractions and densities of water, oil and gas in the flow, respectively. Λ^w is given by EIT measurement. Since the weight of gas can be ignored in the comparison to those of water and oil, therefore, we have W^w-° = V_0FSV -(A" .p" +A- -p") then, _A- ₌ J_. J£ΪL__A. ._p- (6) p⁰ ^F^ω<"

The two key compensation parameters in the use of the Venturi flowmeter can be derived as,

A^ l-A^ -A⁰ (7) A" - p^* ₊A' - p- ₍₈₎

The online flow weight measurement can be made by the use of a suspended balance with pressure sensors for horizontal pipeline flows or the pressure drop method for incline and vertical pipeline flows.

INNOVATIONS TO EXISTING EIT, EMF AND VDF

(1) EIT disperse phase sub-system development and optimisation

In previous researches¹, the inventor used the 'best correlated pixels' technique"'Error! Bookmark not defϊned.Error! Bookmark not defined, to determine the distributions of three orthogonal velocity components (axial, radial and azimuthal) of the dispersed phase in swirling multiphase flows. However a number of challenging issues and implementation will be addressed to enable these velocity component distributions to be measured with sufficient accuracy. These issues are given below.

(a) The normalisation method for pixel-values reconstructed with highly non- uniformed sensitivity distribution in EIT: Due to the nature of electric field distribution and therefore the ill-conditioned sensitivity matrix in the inverse problem, the weights of correlation functions may different, which may causes an erroneously selection of correlated pixels in the use of the 'best correlated pixels' technique for three-dimensional velocity vector distribution implementation. Therefore, the development of an effective normalisation method will be addressed. (b) The influence from 3D effect in EIT: Wang¹" showed that due to the 3D nature of the EIT sensing field, objects lying a short distance apart from the image plane are reconstructed closer to the central axis than their true position would suggest. This lateral displacement of the image of an object towards the central axis was found to increase with increasing the distance apart from the sensing plane. For dual-plane EIT systems, it is not currently known whether this 3D effect can cause errors in measured local particle velocity vectors obtained using the 'best correlated pixels' technique, however, there is a distinct possibility that it may give rise to erroneous velocity components normal to the axial direction. Two techniques will be investigated to minimise velocity measurement errors associated with 3D effects, (a) Wang¹¹¹ showed that the use of appropriate guard electrodes reduces the lateral displacement of reconstructed images of objects, but with the cost of reduced spatial resolution. Consequently, investigation of appropriate guarding techniques will be. carried out. (b) An investigation will also be carried out into the use of 3D reconstruction algorithms which take into account the 3D nature of the EIT sensing field, (c) The interpretation for multi-peak correlation and assessment method for noise or error level of a correlation: The maximum (or minimum) in the correlation function is normally assumed as the correlated point in the cross correlation method even though some other peaks present. This may ignore important information carried by these peaks, particularly in multiphase flows. At other aspect, large noises may be produced in the image reconstruction or generated by the disperse phase passing through the high sensitive area, e.g. the area near electrodes. These noises will also disturb the correctness of the flow information implemented with the cross correlation method.

Besides above issues, the materials for the construction of the conductive ring sensorError! Bookmark not defϊned. Error! Bookmark not defined.Εrror!

Bookmark not defined., the method of calibration of a?'⁰ with auxiliary sensors such as the temperature and conductivity sensors, the design combined with considerations from both EIT and EMF are considered in the design. For horizontal flow measurement, a swirling inducer may be applied to the inlet flow of EIT sensor to produce a dispersed flow.

(2) Modification on EMF continuous phase sub-system The concept of EMF is widely used in the flow measurement. An electromagnetic flowmeter mainly consists three parts, which are electrode system, coils and excitation source and measurement system. The current development of EMF has extended the measurement range from the conventional conductive or ultra- low conductive (O.OlμS/cm) liquid™ to non-conductive medium¹, however, only for single-phase flow or maybe two-phase flows with careful calibration and strictly narrow range. Several developments to the conventional EMF measurement are proposed, which will enhance the performance, simplify the electronics and reduce the physical size of the multi-phase flowmeter. The major issues are,

(a) Manufactures have developed electrodes with shapes and sizes optimised for individual applications. Large electrodes have tried and should result in a more uniform weight function⁷. Electrodes with a non-conductive lining to the flow tube (capacitance measurement) provide a non-invasive fashion for the flow measurement. They may also be less sensitive to fouling^vi and even used for non-conductive liquid (e.g. oil)¹. The single electrode made of a conductive ceramic lining also demonstrated its capability to image stratified flows or even an empty pipe and produce a more uniform sensitivity distributionError! Bookmark not defined. Error! Bookmark not defined/Error! Bookmark not defined.. A similar electrode system as the conductive lining method is used for both EMF and EIT measurement to handle the non-conductive continuous phase even transit phase flows. The ring also can be separated to two or more segments, in order to enhance the EMF signal strength.

(b) An ac source synthesized with dual frequency sinusoidal signals will be designed for the excitation of both EMF and EIT. The dual-frequency technique has been proved in recent development of EMF^1V, where the dual frequencies are applied not at the same time and the highest frequency is around 2.4 kHz^MV. We propose to apply one ac waveform synthesized from two signals with different frequencies, which allows dual frequency excitations to be applied at the same time. One of frequencies would be very low even dc and other is at least as higher as twenty times of the low frequency, e.g. 80 IcHz or above. The use of the high different in frequency is to amplify the frequency-response of the multiphase flows and to cover more wide multiphase flows: from conductive continuous phase to non-conductive continuous phase and even the transient phase. Applying dual frequency excitation at the same time will also enhance the temporal resolution and reduce the error of the data fusion of EMF and EIT. The single source with the same time clock may also provide an easy way to separate the responses from EMF and EIT and simplify the electronics and reduce the cross interference that may be arisen in the use of two independent excitation sources.

(c) Since the current in the EIT' electric field is orthogonal to the current induced by the magnetic field that is excited by the same source of EIT, the responded voltages at the electrode system can be effectively separated and measured using the concept of the phase sensitive demodulation™. The digital matched demodulationError! Bookmark not defined, used in our previous EIT system is adopted to perform the synchronized measurement for both EMF and EIT.

(d) More detailed challenges will be solved case by case, which include the method of magnetic filed installation, the effect of the conductive ceramic ring in magnetic field, the design of physically integration, etc.

(3) Design of Venturi liquid phase sub-system

Differential pressure flowmeter (DPF) is widely used in industry. Venturi is one of DPFs, which is based on the pressure drop across the throat and the wide pipe section of Venturi sensor. It is normally used for measuring incompressible fluids. In the use of Venturi for gas-liquid measurement, the measurement has to be compensated with known parameters of the ratios between the liquid and gas volumetric flow rates, densities or volume fractions. The liquid density should also be known. The Venturi sub-system proposed in the research is for the measurement of two liquid phases (e.g. water and oil) in three-phase flows and the compensation parameters, such as the gas correction factor and the mean density of liquids, can be dynamically obtained from the online flow weighting sub-system.

(4) Data fusion

Calibration is one of the most important procedures for almost all measurement systems, particularly, flow measurement. Tomography can produce instantaneously thousands of local concentration and velocity profiles, which present the dynamics of a process or flow. However, the references for the comparison, particularly of dynamic flow patterns and local volume fraction distribution, are difficult to be obtained. The way to validate and calibrate such a data set is undoubtedly a very challenging taskError! Bookmark not defined.. In this process, we shift our previous attention on the detailed flow features, as mentioned above, to the macro- information of flows. The flows' quantities e.g. flow rates, the spatial distributions, e.g. flow patterns, and the mean volume fractions of individual phases are the key specifications for the validation and calibration (Figure 3b). The use of a priori- knowledge, e.g. power law expressions, based on flow patterns and relevant flow profiles monitored using EIT, and so on is embedded in the process to assure the correctness of flow information.

The proposed system can collect more than 1 million data points per second from four sub-systems and few other additional sensors. Effective and correct methods to process such data and users' friendly interface for data delivery would be another key issue for the success of the research. The concepts of Principal Element Analysis method and Multi-variable Control are introduced into the data fusion of the flow measurement data. A new method with features of simplified computation, effective correlation and priori-knowledge assured flow information is developed in the process.

INTEGRATED SYSTEMS

The schematics of the construction and measurement systems for three-phase flows are given in Figure 3 and Figure 4. Figure 3 describes an integrated system. The EIT measurement sub-system consists of two conducting liners (7,8), a number of electrical contacts (9) connected to the out- walls of the conducting liners (7,8), a conductivity sensor (4) and two temperature sensors (5,6) for the compensation of conductivity measurement of conductive liquid. The EMF measurement sub-system uses two or more coils (10,11) to generate a magnetic field. The same conducting liners (7,8) and electrical contacts (9) are used for the measurement of the induced current/potential due to the conductive phase flowing under the magnetic field. The effective measuring area/region of both EIT and EMF is the throat part of the Veturi tube (12). The differential pressure of Venturi flow measurement is obtained from the two pressure sensors (1,2) or (2,3). The Venturi tube (12) is suspended using two flexible suspension tubes (19,20) and two spring suspensions (15, 16). Two pressure sensors (13,14) supported by two pivots (17,18) are used to measure the differential change of the pressures for weighing the horizontal pipeline flow in the effective volume of the Venturi tube (12). The weight of flow also can be measured using the two pressure sensors (1,3) in inclined or vertical pipeline flows. The measurement system (1-20) is enclosed by a house (23) and supported by a house (23) with junctions to the flexible suspensions (19,20) and pivots (17,18). Two flanges (21,22) are fixed at the two ends of the house (23) and flexible suspensions (19,20) for pipeline connection.

An EIT technique with dual conventional or conductive ring sensors is used to extract local volume fraction distribution (</) and flow rate (O/), and spatial distribution of particle size distribution of disperse phases (e.g. solid). The principle of electromagnetic flowmeter (EMF) is applied to measure the flow rate (Q^w) of continuous phase (e.g. water). The mean volume fraction (Af) of solid phase obtained using the EIT also can be used to correct the measurement obtained from the EMF.

The flow rate of disperse phases can be derived as

Q' = A∑a; .v, (9)

1 where /4 is the area of cross section of the EIT imaging area, v,- is the local velocity at pixel i, which is implemented using the cross-correlation method, Mis the total number of pixels over the cross section imaged by EIT.

The flow rate of the continuous phase can be derived as, ff" = A^W -Ψ" = A - K^v -v^w = A - (I - h^s) -Ψ° = A - (I-Ya*)--?- (10)

T^ zBd where A^w is the effective water coverage area, v" is the average water flow velocity, M is electric potential, z denote the

Now, we can simply derive the total flow rate as, β = β' +β" (11)

INNOVATIONS TO EXISTING EIT

In conventional EIT systems, the measurements are normally made by injecting a constant current and measuring boundary voltages or applying voltage and measuring current to obtain the mutual impedance of the object. The problem of poor signal-to- noise ratio (SNR) always exists if the continuous phase has a high conductivity, e.g. seawater. Therefore, the current value has to be increased in order to improve measurement SNR for application with a high conductive solution. The adjustment of the current is not straightforward. Generally, it has to be made by trial and error a tedious and time-consuming task. Secondly, the performance of current source at high frequency will become poor due to the limited output impedance inherited with operational amplifier and on board stray capacitance. This is also one of key difficulty in the application of EIT at high frequency domain, such as for the spectroscopy or multi-frequency application. The use of a constant voltage would be advantage at the aspect of SNR from boundary voltage measurements. It also has a much better performance at high frequency than that of current in the term of output impedance. However, the actual currents have to be measured corresponding to the boundary voltages, which may cause additional measurement error. A new method proposed as shown in Figure 5 is to apply a constant alternating voltage source 2 to the electrodes in/on the process vessel 1, and then the boundary voltage 3 is converted to current /_/ using a V-I converter 4. Both the converted current Ii and the sensor excitation return current h are applied to the inputs of a logarithmic ratio amplifier 5 to directly measure the mutual impedance, Z_mutuah

Normally, the boundary voltage of EIT has a wide dynamic range. Typically, it is about 1 :30 or more. Therefore, different gain values (e.g. the gain map) have to be applied to relevant voltage signals, which generally is about 2 to 3 decades gain values existing in a voltage measurement profile of one projection. The logarithmic- signal processing proposed can also maintain precise measurements over a wide dynamic range ^vι". The wide-dynamic-range signal undergoes compression, and the use of a lower resolution measurement system without the use of programmable gain amplifier then saves cost and enhances the precision. To further enhance the signal-to- noise ratio over a wide measurement range, the voltage to current converting ratio is programmable. Only one adjustment to N (see below equation) will be applied for all measurements in an application. The transfer function of the circuit in Figure 5 is:

² 'm_utu_al = K lθg 10 Al (12)

where K is the output scale factor, N is the voltage to current converting ratio and V_b is a boundary voltage.

CONSTRUCTION

Figure 6 describes an integrated slurry sensing system. The EIT measurement subsystem consists of two sets of EIT sensor that is made of a number of electrodes 7 fitted through the non-conductive pipe 6 and contacted with the slurry in flows. The EMF measurement sub-system uses two or more coils 8 to generate a magnetic field. The selected electrodes from electrodes 7 are used for the measurement of the induced current/potential due to the conductive phase flowing under the magnetic field. A conductivity sensor 9 and a temperature sensor 10 are used for the compensation of conductivity measurement of conductive liquid. The measurement system (6-10) is enclosed and supported by a metal house 11. Two flanges 12 and 13 are fixed at the two ends of the house 6 for pipeline connection. Figure 7 is the block diagram of measurement systems, where Q, Q^w and Λ^s denote the solids' flow rate, water flow rate and volume fraction of solids. EMF's, EIT's and other sensors' information are acquired and processed with either localized processor (see the figure) or a personal computer to provide flow information.

THEORETICAL CONSIDERATIONS

The slip velocity Slip velocity is a phenomenon that usually occurs in a multi-phase flow. For a liquid- solid two-phase flow, the liquid phase moves much faster than the solid, except in a downward flow. The difference in the in-situ average velocities between the liquid and solid phases will result in a very important phenomenon; the "slip" of one phase relative to the other, or the "hold-up" of one phase relative to the other. This makes the in-situ volume fractions different than the solid loading volume fractions. It is of importance to study this in detail in order to obtain an accurate in-situ fraction. Therefore the present work will use different models to study the influence of the slip velocity on the slurry measurement. The first of these models is the hindered settling velocity, proposed by Richardson and Zaki (1954) [42], which can provide estimates for individual grains of sand. The hindered settling velocity, V_T, can be estimated by:

v_τ = v_τ - (l -ε_SDY (13)

where S_SD is the delivered volumetric solids fraction. The index, n ', a function of the particle's Reynolds number, depends on the dimensionless particle diameter, which is n '=4.6 for particles settling in the range of Stokes' law and n '=2.4 in the range of Newton's law, respectively. V_T is the terminal settling velocity obtained by Stokes' law and Newton's law. When the Reynolds number is less than 0.1 in the Stokes region, the terminal settling velocity can be expressed by:

where p^ is the fluid density, μι is the fluid viscosity, g is the acceleration due to gravity, dis the particle diameter, maps is the particle density.

When the Reynolds number is between 750 and 300,000, the drag coefficient is nearly constant at a value of 0.44 in what is known as the Newton's law region. The terminal settling velocity is then:

The in-situ volumetric solids fraction

The frictional head loss can be described by the equivalent liquid model (ELM) (Matousek, 2002 [39]). For vertical upward flow, the force balance can be given by:

where dp/dx is the pressure gradient, τ_M is the shear stress, D is the tube diameter, and S_M is the in-situ relative density, given by:

S_M = l + (S_s -l) - ε_s (17)

where Ss =P_S ^//PL and εs represent the relative density of the solid and the in-situ volumetric solids fraction, respectively. According to this model the density of the mixture influences the liquid-like wall shear stress so that:

where /?M ^~ PS. SSL + PL(I - SSI)) ^SSL is the solids loading volumetric fraction. The wall shear stress, τ_L defined as

n = ^{pL '}f^V2 ■ . (19) where V is the mixture velocity, and friction factors,^, in a smooth pipe can be approximated by:

f_L = C_L -Rε_L-^H (20) where C_L = 0.079, n = 0.25, for turbulent flow, and C_L = 16, n = 1 for laminar flow. Substitution of Eq.(5) into (4) leads to:

_ (ΦAfe-4τ_M/D)/(g-pJ-l S₅ - I

o - C - Re ^~" - V² where τ_M = -^- — . Equation (9) may be used to calculate approximately the in-situ mean volumetric solid fraction.

The ERT system was used to estimate the in-situ volumetric fraction based on the average of volumetric fractions of individual pixels which constitute the entire image. The simple calculation is given by Eq. (22).

ε_s = ^- (22)

Aolal

where -4/, A_totaiana εsjis the area of pixel, the area of image (the cross-sectional area of pipe) and in-situ local volumetric disperse phase fraction, respectively.

Electromagnetic flow meter

The theory of the voltage-sensing flow meter was first developed by Shercliff (1954) [43]. The weight function, which represents the degree of the contribution of the fluid velocity to the signal in the cross-section of a conduit, was proposed and computed for single-phase flow. For two-phase flow with non-uniform but isotropic conductivity, Bevir (1970) [29] concluded that AU_TP can be expressed as:

AU AU - ^4BQL SP (23)

Ss ) A(l - ε_s) Here, Q_L is liquid flow rate and AU_Tp is the potential difference between electrodes for two-phase flow and AUsp for liquid flow alone (at the same flow rate Q_L). Λ is a homogeneity factor based on the conductivity distribution over the cross section of the EMF sensor in accordance with the flow power law and asymmetric velocity profile.

Bernier and Brennen (1983) [28] used an electromagnetic flow meter to measure a homogenous gas-liquid two-phase flow. They concluded that a homogenous flow would give rise to an equation:

They also investigated — = 1 is also valid irrespective of flow regimes or

AU_τp (l -ε_s) the homogeneity of electrical conductivity.

The difference between the two approaches is obvious: whether the homogeneity of dispersive phase distribution (flow pattern) should be taken into consideration. Since ERT can present the dispersive phase in-situ distribution, we prefer to use Eq.(l 1) in the present work , which could be simplified as:

Q_L = A -(I - ε_s)Q_EMF (25)

where Q_EMF is the mixture flow rate obtained using EMF.

EXPERIMENTAL SETUP AND PROCEDURE

A slurry flow loop with 50mm inside diameter has been designed and built at the School of Process, Materials and Environmental Engineering at the University of Leeds as shown in Figure 8 (Pachowko et al, 2003 [41]). The total PVC pipe work is 22m in length, with a 3m long vertical and two 5m long horizontal testing sections in the loop. The loop consists of a main 500 litres mixing tank, where the solid and liquid are mixed homogeneously and introduced into the loop. A 250 litre measuring tank is used to determine the delivered volumetric solid fraction at high flow velocities, as well as for verification of flow rate readings. A 15kW Warman International 2/11/2 AH heavy-duty centrifugal pump is used to transfer the slurry at velocities between 0.3 and 5 m/s. A frequency inverter was used for the control of the pump and hence the velocity and type of flow pattern that are generated. The flow rate of the solid and liquid mixture was measured by an electromagnetic flow meter (EMF). The selected EMF was a Krohne Aquaflux unit because its body lining was manufactured to be resistant to the slurry material flowing through it. Therefore, an abrasive slurry can be investigated. Mounting the flow sensor on a vertical pipe allows the measured velocity to be interpreted as the mixture velocity.

A range of sand slurries with median particle size from 212μm to 355μm was tested. The solid concentration by volume covered was 5% and 15%, and the corresponding density of 5% is 1078 kg/m³ and for 15% 1238 kg/m³. The flow velocity was between 1.5 m-s^" and 3.0 m-s^"1. A total of 6 experimental tests were conducted. ERT results presented in this paper were obtained from an ITS 2000 ERT system (Industrial Tomography Systems Ltd, Manchester, U.K.) in monitoring slurry transport in vertical pipes at several velocities. The ERT sensor was mounted in the working section at a distance of approximately 1.0 m from the tube bend. The dual-plane ERT Sensor with two dummy rings was configured so that the axial separation of the image planes was 50mm. On each plane, sixteen stainless steel electrodes are mounted flush to the surface of the pipe at equal intervals. The electrodes were designed to have a length to width ratio of 3, giving an electrode size of 18mm by 6mm. The voltage potential differences for tomography images were collected based on the normal adjacent protocol, with a data collection speed of 5 frames per second for the dual planes, at an AC current injection frequency of 9600Hz and a current value of 15mA. This produces 104 independent measurements for each tomographic image. The reconstruction of the image was carried out by the use of the Linear Back Protection (LBP) algorithm (Wang, 2000). The volumetric solids fraction was determined from the Maxwell relationship (Dyakowski et al, 2000 [30]). In this work, prior to experiments we calibrated the ERT system and took the reference frame when the sensor was full of liquid only, so that the reference measurement error could be controlled within 1%. RESULTS AND DISCUSSION

In-situ volumetric solids fraction measurement obtained by ERT

For each experiment, 350 conductivity images were continuously collected over approximately 5 minutes, for all loading volumetric fraction. These images were averaged and merged and then the volumetric fraction profile was obtained using the Maxwell relationship. The results are presented in Figure 9. The solid curves represent theoretical results predicted by Eq. (21) and the points indicate the measured values using ERT system. It is shown that the ERT system gives reasonable estimates of the mean volumetric fraction in vertical flow. It also demonstrates that it is possible the mean concentration in the test section to be higher than that of the loading sand concentration. It is also observed that the decrease of in-situ volumetric fraction as mean mixture velocity (as well as the slip velocity) increases in the solid-water two- phase upward flow. This phenomenon is well known and can be explained with the principle of mass conservation and flow continuity. Furthermore, the comparison with the results obtained by ELM showed that ERT system provided a reasonable estimation of the average volumetric fraction for the mixture flow of the vertical liquid-solid slurry flow.

Slurry flow rate measurement obtained by electromagnetic flow meter (EMF)

In order to investigate the effect of the mixture flow rate on the electromagnetic flow meter, we studied Eq.(25) using a loading volumetric sand fraction of 0.15. Two groups of data are presented in Figure 10. One set of data was obtained using the EMF readings corrected with a constant loading volumetric fraction, 0.15, and the experimental measurement using a measurement tank, respectively. Another data set were obtained using the EMF reading corrected with the in-situ volumetric fractions measured using the ERT system at relevant mixture flow rates, respectively.

It can be seen from Figure 10 that the data corrected by a constant volumetric fraction gives a linear relationship between the mixture and water phase flow rates. However a non-linear correlation is presented from both the experimental measurement and the data with correction made using in-situ volumetric fractions. The gradient of the curve deceases gradually with increased mixture flow rate. The difference may be caused by two reasons: (a) the decrease of volumetric solids fraction due to the increase of slip velocity between solid phase and liquid phase, which are demonstrated in Figure 9; (b) the flow pattern trends to non-homogenous flow when slurry flow rate is increased, namely the homogeneity factor, Λ , may not be constant for a non- homogeneous system. The EMF reading corrected with in-situ volumetric fraction has a consistent tendency similar to that obtained by the experimental method.

In-situ volumetric solids faction and velocity obtained by four different methods

For the sake of the studies of slip velocity in solid-liquid vertical flow, four different methods to obtain the slip velocity v_τ were attempted. If ε_SD is defined as the delivered volumetric solids fraction, then we can obtain from continuity equation:

v_τ = V_u .-^S^^ (14) εs

v_τ plays a very important role in vertical hoisting. Due to the different flow pattern in horizontal and vertical pipes under the same entry conditions, the delivered volumetric solids fraction is different in different pipes, especially for the experiment loop of the present work. The solid and liquid are mixed homogeneously and first introduced into the horizontal pipe and then flows into the vertical pipe section. Thus the delivered volumetric solids fraction ε_SD in vertical pipe would be re-measured with T2 as is shown in Figure 8. Table 1 shows the results calculated by different models.

15% loading sand volume (ε_SD = 0.134)

Methods s_s v_τ

Stokes' law 0.138 <m 0.051

(w^' = 4.6) Newton' law 0.140 0.073 (n = 2.4)

ERT system 0.198 t=> 0.520

ELM 0.192 i > 0.486

Table 1: A comparison of the mean in-situ volumetric solids fraction obtained and the slip velocity v_τ by four methods (The mixture velocity, V_M , is 1.61 m/s).

The arrow shows the derivation direction.

It is seen in table 1 that Stokes' law obtained the lowest ε_s and v_τ values. It should be emphasized that in practice Stokes and Newton models were based on the properties of single particles, so they only provide a rough estimate of the expected in- situ volumetric solids fraction. Furthermore, due to the size, velocity and density of the solid phase there will be segregation at the bottom of the vertical pipe. The two models did not take into account the interaction between different sized particles, either. Thus it would be better that the results of ELM are used to validate the ERT system. It can be seen in table 1 that the slip velocities in the test section reach to 0.52 m/s so that we should consider the effects of the slip velocity on slurry measurement. This aspect of the work will be studied further to correct the measurement results of EMF in the future.

CONCLUSIONS

To understand the performance of a liquid-solid slurry flow in a vertical pipe and measure the individual phase flow rate, the presented study was carried out conducting an experimental and theoretical investigation of the slurry vertical flow with EMF and ERT techniques. A series of experiments were carried out. As has been shown above, in the present work the flow rates of the continuous phase and two- phase mixture are measured using EMF, the volumetric disperse phase fraction is obtained with an ERT system, and the slip velocity can be predicted with ELM in a vertical pipe transporting slurry. Some significant results are obtained: For the measurement of flow rate it should be noted that the mounting position of the EMF instrument would have an important effect on results displayed by the EMF. In this study the EMF was mounted in the working section at a distance of about 0.1 m from the tube bend. As the mixture flows through a pipe bend this will result in an accumulation of particles at the bottom so that the accuracy of measurement is affected and there will be a distortion of velocity distribution in the pipe cross-section. In future work the EMF should be installed in a position where the vertical slurry flow is developed. Otherwise the EMF measurement has to be revised due to the influence of non-homogenous flow.

For the measurement of the disperse phase, a new in-situ measurement method based on ERT in a vertical flow is proposed. The results were checked by the ELM. Figure 11 shows that axial solids volume fraction distribution obtained using the ERT system at various mixture velocities at the loading solid concentration of 5% and 15%. It can be seen that there is an accumulation of particles at the outer wall of the pipe. Due to the ERT sensor being mounted in the working section at a distance of approximately 1.0 m from the tube bend and solid particle inertia, the mixture flow through a pipe bend will result in an accumulation of particles at the bottom and outer wall of the bend. In the connecting vertical pipe, the accumulation will disintegrate due to the secondary flow induced by the bend and due to flow turbulence. Similar results were also found by N. Huber and M. Sommerfeld (1994) [34] in a gas-solid two-phase flow. The results further prove the flow pattern of non-homogenous flow in the test section showing that inevitable errors exist for the measurement of non-homogenous a two-phase flow using the EMF. Furthermore for non-homogenous flow the slip velocity has to be considered to correct the results of EMF, and the equivalent liquid model (ELM) was used to calculate the slip velocity and validate the ERT system.

In summary, it should be emphasized that the EMF must be treated with reservations when the flow pattern at the EMF mounting point is a non-homogenous flow. The slip velocity and flow pattern have to be considered to correct the results using the equivalent liquid model. The results have demonstrated that the ERT technique can provide in-situ volumetric fraction and therefore can be used in conjunction with an electromagnetic flow meter as a way of measuring slurry flow rate in a vertical flow. (

It will be appreciated that embodiments of the present invention can be realised in the form of hardware, software or a combination of hardware and software. Any such software may be stored in the form of volatile or non- volatile storage such as, for example, a storage device like a ROM, whether erasable or rewritable or not, or in the form of memory such as, for example, RAM, memory chips, device or integrated circuits or on an optically or magnetically readable medium such as, for example, a CD, DVD, magnetic disk or magnetic tape. It will be appreciated that the storage devices and storage media are embodiments of machine-readable storage that are suitable for storing a program or programs that, when executed, implement embodiments of the present invention. Accordingly, embodiments provide a program comprising code for implementing a system or method as claimed in any preceding claim and a machine readable storage storing such a program. Still further, embodiments of the present invention may be conveyed electronically via any medium such as a communication signal carried over a wired or wireless connection and embodiments suitably encompass the same.

All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and/or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features and/or steps are mutually exclusive.

Each feature disclosed in this specification (including any accompanying claims, abstract and drawings), may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise. Thus, unless expressly stated otherwise, each feature disclosed is one example only of a generic series of equivalent or similar features.

The invention is not restricted to the details of any foregoing embodiments. The invention extends to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed. The claims should not be construed to cover merely the foregoing embodiments, but also any embodiments which fall within the scope of the claims. References

The following references are incorporated herein by reference for all purposes.

[I] Wang M₃ Lucas G and Williams R A 2001-2004 A high performance two-phase flowmeter, EPSRC GR/N28580, GR/N28610

[2] Wang M₅ Ma Y, Holliday N, Dai Y, Williams R A and Lucas G 2005 A High Performance EIT System, IEEE Sensors Journal, 5(2) 289-299 [3] Wang, M 2003 EIT data processing system and method, World Patent, PCT/GB04/03670

[4] Wang M, A highly adaptive EIT sensor 2000-2003, EPSRC GR/M94298 [5] Wang M and Yin W 2002 Electrical impedance tomography for flow measurements, World Patent, PCT/GBOl/05636 [6] Wang M, Jones T F and Williams R A 2003 Visualisation of asymmetric solids distribution in horizontal swirling flows using electrical resistance tomography, Chem. Eng. Res. Des, 81(A8) 854-861

[7] Wu Y, Li H, Wang M and Williams R A (2005) A study on the characterization of air- water two-phase vertical flow by using electrical resistance imaging, Canadian Chem. Eng. J, 83(1) 37-41

[8] Li H, Wang M, Wu Y, Ma Y, Williams R 2005 Measurement of oil volume fraction and velocity distributions in vertical oil-in-water flows using Electrical Resistance Tomography and a local probe, J Zhejiang Univ. Sci., 6A(12) 1412-1415 [9] Thorn R, Johansen G A and Hammer E A 1997 Recent developments in three- phase flow measurement, Meas. Sci. Technology 8 691-701

[10] Van Santen H, Kolar Z I and Schees A M 1995 Photon energy selection for dual energy γ- and x— ray absorption composition measurements in oil-water-gas mixture, Nucl.Geophysics. 9 193-202

[I I] Wylie, Shaw A and Shamma's A 12005 RF sensor for multiphase flow measurement through an oil pipeline, submitted to Meas. Sci Technology

[12] George D L, Torczynski J R, Shollenbeger K A, O'hen T J and Ceceio S L 2000 Validation of electrical-impedance tomography for measurements of material distribution in two-phase flows, Internal J. multiphase flow, 26 549-581 [13] York T 2001 Status of electrical tomography in industrial applications, J. Electron. Imag. Vol.10.3

[14] Lucas G P, Cory J, Waterfall R, Loh W W and Dickin F J 1999 Measurement of the solids volume fraction and velocity distributions in solids-liquid flows using dual- plane electrical resistance tomography, J Flow Meas. Instru. 10(4) 249-258

[15] Deng X, Dong F, Xu L J, Liu X P and Xu L A 2001 The design of a dual-plane ERT system for cross correlation measurement of bubbly gas/liquid pipe flow, Meas. Sci. Technol. 12 1024-1031 [16] Beck M S and Plaskowski A 1986 Cross Correlation Flowmeters - their design and application, Adam Hilger, Bristol

[17] Ma Y and Wang M 2004 Performance of a high-speed impedance camera for flow informatics, Proceedings of EDSA04, ASME, Manchester [18] Wang M, Yin W and Holliday N 2002 A highly adaptive electrical impedance sensing system for flow measurement, Meas. Sci. Technol. 1 13 1884-1889 [19] Mosorov V, Sankowski D, Mazurkiewicz L and Dyakowski T 2002 The 'best- correlated pixels' method for solid mass flow measurements using electrical capacitance tomography, Meas. Sci. Technol, 13 1810-1814 [20] Lucas G and Wang M (2005) Comparison of bubble velocity components in a swirling gas-liquid pipe flow using dual-plane EIT and a novel 4-sensor local probe, Proceedings for 4th World Congress on Industrial Process Tomography, Aizu: VCIPT 392-397

[21] Amare T 1999 Design of an electromagnetic flowmeter for insulating liquid, Meas. Sci. Technol. 10 755-758 [22] Dai Y., Wang M., Panayotopoulos N., Lucas G., Williams R. A. 3-D visualisation of a swirling flow using electrical resistance tomography, Proceedings for 4th World Congress on Industrial Process Tomography, Aizu, VCIPT 362-367 [23] Wang M 1999 Three-dimensional effects in electrical impedance tomography, Proceedings for 1st World Congress on Industrial Process Tomography, Buxton, VCIPT 410-415 [24] Yokogawa Electric Corporation 1995 Model CA100SG/SN and 200CS/SN capacitance magnetic flowmeter, Nakacho, Musashino-si, Tokyo, 180-8750, Japan [25] Baker R C 2000 Flow measurement handbook, Cambridge University Press [26] Rose C and Vass G 1995 New developments in flow measurement technology provide solutions to difficult process applications. ISA Advances in Instrumentation and Control: Int. Conf. Exhib., 50(3) 791-809

[27] Smith R W₅ Freeston I L, Brown B H and Sinton A M 1992 Design of a phase- sensitive detector to maximize signal-to-noise ratio in the presence of Gaussian wideband noise, Meas. Sci. Technol. 3 1054-1062

[28] BERNIER, R.N., BRENNEN, C.E., 1983. Use of the electromagnetic flow meter in a two-phase flow, Int. J. Multiphase Flow 9, 251-257. [29] BEVIR, M.K., 1970. The theory of induced voltage electromagnetic flow meters. J. Fluid Mech. 43, 577-590.

[30] DYAKOWSKI, T., JEANMEURE, L.F.C., JAWORSKI, A.J., 2000. Applications of electrical resistance tomography for gas-liquid and liquid-solids flows- A review. Powder Technology 112, 174-192. [31] GIDASPOW, D., 1994. Multiphase flow and fluidization - Continuum and kinetic theory descriptions. Academic press.

[32] HEYWOOD NI, MEHTA KB, POPLAR D. 1993. Evaluation of seven commercially available electromagnetic flow meters with Newtonian and non- Newtonian china clay slurry in pipe flow. 12th Int. Conf. Slurry Handling and Pipeline Transport-Hydrotransport 12. BHRG, 353-76 [33] HEYWOOD NI, MEHTA KB. 1999. Performance evaluation of eight electromagnetic flow meters with fine sand slurries. Hydrotransport 14. BHRG, 413- 31

[34] HUBER, N. and SOMMERFELD, M., 1994. Characterization of the cross- sectional particle concentration distribution in pneumatic conveying systems. Powder Technology 79, 191-210.

[35] LUCAS, G.P., CORY, J.C., WATERFALL, RC, 2000. A six-electrode local probe for measuring solids velocity and volume fraction profiles in solids-water flows. Measurement Science and Technology 11, 1498-1509. [36] MANN, R. and WANG, M., 1997. Electrical process tomography: simple and inexpensive techniques for process Imaging. Measurement and Control 30, 206-211. [37] WANG, M., YIN, W., 2001. Measurement of the concentration and velocity distribution in miscible liquid mixing using electrical resistance tomography. Transactions of the Institution of Chemical Engineers 79, 883-886. [38] WANG M (2002) Inverse solutions for electrical impedance tomography based on conjugate gradients methods, Meas. Sci. & Tech., IOP, 13, pp.101-117

[39] MATOUSEK, V., 2002. Pressure drops and flow patterns in sand-mixture pipes.

Experimental Thermal and Fluid Science 26, 693-702. [40] Mckee, S.L., WILLIAMS, RA. and BOXMAN, A., 1995. Development of solid-liquid mixing models using tomographic techniques. Chemical Engineering

Journal 56, 101-107

[41] PACHOWKO, A.D., WANG, M., POOLE, C. and RHODES, D. (2003) The use of electrical resistance tomography (ERT) to monitor flow patterns in horizontal slurry transport pipelines, Proceedings for 3rd World Congress on Industrial Process

Tomography, Banff, VCIPT, ρp.305-311

[42] RICHARDSON, J.F., ZAKI, W.N., 1954. Sedimentation and fluidisation.

Transactions of the Institution of Chemical Engineers 32, 35-53.

[43] SHERCLIFF, J. A., 1954. Relation between the velocity profile and the sensitivity of electromagnetic flow meters. J. Appl. Phys. 25, 817-818.

[44] WILLIAMS, R.A., JIA, X., MCKEE, S.L., 1996. Development of slurry mixing models using resistance tomography. Powder Technology 87, 21-27.

[45] WILSON, K. C. et al, 2006. Slurry transport using centrifugal pumps. Third edition, Springer.

¹¹ Dai Y., Wang M., Panayotopoulos N., Lucas G._s Williams R. A. 3-D visualisation of a swirling flow using electrical resistance tomography, Proceedings for 4th World Congress on Industrial Process Tomography, Aizu, yCIPT 362-367

'" Wang M 1999 Three-dimensional effects in electrical impedance tomography, Proceedings for I^st World

Congress on Industrial Process Tomography, Buxton, VCIPT 410-415 i^v Yokogawa Electric Corporation 1995 Model CA100SG/SN and 200CS/SN capacitance magnetic flowmeter,

Nakacho, Musashino-si, Tokyo, 180-8750, Japan v Baker R C 2000 Flow measurement handbook, Cambridge University Press v^ι Rose C and Vass G 1995 New developments in flow measurement technology provide solutions to difficult process applications. ISA Advances in Instrumentation and Control: Int. Conf. Exhib., 50(3) 791-809

™ Smith R W, Freeston I L, Brown B H and Sinton A M 1992 Design of a phase-sensitive detector to maximize signal-to-noise ratio in the presence of Gaussian wideband noise, Meas. Sci. Technol. 3 1054-1062 vⁱⁱⁱ Sheingold, Dan, Editor, Nonlinear Circuits Handbook, Analog Devices, ISBN: 0-916550-01-X.

Claims

1. A method of measuring flow rate of a flow comprising at least two phases, the method comprising: . measuring a first flow rate of a disperse phase using a first flow measurement system; measuring a second flow rate of a continuous phase a second flow measurement system; and combining the first and second flow rates to obtain a total flow rate.

2. A method as claimed in claim 1, wherein the first measurement system comprises at least one of an EIT, ECT and ERT system.

3. A method as claimed in claim 1 or 2, wherein the second measurement system comprises an EMF system.

4. A method as claimed in any of the preceding claims, comprising measuring a third flow rate of a liquid phase of the flow using a Venturi flow meter.

5. A method as claimed in claim 4, comprising measuring at least one of a volume fraction of gas phase and mean density of the flow using an online density meter.

6. A method as claimed in claim 5, comprising determining a flow weight (W°^FW, W^'⁰) from the at least one of a volume fraction of gas phase and mean density of the flow.

7. A method as claimed in any of claims 4 to 6, comprising measuring the first flow rate of at least two disperse phases using the first flow measurement system.

8. A method as claimed in claim 7, comprising determining respective flow rates of at least three phases from the first, second and third flow rates.

9. A method as claimed in any of the preceding claims, wherein the total flow rate comprises the sum of the first and second flow rates.

10. A system for measuring flow rate of a flow comprising at least two phases, the system comprising: a first flow measurement system for measuring a first flow rate of a disperse phase; a second flow measurement system for measuring a second flow rate of a continuous phase; and a combiner for combining the first and second flow rates to obtain a total flow rate.

11. A system as claimed in claim 10, wherein the first measurement system comprises at least one of an EIT, ECT and ERT system.

12. A system as claimed in claim 10 or 11 , wherein the second measurement system comprises an EMF system.

13. A system as claimed in any of claims 10 to 12, comprising a Venturi flow meter for measuring a third flow rate of a liquid phase of the flow.

14. A system as claimed in claim 13, comprising an online density meter for measuring at least one of a volume fraction of gas phase and mean density of the flow.

15. A system as claimed in claim 14, arranged to determine a flow weight (W°^FW, W^'⁰) from the at least one of a volume fraction of gas phase and mean density of the flow.

16. A system as claimed in any of claims 13 to 15, wherein the first flow measurement system measures the first flow rate of at least two disperse phases using the first flow measurement system.

17. A system as claimed in claim 16, arranged to determine respective flow rates of at least three phases from the first, second and third flow rates.

18. A system as claimed in any of claims 10 to 17, wherein the combiner determines the total flow rate by determining the sum of the first and second flow rates.

19. A system for implementing a method as claimed in any of claims 1 to 9.

20. A controller for implementing at least one of a method as claimed in any of claims 1 to 9 and a system as claimed in any of claims 10 to 19.