- Email: [email protected]
Flow imaging for multi-component flow measurement
Flow Meas. Instrum. Vol 1 October 1990
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Flow imaging for multi-component flow measurement R. T H O R N , S. M. H U A N G , C. G. XlE, J. A. SALKELD, A. H U N T and M. S. BECK
For pseudo-homogeneous flows, measurements of density and mean velocity can give the component mass flow rate of a two-component mixture. However, for accurate measurement of non-homogeneous flow rate, the density and velocity distribution across the cross-section of the pipe must be known. The most practical way of obtaining this information is by using the flow imaging technique. A recently developed capacitance system gives 60 frames per second images of oil/water flow in a 78 mm pipe. The target spatial resolution is one part in 20 by distance (one in 400 by area). The electrical properties of each imaged boundary are functionally related to the imaged value, so the component ratio of a two-component mixture within a boundary can be measured, although individual particles cannot be imaged. Design data shows how the basic system can be part of a complete system for component mass flow measurement. Keywords: multi-component flow, imaging, tomography, capacitance transducers
The importance of multi-component flow measurement Until recently, most flowmeters have been used to measure single-component materials (petrol, gas, water, etc) at points of use or in production plants. However, the increasing need to use resources more efficiently and build processing plants that can be operated cost-effectively, while minimizing pollution, has led to an increasing demand for multi-component flowmeters. The development of multi-component flowmeters is both a fascinating and expanding area of measurement. Future process requirements, with their need for ever more detailed measurements, will ensure that this expansion continues. The growing demand for flowmeters capable of metering multi-component flows can be illustrated by considering two examples from the petroleum industry. The first concerns the problem of three-component measurement. In a typical offshore production facility, fluid from each well is pumped to the production platform where it undergoes preliminary processing before being shipped or piped directly to shore. The crude oil produced by an offshore reservoir usually contains both gas and water components. The flow pattern of the resulting mixture varies with the flow's conditions and is generally not predictable. It is important for the operator of a production platform to
R. T. is with the SouthAustralianInstituteof Technology,5. /H. H., C. G. X., J. A. S. andM. 5. B. are with the Universityof Manchester Instituteof Scienceand Technology,andA. H. is with 5chlumberger CambridgeResearchLtd. 0955-5986/90/050259-10
know which types of fluid a well is producing. The current method of solving this problem is to separate the fluids first, and then monitor each using conventional single-component flowmeters (e.g. orifice plate for gas, turbine meter for oil). With the space on a production platform becoming more expensive, and the development of subsea production systems increasing, the use of conventional offshore separators is becoming less desirable. Therefore a particularly interesting but difficult flow measurement problem arises: namely, how the component fractions of an oil/gas/water mixture can be reliably monitored without separation in a hostile environment. The qualities required for such a measurement system are that it should be: [] non-intrusive, to avoid sensor erosion and pressure drop [] a real-time measurement, to provide instantaneous feedback to the production operator [] in-line to avoid the problem of sample representivity [] reliable, because maintenance will be costly, and perhaps impossible in the short-term [] easily calibrated for use subsea. A number of solutions have been proposed to this problem. However, one of the most promising methods currently under development uses the combination of a gamma radiation sensor and a capacitance sensor I. The gamma radiation sensor is used to measure the mean density of the multi-component flow, while the capacitance sensor is used to determine the mean permittivity of the flow. These two independent measurements are then used to determine (~) 1990 Butterworth-HeinemannLtd
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R. Thorn et al - Flow imaging for multi-component flow measurement
the component ratio of the flowing oil/water/gas mixture. Results so far show that this system is capable of determining the composition of a well-mixed flow with an accuracy of better than +3% of full scale. While there are still many problems to solve, such as how to deal with changes in flow regime, ten years ago such a flow measurement system would have been inconceivable. A second illustration of how the development of multi-component flowmeters has progressed can be found by considering a later stage of the oil production process. Even after separation, the water content of a ship's crude oil cargo may lie in the range 0 - 5 % . This may not seem a great deal, but an error of only 0.15% in measuring the water content of a ship's 250000 ton oil cargo would result in a loss of approximately £1m (1990 prices). An accurate twocomponent measurement is therefore required; however, most currently used methods have limitations. The usual method of measuring water content today is by use of an isokinetic sampling system. This basically consists of a probe inserted into the pipeline through which samples of the flow are drawn for off-line laboratory analysis. This technique presents a number of problems, the most serious being the ability of the system to take representative samples and the time required to obtain the measurement. Recently, a number of organizations have investigated on-line water content measurement using capacitance sensors 2. The measurement principle has attracted a great deal of interest because it has a fast dynamic response and offers the possibility of constructing a non-intrusive sensor which can be used on-line. Capacitance based water content meters produced so far are an improvement on isokinetic samplers in that they produce instantaneous measurements. However, their calibration is dependent on flow regime, temperature and whether the water or oil is the dispersed component in the flow. The above examples show how rapid advances in process production techniques have encouraged the development of specialized multi-component flowmeters. The principles on which such flowmeters can be based are described below.
Terminology In this article we consider multi-component flows to be those where the components exist in a separated form; that is, either solid, liquid or gas. In many publications the term 'multi-phase flow' is used instead of 'multi-component flow', although multi-phase flows should strictly be only those composed of separate phases such as a liquid and a gas. An oil/water flow is therefore by definition a two-component flow while a gas/oil flow may be classified as a multi-phase or multi-component flow. Throughout this article only the term multi-component will be used, since this is applicable in all cases.
matter, the first problem being to decide what parameter actually needs to be measured. When used by itself, the term 'flow measurement' is rather vague and can often mean different things to different people. For instance, one user may be interested in measuring a mixture's volumetric flow rate, while in another application the mass flow rate will be required. Since both these may be called 'flow measurements', care should be taken when specifying the actual measurement required. A pseudo-homogeneous fluid is probably the easiest two-component mixture to measure. In this particular case one component is finely and evenly dispersed in the other, and so the mixture can be treated as a single fluid that obeys all the usual equations of single-component flow. Referring to the pseudo-homogeneous flow shown in Figure 1, the volumetric flow rate Q of the mixture can be calculated using: F
R
Q = J0 2~rv(r)~r
(1)
where v(r) is the velocity of the fluid at r. This assumes that both components are travelling at the same velocity. Although a velocity profile exists across the crosssectional area of the pipe, it is usually not practical to determine Q by measuring v across the whole pipe cross-section. For a single-component flow, this problem is overcome by assuming a velocity profile across the pipe, and then using the cross-sectional average of this profile v to calculate the volumetric flow rate. A similar approach can be used in the case of a pseudohomogeneous flow, although the characterization of a two-component flow as either laminar or turbulent in order to determine the appropriate flow velocity profile required is more difficult than for single-component flows. Equation (1) can therefore be written as: Q = 2~R~ = Aft
(2)
The mass flow rate M of the mixture can be calculated from: (3)
M = pmA~
where pm is the density of the mixture. Equation (3) assumes that the two components are so well mixed that any portion of the flow will have the same density as any other portion. This mixture density will lie somewhere between the densities of the individual components and will depend on the ratio of the mixture. The usefulness of equation (3) will depend on whether or not the flow can be classified as pseudohomogeneous. The homogeneity of the flow mixture
v(r)
Two-component flow measurement:the basic problem Two-component flow measurement is not an easy
Figure 1 Measurement of pseudo-homogeneous flow
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will depend on the degree of turbulence present, the density of each component, and the component ratio of the mixture. The less homogeneous the mixture the greater will be the measurement error if equation (3) is used to calculate mass flow rate. Unfortunately, in many cases the flow's components are neither well mixed nor moving at the same velocity. For example, in liquid/gas flows, groups of bubbles can be followed by a large slug of gas. Since they experience different frictional, surface tension, and gravitational forces, bubbles and gas slugs will not only move at different velocities to the main liquid phase, but also to each other. In such circumstances, the use of mixture density prn and mixture velocity ~, as used in equations (2) and (3) become less valid. To add to these problems, in many industrial flow measurement applications, measuring the total mass flow rate of the mixture itself is often not enough. As a result of ever more elaborate operational demands and tighter costing requirements, in many circumstances it is the mass flow rate of each component, not just the mixture, that is required. The mass flow rate M~ of component 1 and the mass flow rate M2 of component 2 of the two-component mixture can be calculated from: M1 = plA51ol
(4)
M2 = p2A/32(1 - a')
(5)
and where a" is the fraction of the pipe cross-sectional area occupied by component 1, and p~, P2 are the individual component densities. Although equations (4) and (5) have an advantage over (3) in that they may be used for flows where the components are not well mixed, three independent measurements are now required to determine M~ and M2 (it is reasonable to assume that A, p~ and P2 are known). There are still situations, however, where even equations (4) and (5) will be unsuitable. For example, consider a horizontal flow of a liquid/solid mixture, where M~ is the solid and M2 is the liquid. It is not uncommon, with this type of two-component flow, for some of the solids to settle on the bottom of the pipe in a static or sliding bed. In these circumstances, the measured solids velocity will be that of the solids suspended in the liquid phase, while the measured void fraction will include the static solids bed, hence the solids mass flow obtained from equation (4) will be erroneously high. Despite the difficulties outlined above, if care is taken over the choice of application, two-component flows can often be successfully metered using a combination of measurement techniques 3-s.
The flow imaging method of two-component flow measurement If they are applied with care, the techniques described in references 3, 4 and 5 may be used to obtain adequate measurements in many two-component flow applications. However, if the components in the flow are moving at different velocities, and the flow regime is non-homogeneous and unstable, then the reliability of the measurement will often be uncertain. As a
result, measurement errors will usually be variable and large. In these circumstances, if accurate measurements of volumetric or mass flow rate are required, then both the density and the velocity distribution across the cross-section of the pipe must be known. The most practical way of obtaining this information is by using the flow imaging (or tomography) technique. Most people today associate tomography with complex systems which are used to obtain images of internal parts of the human body. Tomography systems, however, have applications in other areas of science and technology, one of these being multicomponent flow measurement. In medical imaging, the sensing system must be moved axially along the body to obtain a 'multi-slice' cross-section; however, in flow imaging the flow field moves along the pipe so that a single image plane is sufficient to characterize the flow. In addition, the axial velocity of each of the components over the cross-section of the pipe must be measured, and this may be done by cross-correlation of information from two image planes spaced along the pipe axis. Figure 2 shows the basic principle of the flow imaging method of two-component flow measurement. A two-component flow is moving axially between the two image planes I1 and /2, which are spaced sufficiently close together for there to be only a small dispersion of the flow field between the planes. Consider a small element 6x 6y in the cross-section of the flow, located at position x, y in image plane 1. The element may consist of either component 1 or component 2 and letting the element mass flow rate at time t be M~ or M2 (depending on whether it is component 1 or 2) we can write: M~(6x, 6y, t) = 6xbyp(x, y, t)v(x, y, t)wl(x, y, t)
(6) and M2(bx, 6y, t) = 6x6yp(x, y, t)v(x, y, t)w2(x, y, t)
(7) where p(x, y, t) is the density, v is the velocity, and wl, w2 are binary weighting functions to denote whether the element is composed of component 1 or component 2, i.e. Image planes
r,,
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v(x,y,,t)
,
i I I
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Figure2 Flow imaging for homogeneous flow
I
262
R. Thorn et al w~(x, y, t) = 1 and w2(x, y, t) = 0
(8)
if p(x, y, t ) = Pl and wl(x, y, t) = 0 and w2(x, y, t) = 1
if p(x, y, t) = P2
(9)
The average mass flow rates of the two components over the whole cross-section of the pipe are obtained by integrating the small element flow rates in equations (6) and (7) over space and time. The result is: M1 = -T
=0
=0
=0 p(x, y, t)u(x, y, t)
x wl(x, y, t ) 6 x b y b t
(10)
and M2 = T
=0
=0
(11)
Equations (10) and (11) represent a complete solution to the two-component flow measurement problem. This solution requires measurement of the cross-sectional density profile p(x, y, t) which is obtained by a tomographic imaging system, such as that described later in this paper. In addition, the cross-sectional velocity profile u(x, y, t) is needed, this being obtained by cross-correlating the density information between the two image planes /1 and 12 in Figure 2 to give the cross-correlation function: y, r) = --~
Flow imaging for multi-component flow measurement
centration measurements (i.e. void fraction or holdup). The value of the diagnostic display should not be underestimated since in many processes involving two-component flow the interpretation of existing measurements is severely handicapped by lack of information on the flow regime, and this system would provide such information. The flow regime needs to be identified before mathematical modelling of twocomponent flows can be carried out. For measuring the component mass flow rate of two-component mixtures, two imaging systems would be required. Figure 3 shows the algorithmic blocks required to calculate the component mass flow rate from equations (10) and (11). Some important potential applications of these techniques can be found in industry, where multi-component flow measurement has been highlighted as one of the highest priority areas of development. The examples given below are meant to be illustrative, most pipeline flows in industry may be multi-component, and similar applications to those listed abound.
=0P(X' y, t)v(x, y, t)
x w2(x, y, t ) 6 x 6 y 6 t
R~,~(x,
-
p ( l > x, y, t)p(l~, x, y, (t - r))~t
(12) From Equation (12) we compute the time delay T*(X, y, t) of the maximum value of the function R~)~:(x, y, ~). The velocity profile is therefore given by: u(x, y, t ) =
(13) T*(x, y, t) where ~ is the spacing between I1 and /2. Further details of the basic principles of cross-correlation velocity measurement are given in the book by Beck and PlaskowskP.
Potential applications of flow imaging The tomographic flow imaging method described in the next section would give cross-sectional images of the component distribution in the flow. The images are derived from capacitance, ultrasonic or other measurements (Table 1) and could be used in two ways: firstly as a diagnostic, where the images are updated to provide a real-time 'picture' of the flow; and secondly for measurement purposes, the images being interpreted to give quantitative component con-
Petroleum production systems and well testing In order to perform production tests on individual wells, the particular line must be disconnected, attached to a test separator, and the individual component flow rates (of oil/gas/water) then measured. This is an expensive and time-consuming process and does not allow real-time monitoring of the system performance. The flow imaging system will enable real-time multi-component flow rate information to be gathered, thus leading to optimized production and increased recovery. Even simple flow imaging instruments for flow regime identification will provide early warning of the development of large gas slugs which can overload separation plant, damage subsea pump bearings, and sometimes cause safety problems.
Further subsea and remote collection systems Flow imaging will provide continuous monitoring of individual wellheads, which are connected to subsea collection manifolds. The imaging system alone would provide useful diagnostic information as the well flow changes with time, and the future application of flow rate measurement would enable real-time monitoring without separation.
Oil custody transfer This involves sampling oil/water mixtures to determine the oil content. The sampling is accurate provided that the mixture is homogeneous, but sometimes changes in flow regime can cause inhomogeneous flow and result in large sampling errors. A flow imaging system could be used to detect inhomogeneous flow so that appropriate action could be taken to reduce the custody transfer error.
Conveying dry solids Applications to gas/solids flows in power generation, metals, chemicals and foodstuffs are also important. Existing devices are affected by the flow regime. Any change in upstream flow conditions can lead to significant changes in the output of the device due to
Flow Meas. Instrum.
Vol I October 1990
263
Table I Sensorsfor flow imaging Principle
Practical realisation
Modulation of beam Optical techniques of electromagnetic radiation by the dispersed components in the flowing fluid,
Ionising radiation: Xray and y-ray
Typical applications
Generalremarks
Remarks re reconstruction algorithms
Many two-component flows where the carrier phase is transparent to the radiation used.
Conceptually simple, high Similar algorithms well definition possible, fibre establishedfor medoptic light guides can simical CT plify optical arrangements. Images of central region poor if second phase concentration is high, dueto absorption near walls. Flows where there is a Heavy shielding may be resubstantial density dif- quired to collimate beams ference between the and for safety. Photon statistical noise limits response components time (only low-speed flows unless large sources are used). Two-component flows where reflections occur at boundaries, e.g. liquid/gas flows
Reflection of external radiation.
Ultrasonic pulse echo systems.
Instantaneous measurement of electrical properties of the flowing fluid,
Electrical capacitance Oil/gas, oil/water, plates on walls of pipe gas/solids flows, etc detectthe presence of the second component
Conductivity sensing Water/oil, water/gas, electrodes near wall of water/solids flows. pipe.
fluctuations in flow regime. Imaging would be of direct use in monitoring these changes, and making accurate concentration measurements would be a significant improvement on current practice.
Basic elements of a flow imaging system A flow imaging system can be subdivided into three basic blocks: the sensor, the sensor electronics and the image reconstruction interpretation and display (Figure 4). A s w i t h all measurement systems, the sensor is probably the most critical part of a flow imaging system. The manner in which the sensor interrogates the flowing mixture, and the quality of information obtained as a result, has a profound effect on the reliability and accuracy of the complete system. Practical considerations place a number of constraints on the sensor. It must be compact, non-invasive, require minimum maintenance or calibration, and in many cases also be intrinsically safe. Sensing techniques currently under consideration
Ultrasound 1 MHz pass through metal/liquid interface so a 'clip-on' system is feasible for liquid flow. 'Ringing' of transmitter may cause difficulty in imaging discontinuities close to the pipe walls.
Similar to some NDT and medical applications.
Inexpensive, fast and rugged. High definition not possible, but good for slug and annular flow, water separation measurements, dune and spiral flow patterns in pneumatic conveyors. Loss of definition near centre of pipe. Similar to capacitance but electrode polarization, greasy deposits, etc, may be a problem.
Sensor field is affected by distribution of second phase so algorithms must allow for this.
Similar to capacitance, similar methods used for some medical applications
for use in flow imaging systems include electrical, ultrasound, nucleonic and optical (Table 1). Most sensors can be categorized as belonging to either hard or soft field. With hard field sensors, such as nucleonic and optical, the sensor field sensitivity is not influenced by the nature of the flow being imaged. However, with soft field sensors, such as capacitance and conductivity, the sensing field is altered by the phase distribution and physical properties of the mixture being imaged. Flow images are usually required in real-time, therefore the dynamic response of the sensors is also an important parameter. With electrical sensors this does not represent a significant problem; however, with nucleonic sensors the usual radiation noise effect means that rather longer averaging times have to be used. The most critical part of the system software is the image reconstruction algorithm. Although image reconstruction techniques have been extensively developed for medical and industrial applications, a particular problem encountered with flow imaging is that the distribution of the mixture passing the sensor usually changes rapidly.
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R. Thorn et al - Flow imaging for multi-component flow measurement
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System shown
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/'ii
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A capacitance system for tomographic imaging of process pipelines The capacitance flow imaging system (Figure 5) consists of an eight-electrode capacitance sensor, a data collection system, and an image reconstruction computer. The sensor is made by mounting eight metal plates on the outer surface of an insulating pipe section. The data collection system measures the capacitances between any two of the eight electrodes in all possible combinations. The measured capacitance values, whose amplitude depends on the dielectric distribution in the pipe, are fed into the computer and a cross-sectional image of the component distribution is reconstructed using a linear backprojection algorithm. The computer also provides control signals for the data collection process.
Measurement method The basic capacitance measuring circuit of the system is shown in Figure 6 (see Huang et al 7 for details). When a pair of electrodes is selected, one of them (known as the active electrode) is continuously
Figure 5 The capacitance flow imaging system
charged and discharged by CMOS switches $2 and $4; the other one (known as the detecting electrode) is connected to earth by switch $1, when the active electrode is charged to voltage Vc, and to the input of the current detector (which is at virtual earth potential) via $3, when the active electrode is discharged to earth. The current detector averages the discharging current pulses flowing through the detecting electrode, producing a voltage signal, V0, proportional to the unknown capacitance value, C×, i.e. Vo = (KfVc)C×
(14)
where K is the gain factor of the current detector and f is the frequency of the charge/discharge switching operation. In our system, f is 2 MHz, which is approaching the upper frequency limit of the CMOS switches and associated circuits. In a complete data collection cycle, electrode 1 (Figure 5) is first selected as the active one, and the capacitances between electrodes 1 and 2, 1 and 3,
Flow Meas. Instrum.
Vol I October 1990
265 off
m
on
s~ s~ s ~ ~ s~ - L _ r - L _ r - L _ S4
S2
~
Cf
a --
S3 O.
~
b
,~'~-'~ ~ a ' I D ~ R ~ 4 ~ PlIIIIII
Figure 6 The capacitance measuring circuit
1)/2
(15)
In the above measurement process, the redundant electrodes (those not selected as active or'detecting in a measurement) are always connected to earth or virtual earth potential, forming 'guard rings' for the measuring electrodes. This arrangement enables the measurement sensitivity to be focused into a relatively narrow area between the selected electrode pair. The field pattern resulting from the electrode configuration and switching connections described above has been modelled using the finite element method ~. The relationship between the capacitance of an electrode pair, C~, the measurement sensitivity distribution function, S~(x, y, ~(x, y)), and the dielectric distribution in the pipe, 8(x, y), is expressed as
C, = L ~ ~(x, y)S,(x, y, ~(x, y))dxdy
~,
NN"
• o •, 1 and 8 are measured. Next, electrode 2 is selected and electrode pairs 2-3, 2 - 4 . . . . . 2 - 8 are measured. This process continues until electrode pair 7-8 is measured• This produces a total of 28 independent measurements. Generally, for an N-electrode system, the number of possible two-electrode combinations (the number of independent measurements), n, is given by
n = N(N-
b
(16)
where D is the cross-section of the pipe. C~ in equation (16) depends mainly on the dielectric distributions in the narrow area where the sensitivity is positive. We call this area the positive sensing area of the selected electrode pair. Figure 7 shows the positive sensing areas (the dark areas) of four typical electrode pairs, obtained using the finite element method. Those of other electrode pairs can be obtained by rotating the four typical patterns around the centre of the pipe.
Image reconstruction algorithm For an n-output measurement system, the vector of the measurement results, [C~, C~. . . . . Cn], is determined by the dielectric distribution, ~(x, y). According to equation (16), we have
c
d
Figure 7 Four typical positive sensing areas. Electrode pairs: (a) 2-3; (b) 2-4; (c) 2-5; (d) 2-6
[C,, Q . . . Cn] = [ L J" ~(x, y)S,(x, ,v, ~(x, y))dxdy, •[D f E'(X, .y)S2(X, y, £(X, y))dxdy .....
~D~E(X, y)Sn(X, y,E(X, y))dxdy](17) Our task of image reconstruction is to solve the inverse problem of determining ~(x, ,v) from a limited number of measurements• Since component distribution in two-component flows is very complicated, a complete solution to the integration functions given in equation (17) is not possible with only 28 measurements. To obtain an approximate solution, we simplify the problem by making the following assumptions. First, it is assumed that the effect of the dielectric distribution on the sensitivity distributions of the sensors is insignificant, and the sensitivity distribution in the sensing area is uniform. Therefore the function Sj(x, y, ~(x, y)) is simplified to constant Si
Si(x, y, ~(x, y)) = 0
in the ith positive sensing area elsewhere. (18)
Secondly, we assume that any change in a measured capacitance results from a uniform dielectric change over the entire sensing area. Therefore, on this (ith) sensing area, the dielectric distribution in equation (16) can be solved to give
Ei = Ci/DiSi
(19)
Equation (19) can be normalized by using the value of C/measured when ~i = 1, and the normalized form is given by
266
R. Thorn et al - Flow imaging for multi-component flow measurement cni = Cni
(20)
To produce an image of the dielectric distribution, the sensing area can be a grey level whose value is proportional to the measured capacitance value. By summing up all the 28 grey areas over the cross-section of the pipe, the grey level in the areas where objects with higher permittivity are found will be enhanced. Thus a grey level image representing the component distribution of the two-component flow can be obtained. This summation process is known as 'backprojection' and involves the following steps. First, the boundaries of all the 28 sensing areas (Figure 7) are plotted on the cross-section of the pipe. These boundaries intercept each other, forming many small pixels (Figure 8). Each of the pixels is related uniquely to some of the 28 areas, i.e. it is the common pixel of these areas. Secondly, a relational matrix, V, can be written out according to the relationship between each pixel and the 28 measurements. Each line in V corresponds to a pixel in Figure 8. Each line consists of 28 elements, each of them corresponding to one of the 28 sensing areas. An element is equal to 1 if the pixel is in the corresponding area, 0 otherwise. The grey level Gi in the /th pixel can be obtained by multiplying the vector Vi in V with the vector of 28 measurement values; thus we have G2
=
V2
x [C~, C2. . . . . C281T
(21)
k
where k is the total number of the pixels. In this system k = 362. Now the flow image can be obtained by performing the matrix multiplication in equation (21) and then displaying the grey level of the pixels shown in Figure 8.
Further details of the reconstruction method are given in a recent paper 9.
Experimental results The system described above has been constructed using an array processor (Transputer) for image reconstruction :0. Typically, capacitances of the order of 1 pF can be measured to an accuracy of 1% FS in the presence of 50 pF stray capacitance. Under computer control the data capture time is 2.5 ms. The program structure consists of processes for data input, calibration, reconstruction, display and interpretation, together with an overall control/monitor process. Of these, reconstruction is computationally the most intensive task. The reconstruction process consists of around 5000 arithmetic operations and takes 24 ms to execute on one processor. Tests with a four-processor network show this time to reduce linearly. In the present system, reconstruction is allocated to two processors. One of the processors is also used for data input and calibration, so the allocation is biased to balance the processing burden. In the present implementation, a network of four T4~4 Transputers is used, together with two other processors. The Transputers are arranged in a ring configuration, the allocation of processors being shown in Figure 9. A fifth processor controls data acquisition and interfacing, while a sixth, the IBM PS/2, provides user interface and monitor facilities. All communication is via standard Transputer links running at 10 Mbits -~ Since the processing structure is essentially a pipline, the frame rate is determined by the length of the longest process. By balancing the network this can be reduced to | 7 ms, providing a frame rate of 60 Hz. The display is refreshed every second image to avoid a graphics overload. A series of tests was performed using a 2.5 m long experimental flow loop. The test section was fully inclinable to produce asymmetric flow profiles. Figure 10 shows an oil/water flow (composed of 40% water v/v) with the 75 mm diameter test section inclined at 30 ° to the vertical. The higher concentration component is clearly shown in the lower part of the pipe. This is the distribution expected, because of the gravitational effects on the denser medium. Other results showed an equally encouraging correspondence between theoretical and actual images. Figure 11 shows an image obtained with a pipe having a stratified layer of PVC chips occupying part of the crosssection. (In Figure 10 the image has been expressed on a rectangular pixel grid, rather than the pixels shown in Figure 11 which were formed by the field between the electrodes).
Conclusions
Figure 8 The image pixels formed by the boundaries of the 28 positive sensing areas
The results in this paper confirm the feasibility of high-speed tomographic imaging for measuring the component distribution in multi-component flows. The system we have described generates two-component flow images at 60 frames per second; this could be increased to 400 frames per second by using more
Flow Meas. Instrum.
Vol I October 1990
267
~P
To transducer
T414
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T41
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Figure 9 Transputer system for image reconstruction
Figure 10 Image for inclined oil/water flow Figure I 1 Image for inclined flow of plastic chips Transputer chips for image reconstruction. The spatial resolution of these electrical field sensing systems is limited by field spreading, but we feel that a spatial resolution of one in 20 along the projection distance could be obtained in many applications (corresponding to one part in 400 over the projection area). Fortunately, the electrical properties of each image boundary are functionally related to the image grey level, so that the component ratio of a two-component mixture within a boundary can be measured, although individual particles cannot be imaged. High-speed imaging will be required for measuring the velocity profile as part of the component mass flow measurement system shown in Figure 3. For a flow velocity of 5 ms -1 in a 200 mm diameter pipeline we expect the image feature size to be 10 mm (corresponding to the resolution limit of one in 20 of the projection distance). This size of feature or zone in
the flow (assuming it is spherical) takes 2 ms to cross the image plane. In order to avoid aliasing it should be sampled (imaged) twice during its transit, thus requiring a frame interval of 1 ms (or 1000 frames per second). We believe that by using all-electronic measurement systems, image rates of 1000 per second are technically feasible. This is much faster than previously used X-ray and ],-ray methods which are limited to much lower speeds because of safety/photon-count considerations. Ultrasound methods of imaging are also slow due to the sonic velocities being quite low, although by using recently developed wideangle transmitters speeds of 400 frames per second in a 100 mm diameter vessel using 12 interrogating transducers are possible 11. The most computer-intensive part of the component flow measurement system (Figure 3) is the crosscorrelation calculation.
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Assuming 400 pixel images (corresponding to 5% spatial resolution), 1000 off 4-bit data values to be correlated with up to 100 correlation delays and declaring 10 velocity profiles per second, the corresponding bit rate is 400 x 1000 x 4 x 100 x 10 = 16 x 108 bitss -~, which is achievable using low-cost array processors. The capacitance sensing method we have described can be used only where the major component in the process is not electrically conducting. For application to flows of electrically conducting fluids, sensors measuring electrical impedance (at a low frequency of say 25 kHz) are recommended (Table 1). Impedance measurement has been successfully used for obtaining tomographic images of the human body 12 and our preliminary tests for flow imaging are encouraging. A most significant need is the in-depth study and development of the coherent body of knowledge required to establish a sound practical and theoretical design framework for the emerging science of flow imaging. Specific future investigations could include: [] fundamental limitations in spatial and temporal resolution of various sensor configurations (capacitance, impedance, ultrasonic, optical and radiation); [] the spatial and temporal resolution needed for particular applications; [] image value (contrast or grey scale) requirements, particularly for binary and ternary mixtures where pixel elements are incompletely filled by one component; and [] correction of the image distortion caused by the electrical field equipotentials changing with the varying electrical properties of the material in the image space. We believe that tomographic techniques will have a number of exciting and innovative future applications for multi-component flow measurement, offering opportunities to visualize the internal characteristics of hitherto inaccessible flows and ultimately capable of leading to a complete solution of the component mass flow measurement problem.
Acknowlegements
This work was funded by the British Council and the Science and Engineering Research Council including a grant under the Total Technology Scheme, in collaboration with the Fluids Mechanics Department, Schlumberger Cambridge Research Ltd. References 1 Dykesteen, E. and Frantzen, K. H. The CMI multiphase
2 3
4 5 6
fraction meter. Proc. Int. Conf. on Basic principles and industrial applications of multiphase flow, London (April 1990) Hammer, E. A., Tollefsen, I. and Olsvik, K. Capacitance transducers for non-intrusive measurement of water in crude oil. Flow Meas. Instrum. 1 (1)(1989) 51-58 Beck, M. S., Green, R. G. and Thorn, R. Flow measurement: two-phase systems, tn 'Encyclopaedia of Systems and Control' (Ed. M. G. Singh), Pergamon Press, Oxford (1987) 1685-1694 Medlock, R. S. and Furness, R. A. Mass flow measurement -- a state of the art review. Meas. and Contr. 23(4) (1990) 100-113 Hewitt, G. F. Multiphase flow metering. Proc. Conf. on Process equipment for oil and gas industries (November 1989) Beck, M. S. and Plaskowski, A. Cross correlation flowmeters -- Their design and application. Adam Hilger (1987)
7 Huang, S. M., Green, R. G., Plaskowski, A. B. and Beck,
M. S. A high-frequency and stray-immune capacitance transducer based on the charge transfer principle. IEEE Trans. Instrum. and Meas. IM-37 (1988) 368-373 8 Xie, C. G., Plaskowski, A. and Beck, M. S. 8-electrode capacitance system for two-component flow imaging, lEE Proc. 136A (4) (1989) 173-183 9 Huang, S. M., Plaskowski, A., Xie, C. G. and Beck, M. S.
Tomographic imaging of two-component flow using capacitance sensors. J. Phys. E.: Sci. Instrum. 22 (1989) 173-177 10 Salkeld, J. A. PhD thesis, University of Manchester (1990) (pending) 11 Gai, H., Beck, M. S. and Flemons, R. S. An integral
transducer/pipe structure for flow imaging. IEEEThird Int. Ultrasonics Symp., Montreal, Canada (October 1989) 12 Barber, D. C. and Brown, B. H. Applied potential tomography. J. Phys E.: Sci. Instrum. 17 (1984) 723-733
259
Flow imaging for multi-component flow measurement R. T H O R N , S. M. H U A N G , C. G. XlE, J. A. SALKELD, A. H U N T and M. S. BECK
For pseudo-homogeneous flows, measurements of density and mean velocity can give the component mass flow rate of a two-component mixture. However, for accurate measurement of non-homogeneous flow rate, the density and velocity distribution across the cross-section of the pipe must be known. The most practical way of obtaining this information is by using the flow imaging technique. A recently developed capacitance system gives 60 frames per second images of oil/water flow in a 78 mm pipe. The target spatial resolution is one part in 20 by distance (one in 400 by area). The electrical properties of each imaged boundary are functionally related to the imaged value, so the component ratio of a two-component mixture within a boundary can be measured, although individual particles cannot be imaged. Design data shows how the basic system can be part of a complete system for component mass flow measurement. Keywords: multi-component flow, imaging, tomography, capacitance transducers
The importance of multi-component flow measurement Until recently, most flowmeters have been used to measure single-component materials (petrol, gas, water, etc) at points of use or in production plants. However, the increasing need to use resources more efficiently and build processing plants that can be operated cost-effectively, while minimizing pollution, has led to an increasing demand for multi-component flowmeters. The development of multi-component flowmeters is both a fascinating and expanding area of measurement. Future process requirements, with their need for ever more detailed measurements, will ensure that this expansion continues. The growing demand for flowmeters capable of metering multi-component flows can be illustrated by considering two examples from the petroleum industry. The first concerns the problem of three-component measurement. In a typical offshore production facility, fluid from each well is pumped to the production platform where it undergoes preliminary processing before being shipped or piped directly to shore. The crude oil produced by an offshore reservoir usually contains both gas and water components. The flow pattern of the resulting mixture varies with the flow's conditions and is generally not predictable. It is important for the operator of a production platform to
R. T. is with the SouthAustralianInstituteof Technology,5. /H. H., C. G. X., J. A. S. andM. 5. B. are with the Universityof Manchester Instituteof Scienceand Technology,andA. H. is with 5chlumberger CambridgeResearchLtd. 0955-5986/90/050259-10
know which types of fluid a well is producing. The current method of solving this problem is to separate the fluids first, and then monitor each using conventional single-component flowmeters (e.g. orifice plate for gas, turbine meter for oil). With the space on a production platform becoming more expensive, and the development of subsea production systems increasing, the use of conventional offshore separators is becoming less desirable. Therefore a particularly interesting but difficult flow measurement problem arises: namely, how the component fractions of an oil/gas/water mixture can be reliably monitored without separation in a hostile environment. The qualities required for such a measurement system are that it should be: [] non-intrusive, to avoid sensor erosion and pressure drop [] a real-time measurement, to provide instantaneous feedback to the production operator [] in-line to avoid the problem of sample representivity [] reliable, because maintenance will be costly, and perhaps impossible in the short-term [] easily calibrated for use subsea. A number of solutions have been proposed to this problem. However, one of the most promising methods currently under development uses the combination of a gamma radiation sensor and a capacitance sensor I. The gamma radiation sensor is used to measure the mean density of the multi-component flow, while the capacitance sensor is used to determine the mean permittivity of the flow. These two independent measurements are then used to determine (~) 1990 Butterworth-HeinemannLtd
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the component ratio of the flowing oil/water/gas mixture. Results so far show that this system is capable of determining the composition of a well-mixed flow with an accuracy of better than +3% of full scale. While there are still many problems to solve, such as how to deal with changes in flow regime, ten years ago such a flow measurement system would have been inconceivable. A second illustration of how the development of multi-component flowmeters has progressed can be found by considering a later stage of the oil production process. Even after separation, the water content of a ship's crude oil cargo may lie in the range 0 - 5 % . This may not seem a great deal, but an error of only 0.15% in measuring the water content of a ship's 250000 ton oil cargo would result in a loss of approximately £1m (1990 prices). An accurate twocomponent measurement is therefore required; however, most currently used methods have limitations. The usual method of measuring water content today is by use of an isokinetic sampling system. This basically consists of a probe inserted into the pipeline through which samples of the flow are drawn for off-line laboratory analysis. This technique presents a number of problems, the most serious being the ability of the system to take representative samples and the time required to obtain the measurement. Recently, a number of organizations have investigated on-line water content measurement using capacitance sensors 2. The measurement principle has attracted a great deal of interest because it has a fast dynamic response and offers the possibility of constructing a non-intrusive sensor which can be used on-line. Capacitance based water content meters produced so far are an improvement on isokinetic samplers in that they produce instantaneous measurements. However, their calibration is dependent on flow regime, temperature and whether the water or oil is the dispersed component in the flow. The above examples show how rapid advances in process production techniques have encouraged the development of specialized multi-component flowmeters. The principles on which such flowmeters can be based are described below.
Terminology In this article we consider multi-component flows to be those where the components exist in a separated form; that is, either solid, liquid or gas. In many publications the term 'multi-phase flow' is used instead of 'multi-component flow', although multi-phase flows should strictly be only those composed of separate phases such as a liquid and a gas. An oil/water flow is therefore by definition a two-component flow while a gas/oil flow may be classified as a multi-phase or multi-component flow. Throughout this article only the term multi-component will be used, since this is applicable in all cases.
matter, the first problem being to decide what parameter actually needs to be measured. When used by itself, the term 'flow measurement' is rather vague and can often mean different things to different people. For instance, one user may be interested in measuring a mixture's volumetric flow rate, while in another application the mass flow rate will be required. Since both these may be called 'flow measurements', care should be taken when specifying the actual measurement required. A pseudo-homogeneous fluid is probably the easiest two-component mixture to measure. In this particular case one component is finely and evenly dispersed in the other, and so the mixture can be treated as a single fluid that obeys all the usual equations of single-component flow. Referring to the pseudo-homogeneous flow shown in Figure 1, the volumetric flow rate Q of the mixture can be calculated using: F
R
Q = J0 2~rv(r)~r
(1)
where v(r) is the velocity of the fluid at r. This assumes that both components are travelling at the same velocity. Although a velocity profile exists across the crosssectional area of the pipe, it is usually not practical to determine Q by measuring v across the whole pipe cross-section. For a single-component flow, this problem is overcome by assuming a velocity profile across the pipe, and then using the cross-sectional average of this profile v to calculate the volumetric flow rate. A similar approach can be used in the case of a pseudohomogeneous flow, although the characterization of a two-component flow as either laminar or turbulent in order to determine the appropriate flow velocity profile required is more difficult than for single-component flows. Equation (1) can therefore be written as: Q = 2~R~ = Aft
(2)
The mass flow rate M of the mixture can be calculated from: (3)
M = pmA~
where pm is the density of the mixture. Equation (3) assumes that the two components are so well mixed that any portion of the flow will have the same density as any other portion. This mixture density will lie somewhere between the densities of the individual components and will depend on the ratio of the mixture. The usefulness of equation (3) will depend on whether or not the flow can be classified as pseudohomogeneous. The homogeneity of the flow mixture
v(r)
Two-component flow measurement:the basic problem Two-component flow measurement is not an easy
Figure 1 Measurement of pseudo-homogeneous flow
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will depend on the degree of turbulence present, the density of each component, and the component ratio of the mixture. The less homogeneous the mixture the greater will be the measurement error if equation (3) is used to calculate mass flow rate. Unfortunately, in many cases the flow's components are neither well mixed nor moving at the same velocity. For example, in liquid/gas flows, groups of bubbles can be followed by a large slug of gas. Since they experience different frictional, surface tension, and gravitational forces, bubbles and gas slugs will not only move at different velocities to the main liquid phase, but also to each other. In such circumstances, the use of mixture density prn and mixture velocity ~, as used in equations (2) and (3) become less valid. To add to these problems, in many industrial flow measurement applications, measuring the total mass flow rate of the mixture itself is often not enough. As a result of ever more elaborate operational demands and tighter costing requirements, in many circumstances it is the mass flow rate of each component, not just the mixture, that is required. The mass flow rate M~ of component 1 and the mass flow rate M2 of component 2 of the two-component mixture can be calculated from: M1 = plA51ol
(4)
M2 = p2A/32(1 - a')
(5)
and where a" is the fraction of the pipe cross-sectional area occupied by component 1, and p~, P2 are the individual component densities. Although equations (4) and (5) have an advantage over (3) in that they may be used for flows where the components are not well mixed, three independent measurements are now required to determine M~ and M2 (it is reasonable to assume that A, p~ and P2 are known). There are still situations, however, where even equations (4) and (5) will be unsuitable. For example, consider a horizontal flow of a liquid/solid mixture, where M~ is the solid and M2 is the liquid. It is not uncommon, with this type of two-component flow, for some of the solids to settle on the bottom of the pipe in a static or sliding bed. In these circumstances, the measured solids velocity will be that of the solids suspended in the liquid phase, while the measured void fraction will include the static solids bed, hence the solids mass flow obtained from equation (4) will be erroneously high. Despite the difficulties outlined above, if care is taken over the choice of application, two-component flows can often be successfully metered using a combination of measurement techniques 3-s.
The flow imaging method of two-component flow measurement If they are applied with care, the techniques described in references 3, 4 and 5 may be used to obtain adequate measurements in many two-component flow applications. However, if the components in the flow are moving at different velocities, and the flow regime is non-homogeneous and unstable, then the reliability of the measurement will often be uncertain. As a
result, measurement errors will usually be variable and large. In these circumstances, if accurate measurements of volumetric or mass flow rate are required, then both the density and the velocity distribution across the cross-section of the pipe must be known. The most practical way of obtaining this information is by using the flow imaging (or tomography) technique. Most people today associate tomography with complex systems which are used to obtain images of internal parts of the human body. Tomography systems, however, have applications in other areas of science and technology, one of these being multicomponent flow measurement. In medical imaging, the sensing system must be moved axially along the body to obtain a 'multi-slice' cross-section; however, in flow imaging the flow field moves along the pipe so that a single image plane is sufficient to characterize the flow. In addition, the axial velocity of each of the components over the cross-section of the pipe must be measured, and this may be done by cross-correlation of information from two image planes spaced along the pipe axis. Figure 2 shows the basic principle of the flow imaging method of two-component flow measurement. A two-component flow is moving axially between the two image planes I1 and /2, which are spaced sufficiently close together for there to be only a small dispersion of the flow field between the planes. Consider a small element 6x 6y in the cross-section of the flow, located at position x, y in image plane 1. The element may consist of either component 1 or component 2 and letting the element mass flow rate at time t be M~ or M2 (depending on whether it is component 1 or 2) we can write: M~(6x, 6y, t) = 6xbyp(x, y, t)v(x, y, t)wl(x, y, t)
(6) and M2(bx, 6y, t) = 6x6yp(x, y, t)v(x, y, t)w2(x, y, t)
(7) where p(x, y, t) is the density, v is the velocity, and wl, w2 are binary weighting functions to denote whether the element is composed of component 1 or component 2, i.e. Image planes
r,,
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,
i I I
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I
I
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Figure2 Flow imaging for homogeneous flow
I
262
R. Thorn et al w~(x, y, t) = 1 and w2(x, y, t) = 0
(8)
if p(x, y, t ) = Pl and wl(x, y, t) = 0 and w2(x, y, t) = 1
if p(x, y, t) = P2
(9)
The average mass flow rates of the two components over the whole cross-section of the pipe are obtained by integrating the small element flow rates in equations (6) and (7) over space and time. The result is: M1 = -T
=0
=0
=0 p(x, y, t)u(x, y, t)
x wl(x, y, t ) 6 x b y b t
(10)
and M2 = T
=0
=0
(11)
Equations (10) and (11) represent a complete solution to the two-component flow measurement problem. This solution requires measurement of the cross-sectional density profile p(x, y, t) which is obtained by a tomographic imaging system, such as that described later in this paper. In addition, the cross-sectional velocity profile u(x, y, t) is needed, this being obtained by cross-correlating the density information between the two image planes /1 and 12 in Figure 2 to give the cross-correlation function: y, r) = --~
Flow imaging for multi-component flow measurement
centration measurements (i.e. void fraction or holdup). The value of the diagnostic display should not be underestimated since in many processes involving two-component flow the interpretation of existing measurements is severely handicapped by lack of information on the flow regime, and this system would provide such information. The flow regime needs to be identified before mathematical modelling of twocomponent flows can be carried out. For measuring the component mass flow rate of two-component mixtures, two imaging systems would be required. Figure 3 shows the algorithmic blocks required to calculate the component mass flow rate from equations (10) and (11). Some important potential applications of these techniques can be found in industry, where multi-component flow measurement has been highlighted as one of the highest priority areas of development. The examples given below are meant to be illustrative, most pipeline flows in industry may be multi-component, and similar applications to those listed abound.
=0P(X' y, t)v(x, y, t)
x w2(x, y, t ) 6 x 6 y 6 t
R~,~(x,
-
p ( l > x, y, t)p(l~, x, y, (t - r))~t
(12) From Equation (12) we compute the time delay T*(X, y, t) of the maximum value of the function R~)~:(x, y, ~). The velocity profile is therefore given by: u(x, y, t ) =
(13) T*(x, y, t) where ~ is the spacing between I1 and /2. Further details of the basic principles of cross-correlation velocity measurement are given in the book by Beck and PlaskowskP.
Potential applications of flow imaging The tomographic flow imaging method described in the next section would give cross-sectional images of the component distribution in the flow. The images are derived from capacitance, ultrasonic or other measurements (Table 1) and could be used in two ways: firstly as a diagnostic, where the images are updated to provide a real-time 'picture' of the flow; and secondly for measurement purposes, the images being interpreted to give quantitative component con-
Petroleum production systems and well testing In order to perform production tests on individual wells, the particular line must be disconnected, attached to a test separator, and the individual component flow rates (of oil/gas/water) then measured. This is an expensive and time-consuming process and does not allow real-time monitoring of the system performance. The flow imaging system will enable real-time multi-component flow rate information to be gathered, thus leading to optimized production and increased recovery. Even simple flow imaging instruments for flow regime identification will provide early warning of the development of large gas slugs which can overload separation plant, damage subsea pump bearings, and sometimes cause safety problems.
Further subsea and remote collection systems Flow imaging will provide continuous monitoring of individual wellheads, which are connected to subsea collection manifolds. The imaging system alone would provide useful diagnostic information as the well flow changes with time, and the future application of flow rate measurement would enable real-time monitoring without separation.
Oil custody transfer This involves sampling oil/water mixtures to determine the oil content. The sampling is accurate provided that the mixture is homogeneous, but sometimes changes in flow regime can cause inhomogeneous flow and result in large sampling errors. A flow imaging system could be used to detect inhomogeneous flow so that appropriate action could be taken to reduce the custody transfer error.
Conveying dry solids Applications to gas/solids flows in power generation, metals, chemicals and foodstuffs are also important. Existing devices are affected by the flow regime. Any change in upstream flow conditions can lead to significant changes in the output of the device due to
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Vol I October 1990
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Table I Sensorsfor flow imaging Principle
Practical realisation
Modulation of beam Optical techniques of electromagnetic radiation by the dispersed components in the flowing fluid,
Ionising radiation: Xray and y-ray
Typical applications
Generalremarks
Remarks re reconstruction algorithms
Many two-component flows where the carrier phase is transparent to the radiation used.
Conceptually simple, high Similar algorithms well definition possible, fibre establishedfor medoptic light guides can simical CT plify optical arrangements. Images of central region poor if second phase concentration is high, dueto absorption near walls. Flows where there is a Heavy shielding may be resubstantial density dif- quired to collimate beams ference between the and for safety. Photon statistical noise limits response components time (only low-speed flows unless large sources are used). Two-component flows where reflections occur at boundaries, e.g. liquid/gas flows
Reflection of external radiation.
Ultrasonic pulse echo systems.
Instantaneous measurement of electrical properties of the flowing fluid,
Electrical capacitance Oil/gas, oil/water, plates on walls of pipe gas/solids flows, etc detectthe presence of the second component
Conductivity sensing Water/oil, water/gas, electrodes near wall of water/solids flows. pipe.
fluctuations in flow regime. Imaging would be of direct use in monitoring these changes, and making accurate concentration measurements would be a significant improvement on current practice.
Basic elements of a flow imaging system A flow imaging system can be subdivided into three basic blocks: the sensor, the sensor electronics and the image reconstruction interpretation and display (Figure 4). A s w i t h all measurement systems, the sensor is probably the most critical part of a flow imaging system. The manner in which the sensor interrogates the flowing mixture, and the quality of information obtained as a result, has a profound effect on the reliability and accuracy of the complete system. Practical considerations place a number of constraints on the sensor. It must be compact, non-invasive, require minimum maintenance or calibration, and in many cases also be intrinsically safe. Sensing techniques currently under consideration
Ultrasound 1 MHz pass through metal/liquid interface so a 'clip-on' system is feasible for liquid flow. 'Ringing' of transmitter may cause difficulty in imaging discontinuities close to the pipe walls.
Similar to some NDT and medical applications.
Inexpensive, fast and rugged. High definition not possible, but good for slug and annular flow, water separation measurements, dune and spiral flow patterns in pneumatic conveyors. Loss of definition near centre of pipe. Similar to capacitance but electrode polarization, greasy deposits, etc, may be a problem.
Sensor field is affected by distribution of second phase so algorithms must allow for this.
Similar to capacitance, similar methods used for some medical applications
for use in flow imaging systems include electrical, ultrasound, nucleonic and optical (Table 1). Most sensors can be categorized as belonging to either hard or soft field. With hard field sensors, such as nucleonic and optical, the sensor field sensitivity is not influenced by the nature of the flow being imaged. However, with soft field sensors, such as capacitance and conductivity, the sensing field is altered by the phase distribution and physical properties of the mixture being imaged. Flow images are usually required in real-time, therefore the dynamic response of the sensors is also an important parameter. With electrical sensors this does not represent a significant problem; however, with nucleonic sensors the usual radiation noise effect means that rather longer averaging times have to be used. The most critical part of the system software is the image reconstruction algorithm. Although image reconstruction techniques have been extensively developed for medical and industrial applications, a particular problem encountered with flow imaging is that the distribution of the mixture passing the sensor usually changes rapidly.
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R. Thorn et al - Flow imaging for multi-component flow measurement
--C
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Figure 4 Principal elements in flow imaging l
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fraction x density x velocity over whole image
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/'ii
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A capacitance system for tomographic imaging of process pipelines The capacitance flow imaging system (Figure 5) consists of an eight-electrode capacitance sensor, a data collection system, and an image reconstruction computer. The sensor is made by mounting eight metal plates on the outer surface of an insulating pipe section. The data collection system measures the capacitances between any two of the eight electrodes in all possible combinations. The measured capacitance values, whose amplitude depends on the dielectric distribution in the pipe, are fed into the computer and a cross-sectional image of the component distribution is reconstructed using a linear backprojection algorithm. The computer also provides control signals for the data collection process.
Measurement method The basic capacitance measuring circuit of the system is shown in Figure 6 (see Huang et al 7 for details). When a pair of electrodes is selected, one of them (known as the active electrode) is continuously
Figure 5 The capacitance flow imaging system
charged and discharged by CMOS switches $2 and $4; the other one (known as the detecting electrode) is connected to earth by switch $1, when the active electrode is charged to voltage Vc, and to the input of the current detector (which is at virtual earth potential) via $3, when the active electrode is discharged to earth. The current detector averages the discharging current pulses flowing through the detecting electrode, producing a voltage signal, V0, proportional to the unknown capacitance value, C×, i.e. Vo = (KfVc)C×
(14)
where K is the gain factor of the current detector and f is the frequency of the charge/discharge switching operation. In our system, f is 2 MHz, which is approaching the upper frequency limit of the CMOS switches and associated circuits. In a complete data collection cycle, electrode 1 (Figure 5) is first selected as the active one, and the capacitances between electrodes 1 and 2, 1 and 3,
Flow Meas. Instrum.
Vol I October 1990
265 off
m
on
s~ s~ s ~ ~ s~ - L _ r - L _ r - L _ S4
S2
~
Cf
a --
S3 O.
~
b
,~'~-'~ ~ a ' I D ~ R ~ 4 ~ PlIIIIII
Figure 6 The capacitance measuring circuit
1)/2
(15)
In the above measurement process, the redundant electrodes (those not selected as active or'detecting in a measurement) are always connected to earth or virtual earth potential, forming 'guard rings' for the measuring electrodes. This arrangement enables the measurement sensitivity to be focused into a relatively narrow area between the selected electrode pair. The field pattern resulting from the electrode configuration and switching connections described above has been modelled using the finite element method ~. The relationship between the capacitance of an electrode pair, C~, the measurement sensitivity distribution function, S~(x, y, ~(x, y)), and the dielectric distribution in the pipe, 8(x, y), is expressed as
C, = L ~ ~(x, y)S,(x, y, ~(x, y))dxdy
~,
NN"
• o •, 1 and 8 are measured. Next, electrode 2 is selected and electrode pairs 2-3, 2 - 4 . . . . . 2 - 8 are measured. This process continues until electrode pair 7-8 is measured• This produces a total of 28 independent measurements. Generally, for an N-electrode system, the number of possible two-electrode combinations (the number of independent measurements), n, is given by
n = N(N-
b
(16)
where D is the cross-section of the pipe. C~ in equation (16) depends mainly on the dielectric distributions in the narrow area where the sensitivity is positive. We call this area the positive sensing area of the selected electrode pair. Figure 7 shows the positive sensing areas (the dark areas) of four typical electrode pairs, obtained using the finite element method. Those of other electrode pairs can be obtained by rotating the four typical patterns around the centre of the pipe.
Image reconstruction algorithm For an n-output measurement system, the vector of the measurement results, [C~, C~. . . . . Cn], is determined by the dielectric distribution, ~(x, y). According to equation (16), we have
c
d
Figure 7 Four typical positive sensing areas. Electrode pairs: (a) 2-3; (b) 2-4; (c) 2-5; (d) 2-6
[C,, Q . . . Cn] = [ L J" ~(x, y)S,(x, ,v, ~(x, y))dxdy, •[D f E'(X, .y)S2(X, y, £(X, y))dxdy .....
~D~E(X, y)Sn(X, y,E(X, y))dxdy](17) Our task of image reconstruction is to solve the inverse problem of determining ~(x, ,v) from a limited number of measurements• Since component distribution in two-component flows is very complicated, a complete solution to the integration functions given in equation (17) is not possible with only 28 measurements. To obtain an approximate solution, we simplify the problem by making the following assumptions. First, it is assumed that the effect of the dielectric distribution on the sensitivity distributions of the sensors is insignificant, and the sensitivity distribution in the sensing area is uniform. Therefore the function Sj(x, y, ~(x, y)) is simplified to constant Si
Si(x, y, ~(x, y)) = 0
in the ith positive sensing area elsewhere. (18)
Secondly, we assume that any change in a measured capacitance results from a uniform dielectric change over the entire sensing area. Therefore, on this (ith) sensing area, the dielectric distribution in equation (16) can be solved to give
Ei = Ci/DiSi
(19)
Equation (19) can be normalized by using the value of C/measured when ~i = 1, and the normalized form is given by
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(20)
To produce an image of the dielectric distribution, the sensing area can be a grey level whose value is proportional to the measured capacitance value. By summing up all the 28 grey areas over the cross-section of the pipe, the grey level in the areas where objects with higher permittivity are found will be enhanced. Thus a grey level image representing the component distribution of the two-component flow can be obtained. This summation process is known as 'backprojection' and involves the following steps. First, the boundaries of all the 28 sensing areas (Figure 7) are plotted on the cross-section of the pipe. These boundaries intercept each other, forming many small pixels (Figure 8). Each of the pixels is related uniquely to some of the 28 areas, i.e. it is the common pixel of these areas. Secondly, a relational matrix, V, can be written out according to the relationship between each pixel and the 28 measurements. Each line in V corresponds to a pixel in Figure 8. Each line consists of 28 elements, each of them corresponding to one of the 28 sensing areas. An element is equal to 1 if the pixel is in the corresponding area, 0 otherwise. The grey level Gi in the /th pixel can be obtained by multiplying the vector Vi in V with the vector of 28 measurement values; thus we have G2
=
V2
x [C~, C2. . . . . C281T
(21)
k
where k is the total number of the pixels. In this system k = 362. Now the flow image can be obtained by performing the matrix multiplication in equation (21) and then displaying the grey level of the pixels shown in Figure 8.
Further details of the reconstruction method are given in a recent paper 9.
Experimental results The system described above has been constructed using an array processor (Transputer) for image reconstruction :0. Typically, capacitances of the order of 1 pF can be measured to an accuracy of 1% FS in the presence of 50 pF stray capacitance. Under computer control the data capture time is 2.5 ms. The program structure consists of processes for data input, calibration, reconstruction, display and interpretation, together with an overall control/monitor process. Of these, reconstruction is computationally the most intensive task. The reconstruction process consists of around 5000 arithmetic operations and takes 24 ms to execute on one processor. Tests with a four-processor network show this time to reduce linearly. In the present system, reconstruction is allocated to two processors. One of the processors is also used for data input and calibration, so the allocation is biased to balance the processing burden. In the present implementation, a network of four T4~4 Transputers is used, together with two other processors. The Transputers are arranged in a ring configuration, the allocation of processors being shown in Figure 9. A fifth processor controls data acquisition and interfacing, while a sixth, the IBM PS/2, provides user interface and monitor facilities. All communication is via standard Transputer links running at 10 Mbits -~ Since the processing structure is essentially a pipline, the frame rate is determined by the length of the longest process. By balancing the network this can be reduced to | 7 ms, providing a frame rate of 60 Hz. The display is refreshed every second image to avoid a graphics overload. A series of tests was performed using a 2.5 m long experimental flow loop. The test section was fully inclinable to produce asymmetric flow profiles. Figure 10 shows an oil/water flow (composed of 40% water v/v) with the 75 mm diameter test section inclined at 30 ° to the vertical. The higher concentration component is clearly shown in the lower part of the pipe. This is the distribution expected, because of the gravitational effects on the denser medium. Other results showed an equally encouraging correspondence between theoretical and actual images. Figure 11 shows an image obtained with a pipe having a stratified layer of PVC chips occupying part of the crosssection. (In Figure 10 the image has been expressed on a rectangular pixel grid, rather than the pixels shown in Figure 11 which were formed by the field between the electrodes).
Conclusions
Figure 8 The image pixels formed by the boundaries of the 28 positive sensing areas
The results in this paper confirm the feasibility of high-speed tomographic imaging for measuring the component distribution in multi-component flows. The system we have described generates two-component flow images at 60 frames per second; this could be increased to 400 frames per second by using more
Flow Meas. Instrum.
Vol I October 1990
267
~P
To transducer
T414
__i
/ J
T41
To host PC
Figure 9 Transputer system for image reconstruction
Figure 10 Image for inclined oil/water flow Figure I 1 Image for inclined flow of plastic chips Transputer chips for image reconstruction. The spatial resolution of these electrical field sensing systems is limited by field spreading, but we feel that a spatial resolution of one in 20 along the projection distance could be obtained in many applications (corresponding to one part in 400 over the projection area). Fortunately, the electrical properties of each image boundary are functionally related to the image grey level, so that the component ratio of a two-component mixture within a boundary can be measured, although individual particles cannot be imaged. High-speed imaging will be required for measuring the velocity profile as part of the component mass flow measurement system shown in Figure 3. For a flow velocity of 5 ms -1 in a 200 mm diameter pipeline we expect the image feature size to be 10 mm (corresponding to the resolution limit of one in 20 of the projection distance). This size of feature or zone in
the flow (assuming it is spherical) takes 2 ms to cross the image plane. In order to avoid aliasing it should be sampled (imaged) twice during its transit, thus requiring a frame interval of 1 ms (or 1000 frames per second). We believe that by using all-electronic measurement systems, image rates of 1000 per second are technically feasible. This is much faster than previously used X-ray and ],-ray methods which are limited to much lower speeds because of safety/photon-count considerations. Ultrasound methods of imaging are also slow due to the sonic velocities being quite low, although by using recently developed wideangle transmitters speeds of 400 frames per second in a 100 mm diameter vessel using 12 interrogating transducers are possible 11. The most computer-intensive part of the component flow measurement system (Figure 3) is the crosscorrelation calculation.
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R. Thorn et al - Flow imaging for multi-component flow measurement
Assuming 400 pixel images (corresponding to 5% spatial resolution), 1000 off 4-bit data values to be correlated with up to 100 correlation delays and declaring 10 velocity profiles per second, the corresponding bit rate is 400 x 1000 x 4 x 100 x 10 = 16 x 108 bitss -~, which is achievable using low-cost array processors. The capacitance sensing method we have described can be used only where the major component in the process is not electrically conducting. For application to flows of electrically conducting fluids, sensors measuring electrical impedance (at a low frequency of say 25 kHz) are recommended (Table 1). Impedance measurement has been successfully used for obtaining tomographic images of the human body 12 and our preliminary tests for flow imaging are encouraging. A most significant need is the in-depth study and development of the coherent body of knowledge required to establish a sound practical and theoretical design framework for the emerging science of flow imaging. Specific future investigations could include: [] fundamental limitations in spatial and temporal resolution of various sensor configurations (capacitance, impedance, ultrasonic, optical and radiation); [] the spatial and temporal resolution needed for particular applications; [] image value (contrast or grey scale) requirements, particularly for binary and ternary mixtures where pixel elements are incompletely filled by one component; and [] correction of the image distortion caused by the electrical field equipotentials changing with the varying electrical properties of the material in the image space. We believe that tomographic techniques will have a number of exciting and innovative future applications for multi-component flow measurement, offering opportunities to visualize the internal characteristics of hitherto inaccessible flows and ultimately capable of leading to a complete solution of the component mass flow measurement problem.
Acknowlegements
This work was funded by the British Council and the Science and Engineering Research Council including a grant under the Total Technology Scheme, in collaboration with the Fluids Mechanics Department, Schlumberger Cambridge Research Ltd. References 1 Dykesteen, E. and Frantzen, K. H. The CMI multiphase
2 3
4 5 6
fraction meter. Proc. Int. Conf. on Basic principles and industrial applications of multiphase flow, London (April 1990) Hammer, E. A., Tollefsen, I. and Olsvik, K. Capacitance transducers for non-intrusive measurement of water in crude oil. Flow Meas. Instrum. 1 (1)(1989) 51-58 Beck, M. S., Green, R. G. and Thorn, R. Flow measurement: two-phase systems, tn 'Encyclopaedia of Systems and Control' (Ed. M. G. Singh), Pergamon Press, Oxford (1987) 1685-1694 Medlock, R. S. and Furness, R. A. Mass flow measurement -- a state of the art review. Meas. and Contr. 23(4) (1990) 100-113 Hewitt, G. F. Multiphase flow metering. Proc. Conf. on Process equipment for oil and gas industries (November 1989) Beck, M. S. and Plaskowski, A. Cross correlation flowmeters -- Their design and application. Adam Hilger (1987)
7 Huang, S. M., Green, R. G., Plaskowski, A. B. and Beck,
M. S. A high-frequency and stray-immune capacitance transducer based on the charge transfer principle. IEEE Trans. Instrum. and Meas. IM-37 (1988) 368-373 8 Xie, C. G., Plaskowski, A. and Beck, M. S. 8-electrode capacitance system for two-component flow imaging, lEE Proc. 136A (4) (1989) 173-183 9 Huang, S. M., Plaskowski, A., Xie, C. G. and Beck, M. S.
Tomographic imaging of two-component flow using capacitance sensors. J. Phys. E.: Sci. Instrum. 22 (1989) 173-177 10 Salkeld, J. A. PhD thesis, University of Manchester (1990) (pending) 11 Gai, H., Beck, M. S. and Flemons, R. S. An integral
transducer/pipe structure for flow imaging. IEEEThird Int. Ultrasonics Symp., Montreal, Canada (October 1989) 12 Barber, D. C. and Brown, B. H. Applied potential tomography. J. Phys E.: Sci. Instrum. 17 (1984) 723-733