Method and apparatus for determining properties of a contained fluid

Abstract

In order to measure a fluid flow or flow conditions of a fluid flow through an apparatus, electrodes are provided across which capacitance values are determined. The capacitances are used in conjunction with a predetermined model to determine a revised model for the system. If the modelled to be satisfactory, then the values representative of the flow conditions are output. If it is not, then the model is tuned to reduce the error. A novel arrangement of electrodes is also provided along with apparatus embodying the method. The invention also provides a way of determining fluid properties, for example, density, volume present contained within a vessel or tank whether flowing or stationary.

Claims

1. A method for determining a flow of a fluid comprising the steps of: providing an arrangement of electrodes to, in use, be exposed to a fluid flow; providing a first model of a fluid flow for a particular arrangement of electrodes; providing a set of penalty functions; providing the fluid flow; determining from the electrodes a set of capacitance values; deriving from the set of values and the first model a second model of fluid flow; comparing the second model of fluid flow with the set of values to provide a global system penalty; and comparing the global system penalty with a predetermined threshold value and, responsive to the comparison, modifying the first model or outputting a rate of flow determined from the set of values and the second model of fluid flow.

2. A method as claimed in claim 1 wherein the penalty functions are a difference between a predicted set of capacitances and measured set of capacitances.

3. A method as claimed in claim 2 wherein the first model is a reverse model of flow conditions relative to potential electrode capacitance values.

4. A method as claimed in claim 2 wherein the second model is a forward model of measured electrode capacitance or resistance values relative to flow conditions.

5. Apparatus for determining fluid flow comprising: an arrangement of electrodes to, in use, be exposed to a fluid flow; a first model of a fluid flow for the arrangement of electrodes; a set of penalty functions; a processor responsive to the outputs of the electrodes to determine a set of values representative of electrical properties therebetween capacitance or resistance; a modeller to derive from the set of values and the first model a second model of fluid flow; a comparator to compare the second model of fluid flow with the set of values to provide a global system penalty; and a comparator to compare the global system penalty with a predetermined threshold value and a processor responsive to the comparison for modifying the first model or outputting a rate of flow determined from the set of values and the second model of fluid flow.

6. Apparatus as claimed in claim 5 wherein the penalty functions are a difference between a predicted set of values and the measured set of values.

7. Apparatus as claimed in claim 5 wherein the first model is a reverse model of flow conditions relative to potential set of values provided by the electrodes.

8. Apparatus as claimed in claim 5 wherein the second model is a forward model of measured electrode capacitance values relative to flow conditions.

9. Apparatus as claimed in claim 5 wherein the electrodes are disposed either side of a constriction in the flow.

10. Apparatus as claimed in claim 5 wherein the electrodes are provided, at least in part, on a restriction placed in the flow.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Specific embodiments of the invention will now be described, by way of example only, with reference to, the figures in which:

(2) FIG. 1 is an overview of an apparatus for measuring fluid flow in accordance with the invention;

(3) FIG. 2 is a schematic diagram showing blocks of functionality provide by a processor forming part of the apparatus shown in FIG. 1;

(4) FIG. 3A is a cross-section through within pipe containing fluid flow of interest in accordance with a first embodiment of the invention;

(5) FIG. 3B is a longitudinal section of the pipe shown in FIG. 1 with an internally located set of electrodes circumferentially arranged about the inner periphery of a wall defining the internal bore of the pipe;

(6) FIG. 4A is a cross-section of a second embodiment of the invention in which electrodes are arranged about the periphery of a pipe containing a fluid flow of interest with FIG. 4B being a longitudinal section;

(7) FIGS. 5A, 5B, 6A, 6B, 7A, 7B, 8A, 8B, 9A, 9B, 10A, 10B, 11, 12A, and 12B are further embodiments of the invention;

(8) FIG. 13 is an explanatory diagram describing the method in accordance with a preferred embodiment; and

(9) FIGS. 14A and 14B show a further embodiment of the invention for determining the amount of propellant within a storage vessel within a spacecraft.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

(10) As is shown in FIG. 1, a flow sensing device apparatus 1 in accordance with the invention comprises a set of electrodes 6 generally indicated at a location in or about a pipe 2 within which a flow is contained. The pipe is shown as a limited length longitudinal section but will be understood to extend over a great length from a source of supply (not shown) to an outlet (not shown). The flow has a direction as indicated by labelled arrows 3 and 4. A wire bus 5 is provided to link the electrodes 6 to a fluid flow analyser 7.

(11) Within the pipe 2, and shown in broken outline, is a constriction or obstruction 8. In this case it is depicted as a planar disc with a centrally located hole. The disc acts to constrict the fluid flow to the hole. Other means of causing a pressure drop will be apparent to a person skilled in the art.

(12) The electrodes 6 are arranged to provide electrodes 6a upstream of the constriction (to the right in the figure) and downstream 6b of the constriction (to the left of the figure). In some embodiments of the invention, the electrodes 6 will be arranged outside of the pipe 2 or internally or within the body of the wall of the pipe. As will be later described, the electrodes provide a set of electrical values in this case capacitance values from which the flow before and after the restriction may be determined to in turn provide a value of the fluid flow through the constriction.

(13) Various forms of the electrodes and the constriction or means to create a pressure drop will be later described.

(14) The flow analyser 7 is a microprocessor based arrangement and comprises a processor 9, an input port 10, a memory 11, an output device 12 such as a visual display unit and a power supply 13. The memory 11 provides storage memory for variables and also a set of instructions (code) for controlling the way in which the microprocessor operates to perform the flow analysis. It includes ROM (read only memory) and RAM (random access memory).

(15) The processor 9 is governed by the set of executable instructions to provide blocks of functionality which are shown schematically in FIG. 2. It will be appreciated that these blocks of functionality may be all or in part replicated by circuitry produced as discrete electronic components or a mixture of such components and processors programmed to provide elements of the functionality.

(16) FIG. 2 shows a set of functions provided by the programmed processor 9 and the way in which they interoperate. The processor 9 provides a first block of functionality 20 which determines a set of e(ij) measures for the electrode combinations which are values of capacitance at particular points in time. These measurements may be made, for example, by means well known to a person skilled in the art and which are commercially available, for example, from Atout Process Ltd (www.atoutprocess.com).

(17) These values of e(ij) are output to a memory 21 which holds a set of pre-programmed non-linear functions. These are defined and loaded into the memory by a user U in a pre-use calibration step. The non-linear functions represent the way in which the capacitance varies between the electrodes at different flow rates and conditions. They are a set of representative parameters for an average pipe. The actual performance represented by the measured values of e(ij) will vary from this set of equations. It is a model of a typical system and may be termed a reverse model in the sense that it provides a set of capacitances which would be detected for the modelled system, at particular flow rates and conditions, whereas the intention for the apparatus is to provide from a set of measured capacitances a determined flow.

(18) In this particular embodiment, the pre-loaded non-linear functions are the following:
rho(ij)=Q(M(ij))
Ku(ij)=G(rho(ij))
e(ij)=F(Ku(ij))
where in a calibration at manufacture of the device a set of fixed relative permittivities Ku may be provided, for example by filling the pipe with a gas or liquid and performing measurements of e(ij) at a range of pressures so that the function rho(ij) is known and the form of F and G may be directly calculated from calibration data of known reference rho(ij) related to measured e(ij).

(19) F and G are a set of functions derived for each sensor at the time of calibration during manufacture. The forms of F and G will be generally developed for each electrode pair and the coefficients fitted ideally through a multi-point calibrationempty, and then full of a well-defined reference product.

(20) e(ij) is expressed in units of Farads, typically ranging from 10 to 1000 fF. Ku is expressed in units of non-dimensional relative permittivity where air (sensor empty) has a value of 1 and mineral oil (for example) is in the order of 2.5. F and G may also be derived from modelling of the sensor using mathematical or numerical models.

(21) Q is a set of functions derived at the time of installation or laboratory calibration by flowing a known fluid at a range of known flowrates. The form of Q will be generally developed for each electrode pair and the coefficients fitted ideally through a multi-point calibration. Q may also be derived from modelling of the sensor using mathematical or numerical models.

(22) M(ij) is thus the output measured mass flowrate over the area represented by the measurement of electrode pair capacitance e(ij) by means of the calibrated or modelled functions F, G and Q. The total mass flowrate of fluid is derived from the sum of all M(ij) and is measured in kg/s or similar units.

(23) The functions F, G and Q are inverted mathematically to their inverse functions F, G and Q and stored in memory 21. Inversion is a well-known process, so that for example if F=a then F=1/a, other more complex functions have more complex inversions well known to practitioners in the art. The set of functions F, G and Q are referred to as the forward model, while F, G and Q are referred to as the inverse model.
Ku(ij)=F(e(ij))
rho(ij)=G(Ku(ij))
M(ij)=Q(rho(ij))

(24) The apparatus performs an iterative training to revise the model. In doing this, a tuner function performs a modification of the non-linear functions held in memory 21 by, in this case, changing parameters within the functions. The tuner formed as a network using neural network techniques of nodes and weighted links.

(25) The reverse model held in memory 21 is used to generate output values of flowrate estimate from the measured values of e(ij). In this process, the model is reversed to provide values of flow based on detected capacitances across the various permutations of electrode couplings. This is held as a matrix of values eij loaded into memory 23 and represents a forward model of the apparatus. That is to say, a model which provides a flow from input capacitance values eij.

(26) The forward model stored in memory 23 is then used to calculate what the capacitance values would be if these values were true. These new estimates of capacitance values are referred to as e(ij)

(27) The resultant forward model is used by a comparator 24 in conjunction with a set of penalty functions held in memory 25 to produce a global system penalty. In this particular example, the penalty functions are:
P(ij)=b(ij)(e(ij)e(ij)) and the global penalty is the sum of all individual P(ij) values P*.

(28) The penalty functions P(ij) represent the weighted difference between the measured values and the estimates based on the inverse/forward modelling process and the global penalty P* represents the overall accuracy of the model relative to the true conditions in the pipe. The global system penalty is a measure of how close to the actual system the forward model held in memory 23 is.

(29) The global system penalty is input to a second comparator 26 which compares the value with a threshold held in memory 27. The threshold is provided at an initial calibration step performed by the user U at the same time as the initial non-linear functions are loaded into memory 21.

(30) In the event that, the comparator determines that the global system penalty is greater than the threshold in memory 27, then an instruction to tune is output to the tuner 22 to modify the functions held in memory 21.

(31) In the event that, the comparator determines that the global system penalty is less than the threshold, then the present flow rate and density values are output.

(32) The modified set of forward and reverse model equations is stored in memory 21 and 23 respectively and may be output as a reference system of equations to start the iterative procedure for other flow conditions which may occur during the lifetime of the measurement installation or in other flow systems of interest to the user.

(33) Various alternative embodiments of the invention will now be described with particular reference to the electrode/sensor elements which may be substituted for those in the above described embodiment. Like elements are identified by the same reference numerals.

(34) FIG. 3A shows electrodes, coils or other electrical sensing elements as curved rectangles distributed around the inside of a pipe cross-section containing a flow. In this case, the pipe wall is electrically conducting but in other embodiments it may be non-conducting. The electrodes, coils or other electrical sensing elements may be any number or arrangement around the pipe being electrically insulated from each other and from the pipe wall.

(35) As will be apparent from FIG. 3A, the electrodes 6a, 6b number eight encompassing the complete internal diameter of the pipe. As shown in FIG. 3B each electrode extends in the axial direction of the pipe. It will be seen that the electrode 6a1 has the same length in the axial direction as electrode 6b2. Electrode 6a2 is longer that electrode 6a1 but the same length as electrode 6b2. However, whilst this arrangement is preferred alternative dimensions may be used in other embodiments.

(36) FIG. 4A and 4B show electrodes, coils or other electrical sensing elements as curved rectangles distributed around the outside of a pipe cross-section containing a flow. In this case the pipe wall must be electrically non-conducting or pro a sheath of non-conducting material disposed between the pipe and the electrodes. The electrodes, coils or other electrical sensing elements may be any number, or arrangement around the pipe and are electrically insulated from each other and from the pipe wall.

(37) FIGS. 5A and 5B show a preferred embodiment of the present invention with electrodes, coils or other electrical sensing elements distributed around the inside of a pipe cross-section containing flow at several axial locations relative to a pressure drop device which is in the form of an annular ring or orifice plate. The electrodes, coils or other electrical sensing elements may be any number, shape or arrangement around the pipe and the pressure drop device may be any shape which blocks the flow to some extent. The pressure drop is also measured by the pressure transducer 50 through pressure tappings 51 communicating with the inner surface of the bore of the pipe at positions either side of the constriction 8. This represents a legacy pressure sensing arrangement augmented by the present invention or it may be provided for the purpose of factory calibration.

(38) FIGS. 6A and 6B show a preferred embodiment of the present invention with electrodes, coils or other electrical sensing elements distributed around the inside of a pipe cross-section containing flow at several axial locations relative to a pressure drop device which is in the form of an annular ring or orifice plate. The electrodes, coils or other electrical sensing elements may be any number, shape or arrangement around the pipe and the pressure drop device may be any shape which blocks the flow to some extent. The pressure drop is measured by the pressure transducer 50 through pressure tappings 51.

(39) FIGS. 7A and 7B show a preferred embodiment of the present invention with electrodes, coils or other electrical sensing elements distributed around the outside of a pipe cross-section containing flow at several axial locations relative to a pressure drop device which is in the form of an venturi insert 70. The electrodes, coils or other electrical sensing elements may be any number, shape or arrangement around the pipe and the pressure drop device may be any shape which blocks the flow to some extent. The pressure drop is measured by the pressure transducer 50 through pressure tappings 51.

(40) FIGS. 8A and 8B show a preferred embodiment of the present invention with electrodes, coils or other electrical sensing elements distributed around the inside of a pipe cross-section containing flow at several axial locations relative to a pressure drop device which is in the form of an annular ring or orifice plate. In addition to the electrodes around the pipe there are also electrodes, coils or other sensing elements on either or both surfaces of the pressure drop device. The electrodes, coils or other electrical sensing elements may be any number, shape or arrangement around the pipe and the pressure drop device may be any shape which blocks the flow to some extent. The pressure drop is measured by the pressure transducer 50 through pressure tappings 51. The constriction 8 is this time formed of a segmented plate. The segments of the plate are configured as further electrodes for use in determining the flow.

(41) FIGS. 9A and 9B show a further embodiment in which the electrodes 6 are provided in regions R1 to R5.

(42) FIGS. 10A and 10B show an embodiment in which the constriction 8 is provided as a plate, the plate itself carries the sensor electrodes hence its apparently segmented appearance when viewed along the direction of flow as shown in FIG. 10A. This preferred, where it is desired to provide a retrofitting of an existing orifice plate. The electrodes may be easily removable from the pipe by means of an orifice-plate carrier, something which is frequently already in place on a pipeline for carrying prior art orifice plates. Commercially then the device can be sold as a direct replacement of a cheap orifice plate, simply fitting in place of the existing replaceable plate, while the pressure drop measurement may be removed entirely, or used as a subsidiary mechanism to improve customer confidence in the capacitance measurement. In this case the electrical connections would be routed through the body of the plate out of the pipe through the carrier access.

(43) FIG. 11 shows the embodiment of FIGS. 10A and 10B with detail of the way in which the electrodes 6a,b are electrically coupled to the analyser 7.

(44) FIG. 12A shows an embodiment in which the electrodes 6 are provided at a surface of the wing of an aircraft. This will be useful for monitoring the flow over the wing surface. Similar arrangements may be provided for determining flow over other vehicles such as boats or submarines. FIG. 12B shows the electrodes provides at the surface of the blades of a fan assembly of a jet engine.

(45) The electrodes may be provided as discrete components or provided as conductive deposited layers. For example, the blade structure of the engine shown in FIG. 12B may be manipulated during manufacture to provide conductive and non-conductive portions as required to provide the electrodes.

(46) The initial step of calibrating the apparatus will now be described.

Calibration

Step 1

(47) The device may be calibrated for one or more particular gases at the time of manufacture or after installation in the case of a retrofit, in the following manner:

(48) 1.1 A flow meter is connected to a short length of pipe and pressurised to a range of pressures covering that of interest in the proposed application.

(49) 1.2 Measure all capacitances between every pair of electrodes and relate each to the density of gas which is in this condition completely uniform throughout:
e.sub.i,j=f.sub.i,j(.sub.g) equation 1
where e.sub.i,j is the measured electrical capacitance between electrode number i of total N and electrode j of N. f .sub.i,j is a simple function such as a polynomial fit between capacitance and density value and .sub.g is the gas density at the pressure in the test pipe. In this simple example, f.sub.i,j is equivalent to the forward model functions F and G described earlier.

Step 2. Single-Phase Flowrate Measurement

(50) 2.1 If all side-by-side pairs (adjacent electrodes in the direction of flow) measure the same value, then the flow is single-phase, because any flow material (liquid or solid) present will tend to be towards the bottom of the pipe under normal conditions of gravity. In this case the values from ring of electrodes R1, one or more diameters upstream represent the upstream fluid density .sub.g1 while the values from ring of electrodes R3 represent the fluid density .sub.g3 at the throat (known as the vena contracta) of the orifice plate. From simple fluid mechanics equations, we know that in a horizontal compressible flow:
conservation of mass: .sub.g1.Math.v.sub.g1.Math.a.sub.1=.sub.g3.Math.v.sub.g3.Math.a.sub.3 equation 2
conservation of energy: .sub.g1.Math.(v.sub.g1).sup.2=.sub.g3.Math.(v.sub.g3).sup.2 equation 3
where a.sub.1 and a.sub.3 are the area of the flow at positions R1 and R3 and v.sub.g1 and v.sub.g3 are the gas velocities at the same positions.

(51) 2.2 We calculate
.sub.g=f.sup.1.sub.i,j(e.sub.i,j) equation 4
at each position R1, R3 (as a minimum, we may also do this at a larger number of electrodes R2, R4, R5 etc. for increased accuracy) where f.sup.1.sub.i,j is the inverse function of f .sub.i,j and is equivalent to the forward model functions F and G described earlier.

(52) 2.3 Since the areas a.sub.1 and a.sub.3 are known by design of the pressure device and .sub.g1 and .sub.g3 have been calculated from the set of measurements represented by equation 4, we have two equations (2 and 3), 6 unknowns and four knowns, enabling us to calculate the two velocities v.sub.g1 and v.sub.g3.

(53) 2.4 The mass flowrate of gas is thus given by:
m.sub.g=.sub.g1v.sub.g1.Math.a.sub.1=.sub.g3v.sub.g3a.sub.3 equation 5

(54) Equations 1 to 5 are equivalent to the non-linear functions for storage in memory 21 described above in general terms as F, G and Q.

(55) The method in accordance with the invention may be implemented after calibration as follows.

(56) Provide a pressure drop device for example a constrictor /orifice plate 8 etc. at the pipe 2.

(57) Mount a set of any number of electrodes 6, coils or other sensing elements around the flow of interest these elements are arranged such that many pairs of measurements can be made. There may be typically 2 to 5 rings of 8 sensing elements so that N, the number of sensing elements may be on the order of 16 to 40 and there are Nx(N1) measurements. The sensing elements should be distributed such that some pairs are close together in different areas of the pipe or vessel and that other pairs are separated by at least 1 pipe diameter from, and on either side of the pressure drop device.

(58) The total number of electrodes, coils or other sensing elements is N. There are Nx (N1) different combinations of measurements between sensing elements. So for 8 sensing elements there are 87=56 pairings measuring the electrical properties between elements (1,2), (1,3), (1,4) . . . (2,1), (2,3) . . . (8,7).

(59) Each measurement is affected in a different way by different physical parameters of the flow. For example, the measurement from a pair of elements close together is dominated by the region local to their common boundary, while for element pairs far apart the measurement is determined by conditions across a large part of the volume of the pipe or vessel. The near pair measurement at the bottom of the pipe will be affected more by any liquid or solid loading than a near pair at the top of the pipe or a far-apart pair, while the far-apart pair measurements will be dominated by the fluid density and liquid loading in the far field away from the pressure drop device.

(60) Thus, the parameters of the flow directly influence the measurements in a way that may be extracted by considering the weight that each parameter has on each pairing.

(61) The physical parameters of interest in the flow of dispersed multiphase flow such as wet gas or solids conveying are the flowrates of each phase expressed in kg/s or similar units. Typically, 2, 3 or 4 phases or flow components are present so 2, 3, or 4 outputs are required. Thus, few outputs are required from the many (Nx(N1)) measurements available from the present invention.

(62) The Nx(N1) measurements are processed by a processer 9 of FIG. 1 using a set of algorithms that provide a multi-parameter fit to output the few required key output flowrates. This processing may be by means of simple multi-variable regression analysis, an artificial intelligence system, or some other set of mathematical algorithms.

3. Calculation of Flowrate In Wet Gas or Solids

(63) 3.1 Compare the electrode measurements from side-by-side pairs in each ring. If there is a second phase present, then there will be a substantial difference between pairs at the top of the pipe and those at the bottom.

(64) 3.2 Calculate the probability density function of all side-by-side values in plane R1, and use the measurement value at peak A (stated here as e.sub.A) as the equivalent gas value, and peak B as the equivalent second phase value.
.sub.g=f.sup.1.sub.i,j(e.sub.A) equation 6

(65) 3.3 Calculate a first guess of the flowrate of gas using the calibration method in step 2.

(66) 3.4 Using the single-phase functions f.sub.i,j, calculate the predicted measurement values e.sub.i,j through the various rings of the sensor which will be different from the values measured directly. This step requires a fluid mechanics model which may be a simple one of a full computational calculation using a commercial computational fluid dynamics software package or other fluid mechanics modelling means. The inputs to the fluid mechanics model include the first guess calculation of density from equation 6 and the first guess estimate of second phase concentration from equation 7.
.sub.l=f.sup.1.sub.i,j(e.sub.B) equation 7

(67) 3.4 Considering the two phases to flow independently (the so-called separated flow model) we can calculate gas and liquid flowrates using these new density estimates and equations in step 2.

(68) 3.5 The set of f.sub.i,j for a wet gas will be different from the set calculated in single-phase because the electrical field and the fluid mechanics field will be affected by the presence of a second phase. Using a mathematical artificial neural network in a processor these differences are used to calculate a new set of f.sub.i,j to minimise the difference between the set of measured e.sub.i,j and the calculated e.sub.i,j.

(69) 3.7 Repeat step 3.5 until the values of f.sub.i,j converge to an acceptable level and the full flowrate of both phases can be calculated from the simple two-phase model used in 3.4.

4. Calculation of Flowrate in Wet Gas or Solids Conveying

(70) The embodiment in FIGS. 10A and 10B has significant commercial advantages, but the mechanism is equivalent to the above. In this case the side-by-side measurements are related to local conditions, while the across-the-pipe pairs have a much greater depth of penetration along the pipe by a diameter or more.

(71) The side-by-sides can therefore be treated as equivalent to ring R3, while the distant pairs where (i,j) is (1,5), (2,6), (3,7), (4,8) represent the density of the fluid at positions equivalent to R1. Otherwise the process of calculation remains the same as above.

(72) FIG. 13 provides a flow chart of the method in accordance with the invention as described above.

(73) In the above described embodiments, there is created a fluid flow within a pipe.

(74) The invention in its broadest aspect may be used to determine a volume of a fluid within a pipe, tank or vessel. That is to say, the fluid is not required to flow but is stationary, or made to flow as the tank moves. A satellite tank may be provided with electrodes, as earlier described, and the described method applied to determine tomographic pixelated images of the permittivity distribution which are processed to determine the density of the fluid present and or other properties. From this, the amount of fluid present in the tank will be determined.

(75) FIG. 14A shows in schematic form a system 140 for determining the amount of fuel remaining in a satellite fuel tank 141. The fuel tank 141 holds a propellant to be delivered via a control valve 142 and hence to a maneuvering nozzle or thruster 143 mounted to the exterior surface of the satellite (not shown). This provides a thrust to position the satellite as desired. As is shown in FIG. 14B, the fuel tank 141 contains the fuel 144 within a substantially spherical void. When the satellite is first positioned in orbit the tank 141 is full and as the fuel is used it breaks up into globules or droplets floating under zero gravity conditions within the tank 141. This may be a mixture of different types of fluids making up the fuel or fluid and space between. It will be appreciated that the globules will break, form and reform in a complex matter. They may become stationary due to friction and surface tension or move as a result of movement by the satellite or as a result of flow to the thruster 143.

(76) The tank 141 is formed with an inner electrically insulating layer 145 within a metal wall 146. About the periphery of the tank are fixed a plurality of electrodes 147. These are five sided segments fixed to the tank in an insulating matrix to insulate them one from the other. The segments are better shown in FIG. 14A where they are depicted with dark and light shading to allow them to more easily perceived. The electrodes are formed of electrically conductive, material such as copper or gold. Each electrode is connected by a wire 148 to a bus 149.

(77) The bus 149 connects the electrodes to a capacitance measuring device 150. This is a microprocessor based processing device programmed by software to perform the required capacitance measuring process. This measures the capacitance across various combinations of the electrodes to provide a range of capacitance values across the volume of the tank. These values will be determined in part by the mixture of fuel in droplets and the intervening volumes as shown in FIG. 14B which will enable a picture or image of the make-up of the volume to be determined. This is performed by a tomographic imager 151.

(78) The tomographic imager 151 creates a set of tomographic pixelated images of the permittivity distribution within the mixture from each set of measured capacitances at each point in time. Thus, over time, these images are output to memory 152.

(79) Memory 152 is coupled to a density function generator 153 for generating a set of probability density functions for the value of each pixel location within the pixelated images against time. These density functions are then output to memory 154.

(80) A processor 155 for deriving the density or other physical or chemical property of the two fluids from the stored probability density functions is coupled to the memory. The derived density or other parameter is output to another system 156 such as a fuel management system.

(81) The various processes carried out in this embodiment will be apparent from the earlier described embodiments.

(82) In the described embodiments, it will be appreciated that the processing functions may be provided by one, or a number of, microprocessors operating under software control.

(83) It will be appreciated that the person skilled in the art may envision many variations to the above described embodiments without departing for the generality thereof and the scope and spirit of the invention as described in the accompanying claims.