GB2509213A

GB2509213A - Method and apparatus for flow measurement

Info

Publication number: GB2509213A
Application number: GB1317973.4A
Authority: GB
Inventors: Stephen Flowers; Alistair Collins; Gary Fish
Original assignee: Taylor Hobson Ltd
Current assignee: Taylor Hobson Ltd
Priority date: 2012-12-20
Filing date: 2012-12-20
Publication date: 2014-06-25
Anticipated expiration: 2032-12-20
Also published as: GB201317973D0; GB2509108A; WO2014096762A1; GB201223083D0; GB2509213B

Abstract

A flow meter 110 adapted for calculating the flow rate of an injection fluid flowing through a subsea pipe into a well head on the sea floor, uses a flow parameter and a measurement of differential pressure in a specified flow model to determine the rate of fluid flow through the pipe; and, sends the determined rate of fluid flow from the subsea flow meter, via a communications interface, to a remote device. The flow meter is adapted to be coupled to a constriction in the pipe, the differential pressure comprises a pressure drop across that constriction, and the flow model comprises a dependence upon the discharge coefficient of the constriction. The flow meter also comprises a memory storing a look-up table relating a plurality of selected Reynolds number values to a corresponding plurality of discharge coefficient values for the constriction. The processor is configured to determine the Reynolds number based on the estimated flow rate and to determine the discharge coefficient from the look-up table based on the Reynolds number.

Description

Method and Apparatus for Flow Measurement The present disclosure relates to flow measurement, and more particularly to methods and apparatus for measuring flow, and still more particularly to methods and apparatus for measuring flow hi subsea installations, for example such as those associated with injecting fluids into, or producing fluids from, oil-wells which may he found on the sea bed, or on the bed of a body of water.

To measure flow in pipes on the sea bed it has been proposed to measure the pressure drop at a constriction and to communicate the measured pressure drop to a computer above the surface of' the water. The computer then performs the flow calculations. These calculations may be performed using multivariate non-linear flow models based on a number of parameters such as, amongst other things, the temperature, viscosity, density, and compressibility of the fluid, the hydrostatic pressure in the fluid, and the Reynolds number of the fluid flow.

Aspects and examples of the invention are set out in the claims and aim to provide an improved flow meter.

Aspects of' the disclosure are also described in detail, by way of' example only, with reference to the accompanying drawings, in which: Figure 1 shows a schematic drawing of a deployment of a flow meter on the sea bed; Figure 2 shows a schematic illustration of a flow meter such as that shown in Figure 1; and, Figure 3 shows a flow diagram indicating a method of operation of a flow meter.

Examples of the disclosure enable parameters of the fluid flow such as the Reynolds number o the flow, and the discharge coefficient of a constriction, to be determined at the flow meter, thereby also providing the ability for calculations of' fluid flow rate to be performed in situ at the flow meter. This is technically significant because it removes the need for measurements collected from pressure and temperature sensors distributed along a flow line to be communicated to a surface installation, such as an oil platform, and collated with differential pressure measurements to enable a flow rate calculation to he performed. This in turn can provide improved accuracy in flow calculations because there is no need for multiple measurements to be collated and synchronised at the surface installation.

To this end, tile disclosure provides a subsea flow meter adapted for calculating the flow rate of an injection or production fluid flowing through a subsea pipe into/out from a well head on the sea floor. The flow meter receives hydrostatic pressure, differential pressure and temperature signals, and determines at least one parameter of the fluid based on the hydrostatic pressure and/or temperature. The flow meter then uses this parameter and the differential pressure in a specified flow model to determine the rate of fluid flow through the pipe before sending the determined rate of fluid flow to a remote device, for example a device at the surface of the sea. The inventors have recognised that this approach enables the need for a high bandwidth link between the flow meter and the surface to be avoided, thereby also providing a flow meter for use in environments where communications might present a difficulty.

Figure I shows an installation 100, at the surface of a body of water, and coupled via an injection pipe 115 to an injection well head 126 on the bed of the body of water for injecting injection fluid 130 into an injection well of a subterranean formation 140. A flow meter 110 is coupled to the injection pipe 115 and an'anged to monitor the flow of injection fluid 130 through the pipe 115. In Figure 1, a production pipe 125 is arranged to cany fluid 150 produced from a production well of the formation 140 back to the surface installation 100.

In the example of Figure 1, the flow meter 110 includes a communication interface 160 for communicating flow rate measurements to a communication interface 165 of the surface installation. The communication interfaces 160 and 165 are ananged to communicate over a physical link, this communication link may be provided by wired and/or wireless communication.

Figure 2 shows one example of the subsea flow meter 110 ofFigure I adapted Ihr calculating the flow rate of the injection fluid 115 flowing through a subsea pipe, such as the injection pipe 115 shown in Figure!.

In Figure 2 a pressure transducer 4 is coupled to the pipe 115 for measuring the hydrostatic pressure of the fluid 130 in the pipe 115, and a temperature transducer 6 is coupled to the pipe 115 for measuring the temperature of the fluid 130 in the pipe 115.

The pipe 115 comprises a constriction 10 arranged to provide a pressure drop, AP, associated with the flow of fluid 130 along the pipe 115. A differential pressure transducer 12 is arranged to measure the pressure drop, AP.

The flow meter 110 comprises a first transducer coupling 2, for coupling the flow meter to the pressure transducer 4 to receive a signal indicating the hydrostatic pressure of the fluid in the pipe. The flow meter 110 also comprises a second transducer coupling 8, for coupling to the differential pressure transducer 12 to receive a signal indicating the pressure drop, AP, across the constriction associated with the flow rate of the fluid through the pipe. The flow meter 110 also comprises a third transducer coupling 14 for coupling to the temperature transducer 6, and a communications interface 160 for communicating with a remote device.

The processor 16 of the flow meter 110 is coupled to a communications interface 160 for communicating flow measurements to a remote device.

The first, second and third transducer couplings 2, 8, 14 are coupled to a processor 16. The processor 1 6 is configured to receive the hydrostatic pressure, differential pressure and temperature signals from the transducer couplings 2, 8, 14.

The processor 16 is coupled to a memory 18 which stores at least one function relating a parameter of the fluid 130 in the pipe I I S to the hydrostatic pressure, and temperature.

The flow meter 110 uses a flow model to calculate the volume flow rate from pressure and temperature measurements. The flow model, depends on certain parameters such as the expansibility, fluid viscosity, fluid density, and the discharge coefficient of the constriction.

These parameters themselves may be temperature and pressure dependent, and may also be dependent on the volume flow rate, for example as the discharge coefficient is. Therefore, in operation, the how meter 110 calculates these parameters of the model, then generates an estimate of the volume flow rate, then updates its estimates of these parameters based on the updated flow rate in an iterative approach.

To simplify calculation of the model parameters, the flow meter stores simplified functions of temperature and pressure that are configured to enable the parameters to be determined.

These fuiictions may comprise look-up tables, polynomial functions and/or other analytic functions.

In more detail, in operation, the processor 16 is configured to determine a parameter of the fluid 130 in the pipe 115 based on the temperature and pressure signals, and the function stored in memory 18. This may avoid the need to use a complete PVT equation of state for the fluid flow.

Thus, based on the determined parameter(s), and the differential pressure signal, the processor 16 is able to determine the rate of fluid flow through the pipe using a specified flow model. The flow model used to determine the flow rate comprises a dependence upon the determined parameter(s) of the fluid, the pressure drop across the constriction 10, and the characteristics of the constriction 10, for example one flow model comprises: = 4E d2y2 * fluid_density * where: * q, is the mass flow rate.

* C is the discharge coefficient of the constriction.

* -f1 is the velocity of approach factor, and f3 is related to the geometry of the pipe 115 and the constriction 10.

* a is the expansibility for the constriction.

* d is the diameter of the constriction.

* itP is the pressure drop across the constriction.

The processor 16 is configured to determine the flow rate value, q,, and to send the flow rate value via the communications interface I 60, to a remote device at an installation 100 at the surface of the sea. Being at the surface of the sea may comprise being above, on or at least partially below the surface.

Flow Model Parameter Determination The Thnction used to detennine a parameter of the flow model may itself comprise a polynomial model of the temperature and/or pressure dependence of that parameter. Such a polynomial model may enable the processor 16 to determine parameters of the flow from the hydrostatic pressure and/or temperature of the fluid in the pipe.

The parameters which may need to be determined include: fluid density, the gas specific heat capacity (or isentropic exponent), the viscosity, the gas molecular weight, MW, the gas compressibility, Z, and the Joule-Thompson coefficient. The memory 18 may store functions for determining one or more of these parameters. The fluid density at standard (atmospheric) temperature and pressure may also be used in the flow model, however generally this is known (or can be calculated in advance) and stored in memory 1 8 and assumed not to alter.

Gas specific gravity, although it may change, can be determined from the gas molecular weight.

Each stored function provides an approximation to a parameter value over a selected range of temperatures and pressures, and the memory 18 may store a plurality of such thnctions for each parameter, each ftinction having been determined for a different selecled range of temperature and/or pressure. Accordingly, the processor may be configured to select a thnction for cacti parameter based on the temperature and/or pressure of the fluid, and then to determine the parameter from the selected function to enable improved accuracy and to avoid the need to reconfigure the flow meter when operational conditions vary.

The stored functions may comprise numerically determined or analytical functions (such as a polynomial model) of temperature and/or pressure. The stored functions may comprise look up tables of pre-calculated values.

One example of a stored polynomial function would be: f(P,T = A.P + B.T + C.P2+ D.T2 + E.F.T + F0 where, P and T represent the pressure and temperalure signals and the polynomial function is defined by its coefficients A, B, C, D, E, Fo. Where the function is a polynomial function, it may be stored as coefficient values, or the memory 18 may comprise a look up table of pie-calculated values of the parameter.

Updating/Selecting Different Parameter functions for different ranges of temperatures and/or pressures The processor 16 may be configured to update the stored parameter function(s) in response to a message received over the communications interface I 60. For example, the processor may be configured to receive a new function via the communication interface 160 and to replace the function stored in memory with the new function. Where a function comprises a look up table, the processor 16 may be configured to receive data to update or replace the values in the look up table. Where a function comprises a polynomial model defined using coefficients the processor 16 may be configured to receive one or more coefficients via the communications interface from a remote device, and to store the received coefficient(s) into the memory 18 to update or replace the polynomial model. In addition the processor tray be configured to receive an updated flow model via the communications interface from a remote device, Flow Model Calculations -Discharge Coefficient & Reynolds Number As set out above, the memory 18 stores the flow model to be used by the processor 16 to determine the rate of fluid flow. This flow model may, as in the example equation provided above, comprise a dependence upon the discharge coefficient, C, of the constriction 10. The processor 16 may be configured to determine the discharge coefficient used in the flow model based on the Reynolds number of the flow. For example, this determination of discharge coefficient may be based on a look-up table of Reynolds number and corresponding discharge coefficients. This table may be determined in an experimental calibration of the constriction andlor the flow meter.

The processor 16 may be configured to determine the Reynolds number according to a relationship of the form: R 4Qm

ILD

in which Q1, is the mass flow rate, D is the diameter of the pipe, p. is the dynamic viscosity of the fluid.

The processor I 6 may be configured to determine the Reynolds number based on an initial fluid flow rate value, and then to determine the discharge coefficient from the look-up table based on the Reynolds number before recalculating the fluid flow rate value. The processor 16 is configured so that, in the event that the determined Reynolds number is not found in the look-up table, the known values stored in the table are used to interpolate to determine the discharge coefficient for that Reynolds number. The processor is also contigured so that, in the event that the Reynolds number value is outside the range defined by the table, the corresponding upper or lower bound value is used from the table.

As with the thnctions used to determine other parameters of the flow model, in some examples the processor may be configured to modify the look-up table in response to a command received, via the communications interface 160, from a remote device 100.

Figure 3 illustrates one method of operation of the apparatus of Figure 2.

In overview, in this method the processor 16 is configured to initialise a Reynolds number value based on a stored flow rate value, to determine an initial estimate of the discharge coefficient based on the Reynolds number value, and then to update the Reynolds number estimate based on the estimated discharge coefficient. Thus, the processor 16 may iteratively update its estimates of the flow rate, qm, the Reynolds number, and the discharge coefficient in order to account for the inter-related nature of the parameters of the flow model.

In more detail: In an initialisation step 521 the processor 16 receives a differential pressure value AP, a pressure value, and a temperature.

The velocity of approach factor, 1 -fl4, and the value /3 are initialised according to the nature of the constriction. In the event that the constriction is an orifice, J3 is initialised to the ratio of the orifice diameter to the pipe diameter. In the event that the constriction is a cone /3 is initialised to,Ji -conejliameter2/pipe_diameter2.

The processor 16 may be configured to adjust the values used for the diameter of the pipe and orifice according to the coefficient of thermal expansion of the pipe and orifice and the received temperature signal by scaling the diameter values according to the temperature.

In step 523, after initialisation, in the event that the transducer 6 is arranged downstream of the constriction I 0 a correction is applied to the measured temperature. The temperature correction may be either: (a) no correction; or (b) a correction based on the Following formula: Tupstream = Tupstream + PJTAW where /1JT is the Joule-Thompson coefficient, and Aw is the pressure loss across the constriction.

Where the constriction is an orifice plate, the pressure loss Aw may be calculated based on the measured pressure drop, W, and the parameter, /3. The discharge coefficient, C, may also be used. Possible formulations include: 1- (1-C2) -C Aw= _________ AP 1-/3 * (1-C2) + C/ or, Aw = (1 -[3'9)ztP.

Other approaches, such as the Joule Thompson Enthaipic Approximation, and the Isentropic method may also be used.

In step 524, the processor 16 performs starting calculations to determine a dimensionless pressure ratio,c, associated with the pressure drop across the constriction, and the processor 16 determines the dimensionless pressure r according to: pressure -AP pressure Where pressure is the hydrostatic pressure of the fluid.

The processor 16 aiso determines a fluid density estimate, for example based on the temperature and pressure signals and a polynomial model as discussed above. In addition, the processor 16 determines a constant mass flow rate value, qinitial. based on a simplified version of the flow model ignoring the fluid expansibility and discharge coefficients, viz.

qinitiai = d2 * fluid_density * The processor 16 then determines an initial estimate of the Reynolds number based on the constant flow rate, qinitial, and detennincs a discharge coefficient from the Reynolds number.

At step 530, the processor 16 determines the expansibility, c. The processor is configured such that, in the event that the fluid consists solely of a liquid the expansibility is set to 1.

Otherwise the expansibility is determined based on the 3 value for the constriction 10, and the dimensionless pressure c to account for expansion of any gas in the fluid flow. The processor 16 then determines the flow rate, q using the calculated expansibility, a, and the estimate of the discharge coefficient C in the flow model: C it = ed2,J2 * fluid_density * 1 -/3 At step 540 the processor 1 6 updates the estimate of Reyno]ds number using the flow rate, q,,, calculated in step 530. The processor 16 then uses the Reynolds number to update the estimate of the discharge coefficient, C, as discussed above with reference to Figure 2. The processor 16 stores the determined flow rate, q, the Reynolds number, and the discharge coefficient, C, into memory 1 8.

At step 542 the processor cheeks to determine the number of times steps 530 arid 540 have been repeated, and in the event that the number of completed iterations is less than a selected number, N, die processor repeats steps 530 and 540. In the event that the number of iterations is greater than N, the processor performs step 544 in which the flow rate estimate is tested for convergence.

At step 544 the processor 16 sends the calculated flow rate to a remote device over the communication interface 160. The processor 16 also detemiines the difference between the most recent estimate of the flow rate q,,,, and the preceding estimate to determine whether the flow calculation has converged. In the event that die difference is greater than a selected tolerance, indicating that the calculation of flow rate has not converged, the processor 16 sends a signal to the remote device 100 over the communication interface 160 to indicate that the calculation has not converged.

The processor 16 may be configured to perform any selected number of iterative updates before testing the flow rate estimate to determine whether the estimates of flow rate converge to within a selected tolerance. The processor may be operable to reconfigure the number of iterations, and/or the selected tolerance value in response to a message received from a remote device 100 over the communications interface 160. In some examples, in addition, or as an alternative to the completion of a fixed number of iterations, the processor 16 may be configured to test for convergence on each iteration and to send the calculated flow rate once the process has converged.

The processor 16 may be provided by any appropriate controller, such as for example an application specific integrated circuit, ASIC, a field programmable gate alTay, FPGA, a combination of logic gates, or by a general purpose programmable processor. The memory 18 may store a computer program comprising program instructions operable to program a processor to perform a method according to any one described herein.

The constriction may comprise any device that provides a pressure drop along the pipe, such as a Venturi, or a coue constriction, or an orifice plate, or a bend in the pipe or a variation in the internal diameter of the pipe. The flow meter 110 may comprise the pressure and temperature transducers 4, 6, 12, and/or the flow meter 110 may comprise transducer couplings to couple to pressure and temperature transducers, which may be provided externally to the flow meter or may be integrated with the flow meter. The pressure and temperature transducers 4, 6, 12, may be provided by any transducer which provides an electrical output signal based on the sensed temperature or pressure.

Embodiments of the disclosure are further defined in the following numbered clauses, Cl to C28: Clauses: Cl. A subsea flow meter adapted for calculating the flow rate of an injection or production fluid flowing through a subsea pipe into a well head on the sea floor, the flow meter comprising: a first pressure transducer coupling for coupling to a first pressure transducer to receive hydrostatic pressure signal based on the hydrostatic pressure of the fluid in the pipe; a second pressure transducer coupling for coupling to a second pressure transducer to receive a differential pressure signal indicating a differential pressure associated with the flow rate of the fluid through the pipe; a temperature transducer coupling for coupling to a temperature transducer to receive a temperature signal indicating the temperature of the fluid in the pipe; a communications interface adapted to communicate a calculated flow rate to a remote device; and, a processor configured to: receive the hydrostatic pressure, differential pressure and temperature signals; determine at least one parameter of the fluid based on the hydrostatic pressure and/or temperature of the fluid in the pipe; use the parameter and the differential pressure in a specified flow model to determine the rate of fluid flow through the pipe; and, send the determined rate of fluid flow from the subsea flow meter, via the communications interface, to a remote device.

C2. The subsea flow meter of Cl in which the processor is configured to determine the at least one parameter based on a polynomial thnction of hydrostatic pressure and/or temperature of the fluid in the pipe.

C3. The subsea flow meter of C2 wherein the polynomial model is selected to provide an approximation to the parameter for a range of temperatures and pressures associated with an estimated temperature and pressure of the fluid in the pipe at the flow meter.

C4. The subsea flow meter of C2 or C3 wherein the polynomial model comprises a plurality of coefficients, and in which the processor is configured to receive a coefficient via the communications interface from a remote device, and to update the polynomial model to include the received coefficient.

CS. The subsea flow meter of any preceding clause in which the at least one parameter is selected from the list comprising: fluid density; gas specific heat capacity; fluid viscosity; gas molecular weight; gas compressibility; and the Joule-Thomson coefficient of the gas.

C6. The subsea flow meter of any preceding clause adapted to be coupled to a constriction in the pipe, wherein the differential pressure comprises a pressure drop across that constriction, and the flow model comprises a dependence upon the discharge coefficient of the constriction.

C?. The subsea flow meter of C6 comprising a memory storing a look-up table relating a plurality of selected Reynolds number values to corresponding plurality of discharge coefficient values for the constriction, wherein the processor is configured to determine the Reynolds number based on the estimated flow rate and to determine the discharge coefficient from the look-up table based on the Reynolds number.

C8. The subsea flow meter of C? in which the processor is configured to modify the look-up table in response to a command received, via the communications interface, from a remote device.

C9. The subsea flow meter of C? or 8 in which the processor is operable to interpolate between the selected Reynolds number values to determine the discharge coefficient.

C I 0. The subsea flow meter of C6 in which the processor is configured to initialise an estimate of Reynolds number based on a stored estimate of the flow rate, to determine an initial estimate of the discharge coefficient based on the estimate of Reynolds number, and then to update the Reynold's number estimate based on the estimated discharge coefficient.

Cli. The subsea flow meter of C 10, in which the processor is configured to iteratively update an estimate of the flow rate, the estimated Reynolds numbers, and the estimated discharge coefficient.

Cl 2. The subsea flow meter of Cli in which the processor is configured to perform a selected number of iterative updates, and then to determine whether the estimates of flow rate converge to within a selected tolerance.

Cl 3. The subsea flow meter of C12, in which fire processor is operable to receive the selected tolerance value from a remote device over the communications interface.

C1i4. The subsea flow meter of C12 or C13 in which the processor is further configured to send an alert to the remote device via the communication interface in the event that the estimates of flow rate do not converge to within the selected tolerance.

Cl 5. The subsea flow meter of any preceding clause further comprising at least one of: a pressure transd icer fot sensing hydrostatic pressure of the fluid in the pipe, and being coupled to the first pressure transducer coupling; a temperature transducer for sensing temperature of fluid in the pipe, and being coupled to fire temperature transducer coupling and a differential pressure transducer, operable to sense die pressure drop across a constriction in the pipe, and being coupled to the second pressure transducer coupling.

Cl 6. The subsea flow meter of any preceding clause adapted to receive tempeniture signals and/or pressure signals from a remote device.

C 17. ilhe subsea flow meter of any preceding clause in which the flow meter comprises a constriction.

Cl 8. The subsea flow meter of C7 in winch die Reynolds number is the Reynolds number of die flow in the pipe, or the Reynolds number of the flow in a throat of the constriction.

C 19. The subsea flow meter of any preceding clause adapted for use with a constriction and in which the flow model may comprise an initial value of discharge coefficient selected based on the type of constriction.

C20. The subsea flow meter ofCl9 in which the constriction comprises a Venturi.

C2 1. A computer implemented method of determining rate of flow in a pipe, using a flow meter located beneath the surface of a body of water, the method comprising: receiving hydrostatic pressure, differential pressure and temperature signals dctcrrnining at lcast onc paramctcr of thc fluid based on the hydrostatic pressure and/or temperature of the fluid in the pipe; using the parameter, and the differential pressure in a specified flow model to determine the rate of fluid flow through the pipe; and, sending the determined rate of fluid flow from the subsea flow meter, via a communications interface, to a remote device located at an installation at the surface of the body of water.

C22. The method of C2 I wherein the flow meter comprises a memory storing a function operable to determine the at least one parameter based on the hydrostatic pressure and/or temperature of the fluid in the pipe, the method further comprising determining the parameter from the at least one function.

C23. The method of C22 wherein the function comprises a polynomial model selected to provide an approximation to the parameter for a range of temperatures and pressures associated with an estimated temperature and pressure of the fluid in the pipe at the well head.

C24. The method of C23 wherein the polynomial model comprises a plurality of coefficients, and the method comprises receiving a coefficient via the communications interface from a remote device, and updating the polynomial model to include the received coefficient.

C25. The method of any preceding clause in which the at least one parameter is selected from the list comprising: fluid density; gas specific heat capacity; fluid viscosity; gas molecu'ar weight; gas compressibility; and the Joule-Thomson coefficient of the gas.

C26. A method of measuring fluid flow rate in an underwater pipe substantially as described herein with reference to the accompanying drawings C27. A computer program product comprising program instmctions, operable to program a processor to perform a method according to any of C2 I to C26.

C28. A flow meter substantially as described herein with reference to the accompanying drawings.

Claims

Claims: I. A flow meter adapted for calculating the flow rate of an injection or production fluid flowing through a subsea pipe into a well head on the sea floor, the flow meter comprising: a first pressure transducer coupling for coupling to a first pressure transducer to receive hydrostatic pressure signal based on the hydrostatic pressure of the fluid in the pipe; a second pressure transducer coupling for coupling to a second pressure transducer to receive a differential pressure signal indicating a differential pressure associated with the tiow rate of the fluid through the pipe; a temperature transducer coupling for coupling to a temperature transducer to receive a temperature signal indicating the temperature of the fluid in the pipe; a communications interface adapted to communicate a calculated flow rate to a remote device; and, a processor configured to: receive the hydrostatic pressure, differential pressure and temperature signals; determine at least one parameter of the fluid based on the hydrostatic pressure and/or temperature of the fluid in the pipe; use the parameter and the differential pressure in a specified flow model to determine the rate of fluid flow through the pipe; send the determined rate of fluid flow from the subsea flow meter, via the communications interface, to a remote device wherein the flow meter is adapted to be coupled to a constriction in the pipe, wherein the differential pressure comprises a pressure drop across that constriction, and the flow model comprises a dependence upon the discharge coefficient of the constriction; and a memory storing a look-up table relating a plurality of selected Reynolds number values to a corresponding plurality of discharge coefficient values for the constriction, wherein the processor is configured to determine a Reynolds number based on the estimated flow rate and to determine the discharge coefficient from the look-up table based on the determined Reynolds number.
2. The flow meter of claim 1 in which the processor is configured to determine the at least one parameter based on a polynomial function of hydrostatic pressure and/or temperature of the fluid in the pipe.
3. The flow meter of claim 2 wherein the polynomial model is selected to provide an approximation to the parameter for a range of temperatures and pressures associated with an estimated temperature and pressure of the tluid in the pipe at the flow meter.
4. The flow meter of claim 2 or 3 wherein the polynomial model comprises a plurality of coefficients, and in which the processor is configured to receive a coefficient via the communications interface from a remote device, and to update the polynomial model to include the received coefficient.
5. The flow meter of any preceding claim in which the at least one parameter is selected from the list comprising: fluid density; gas specific heat capacity; fluid viscosity; gas molecular weight; gas compressibility; and the Joule-Thomson coefficient of the gas.
6. The flow meter of any preceding daim in which the processor is configured to modify the look-up table in response to a command received, via the communications interface, from a remote device.
7. The flow meter of any preceding claim in which the processor is operable to interpolate between the selected Reynolds number values to determine the discharge coefficient.
8. The flow meter of any preceding claim in which the processor is configured to initialise an estimate of Reynolds number based on a stored estimate of the flow rate, to determine an initial estimate of the discharge coefficient based on the estimate of Reynolds number, and then to update the Reynolds number estimate based on the estimated discharge coefficient.
9. The flow meter of claim 8, in which the processor is configured to iteratively update an estimate of the flow rate, the estimated Reynolds numbers, and the estimated discharge coefficient.
10. The flow meter of claim 9 in which the processor is configured to perform a selected number of irative updates, and then th determine whether the estimates of flow rate converge to within a selected tolerance.
11. The flow meter of claim 10, in which the processor is operable to receive the selected tolerance value from a remote device over the communications interface.
12. The flow meter of claim 10 or 11 in which the processor is further configured to send an alert to the remote device via the communication interface in the event that the estimates of flow rate do not converge to within the selected tolerance.
13. The flow meter of any preceding claim further comprising at least one of: a pressure transducer for sensing hydrostatic pressure of the fluid in the pipe, and being coupled to the first pressure transducer coupling; a temperature transducer for sensing temperature of fluid in the pipe, and being coupled to the temperature transducer coupling; and a differential pressure transducer, operable to sense the pressure drop across a constriction in the pipe, and being coupled to the second pressure transducer coupling.
14. The flow meter of any preceding claim adapted to receive temperature signals and/or pressure signals from a remote device.
IS. The flow meter of any preceding claim in which the flow meter compnses a constriction.
16. The flow meter of any preceding claim in which the Reynolds number is the Reynolds number of the flow in the pipe, or the Reyn&ds number of the flow in a throat of the constriction.
17. The flow meter of any preceding claim adapted for use with a constriction and in which the flow model may comprise an initial value of discharge coefficient selected based on the type of constriction.
1K The tiow meter of claim 17 in which the constriction comprises a Venturi.
19. A computer implemented method of determining rate of flow in a pipe, using a flow meter located beneath the surface of a body of water, the method comprising: receiving hydrostatic pressure, differential pressure and temperature signals determining at least one parameter of the fluid based on the hydrostatic pressure and/or temperature of the fluid in the pipe; using the parameter, and the differential pressure in a specified flow model to determine the rate of fluid flow through the pipe; sending the determined rate of fluid flow from the subsea flow meter, via a communications interface, to a remote device located at an installation at the surface of the body of water; wherein the flow meter is adapted to be coupled to a constriction in the pipe, wherein the differential pressure comprises a pressure drop across that constriction, and the specified flow model comprises a dependence upon the discharge coefficient of the constriction; and the flow meter comprises a memoty relating a plurality of selected Reynolds number values to a corresponding plurality of discharge coefficient values for the constriction, the method thither comprising determining a Reynolds number based on the estimated flow rate, and determining the discharge coefficient for the specified flow model by selecting a discharge coefficient value from the memory based on the determined Reynolds number.
20. The method of claim 19 wherein the flow meter comprises a memory storing a ffinction operable to determine the at least one parameter based on the hydrostatic pressure and/or tcmperature of thc fluid in the pipc, thc mcthod furthcr comprising determining thc paramctcr from the at least one fhnction.
21. The method of claim 20 wherein the function comprises a polynomial model selected to provide an approximation to the parameter for a range of temperatures and pressures associated with an estimated temperature and pressure of the fluid in the pipe at the wefl head.
22. The method of claim 21 wherein the p&ynomial model comprises a plurality of coefficients, and the method comprises receiving a coefficient via the communications interface from a remote device, and updating the polynomial model to include the received coefficient.
23. The method of any of claims 19 to 22 in which the at least one parameter is selected from the list comprising: fluid density; gas specific heat capacity; fluid viscosity; gas mo'ecular weight; gas compressibility; and the Joule-Thomson coefficient of the gas.
24. A method of measuring fluid flow rate in an underwater pipe substantially as described herein with reference to the accompanying drawings.
25. A computer proam product comprising program insfructions, operable to proam a processor to perform a method according to any of claims 19 to 24.
26. A flow meter substantially as described herein with reference to the accompanying drawings.