MEASURING FLOW IN A PIPE

Abstract: A gradiomanometer 1 measures the difference in pres­ sure between points 3 and 4 to indicate density and hence proportions of two phases (e.g. liquid and gas), each of known density flowing as indicated by arrow 6. A venturi meter 2 measures the difference in pressure between points 4 and 5 to indicate flow rate, initially assumed to be that of the heavier phase only. An iterative calculation makes it possible to obtain a density measurement corrected to allow for flow friction and individual flow rates of the two components, hav­ ing regard to slippage therebetween. A step discontinuity 8 may be provided downstream to create turbulence and re­ nder the flow homogenous.

Description: The present invention provides a method and apparatus for measuring flow in a pipe such as a bore hole, especially two-phase flow. A venturi meter is one of a number of known devices for measuring the flow rate of one or more liquid or gas phases along a pipe. A differential pressure measurement between two sections of a pipe of different diameters and joined by a smooth change in diameter can be interpreted, using Bernoulli's equation, to provide a measure of momentum change and thus velocity. Venturi meters are useful in pipes such as bore holes because they are more robust and less prone to erosion than other known devices such as the turbine meter. Moreover, they do not intrude into the pipe itself. In order to calculate the flow rate from the differential pressure measurement of the venturi meter it is necessary to know the density of the fluid. The density of a flowing fluid can be inferred from measurement of a differential pressure along a parallel section of pipe; devices for carrying out such measurements are know as Gradiomanometers (trademark), which are differential pressure measuring devices having a tubular section of uniform internal diameter and means for measuring the pressure difference between two longitudinally-spaced locations in the tubular section. GB-A-2,128,756 and US-A-4,231,262 describe flow measuring systems. However, they do not suggest that a venturi meter and a Gradiomanometer can be combined together to measure multi-phase fluid flow. The broad object of the present invention is to provide a particularly simple and robust flow meter incorporating a Gradiomanometer and which does not obstruct the pipe. According to a first aspect of this invention there is provided a flow meter comprising a venturi meter in series in a pipe with a differential-pressure measuring device, known as a Gradiomanometer, having a tubular section of uniform internal diameter and means for measuring the pressure difference between two longitudinally-spaced locations in the tubular section. From these can be obtained a differential pressure measurement along a parallel section of pipe and a differential pressure measurement between two sections of a pipe of different cross-sectional area, with a smooth transition therebetween, i.e. a venturi. The measurement of fluid density by use of the first differential pressure measurement allows a calculation of the flow through the venturi from the second differential pressure measurement. When fluid flows in a pipe there is a contribution to pressure drop along the pipe due to friction between the pipe walls and the fluid contacting the walls. This friction loss is proportional to the square of the flow velocity and inversely proportional to the pipe diameter. In order to obtain a reliable value of density from measurement of differential pressure using a Gradiomanometer it is necessary to take account of, and correct for, the frictional pressure drop. In single phase flows the density is known or can be measured accurately and the venturi meter can give results with good accuracy. However, in multiphase flows, such as liquid/liquid or gas/liquid (e.g. water/oil or gas/oil) it is impossible to determine from the differential pressure measurement whether there is any difference in velocity, or slippage, between the component phases. Slippage is a source of error in the flow rate calculation since the amount of slippage is influenced by the proportion of each phase, known in the oil industry as the holdup, which in turn influences the overall density of the fluid. In the case of gas/liquid flow, the gas holdup is also referred to as the void fraction. Neither the slippage nor the friction loss can be calculated explicitly from information available from differential pressure measurements. However, estimates for correction can be obtained. In a second aspect of the invention there is provided a method of measuring the flow rate of a two-phase fluid comprising a lighter and a heavier phase, using a venturi meter in series in a pipe with a differential pressure measuring device having a tubular section of uniform internal diameter and means for measuring the pressure difference between two longitudinally-spaced locations in the tubular section, said method comprising the steps of: a) measuring a first differential pressure with said device; b) measuring a second differential pressure in the venturi; c) calculating an estimated value of the mean flow density on the basis of the first differential pressure measurement; d) calculating an estimated value of the flow rate of said heavier phase on the basis of the second differential pressure; e) correcting the estimated value of the mean flow density for friction loss between the fluid and said device from the second differential pressure measured in the venturi; and f) correcting the estimated value of the heavier phase flow rate for the velocity differences between the component phases of the two phase fluid from the first differential pressure measured in said device. This method is based on an appreciation that the density measurement is affected by the initially unknown frictional pressure drop while the flow rate measurement is affected by the initially erroneous density measurement. An iterative procedure makes it possible to approach correct values. We have found that the calculations are rapidly convergent and very few reiterations are necessary, say 2 or 3. The above described method may be used for the interpretation of measurements in two phase gas/liquid or liquid/liquid flows if the density of the two separate phases is known. The differential pressure measurements will be misleading if the two-phase fluid is not reasonably homogeneous. The invention further provides a simple and robust flow meter with an integral homogeniser, comprising a pipe formed with, in series, an abrupt change in cross-section for creating turbulence to promote homogenisation, a pipe length within which the turbulence may settle, a Gradiomanometer and a venturi meter. FIGURE 1 shows a first embodiment of the invention comprising a Gradiomanometer and a venturi meter in series; FIGURE 2 shows an alternative embodiment with an integral homogeniser; and FIGURE 3 shows a modified form of the first embodiment. Fig.1 shows a length of pipe with a first section 1 of uniform diameter followed by a section 2 which necks down smoothly to a smaller diameter, forming a venturi. Three pressure transducers, such as are readily commercially available are disposed at points 3, 4 and 5. The lines of the transducers themselves are filled with a liquid of density ρ t . Instead of three transducers, two differential transducers may be employed, this being the preferred arrangement. The point 4 is at the entrance of the venturi, the point 3 well upstream of the point 4, flow being assumed to be in the direction of the arrow 6, and the point 5 is downstream of the venturi. Thus it is possible to determine the differential pressure ΔP m across the Gradiomanometer formed by the section 1 and the differential pressure ΔP v across the venturi. Bubbles 7 symbolise the light phase in two-phase flow. To a first approximation, ΔP m will enable the mean density and hence the ratio of the two phases (each of known density) to be determined and ΔP v will enable the flow rate to be determined on the assumption that the fluid flows as a single phase fluid with the density determined from ΔP m . However, more accurate results are obtained by means of the following iterative procedure: For gas/liquid flow, where the gas density is much less than the liquid density, the system can be expressed mathematically as follows, the notation having the significances described in the Table of Notation shown at page 8. From the venturi pressure drop Δp v : where: Then from the Gradiomanometer pressure drop Δ pm a first estimate of gas holdup y g is obtained: Here f is a friction factor for the pipe (dependent on the Reynolds number of the flow) and ρ m = y g ρ g g + y₁ρ₁. At this point if y g = 0 then there is only liquid flowing and the flow rate is given by the first estimate of v ls . If however there is a positive value of y g then a second estimate of gas velocity is obtained from the slip relationships: Using the second estimate for gas velocity and the first estimate of gas holdup the venturi pressure drop can be reinterpreted to give a second estimate of liquid velocity: At this point the procedure can be checked for convergence. If the current estimates of velocities and holdup are within a certain specified tolerance, then the iteration is finished and we have the final values of v ls , v gs and y g . If convergence has not been reached then the procedure is repeated from equation 4. In the case of liquid/liquid flows the detail of the equations would change, but the basic interpretation scheme would be similar. The foregoing equations assume that the flow meter is vertical. To allow for the possibility of inclination, the quantities h v and h m appearing in the equations must be multiplied by cos ϑ where ϑ is the angle of inclination. In two phase flow through a venturi the measured pressure drop needs to be corrected for the hydrostatic contribution from the mixture density. The higher the degree of homogeneity of the flow (i.e. the lower the void fraction or light phase holdup) the more nearly will the measured pressure drop correspond to the theoretical true pressure drop, with consequent improvement in the accuracy and/or reliability of calculated flow rate. It is particularly preferred if the homogeniser is a non-obstructive homogeniser since this will allow full bore flow in the pipe. In the embodiment shown schematically by way of example in Figure 2 a flow meter comprising a Gradiomanometer 1 and a venturi 2 of the type previously described is provided in a pipe length downstream of the Gradiomanometer with a pipe section 8 which has a step change in diameter from a small diameter d to a larger diameter D. Turbulent stresses caused by the sudden expansion of cross sectional area of the flow cause homogenisation of the flow by turbulent mixing. The flow meters shown in Figures 1 and 2 are suitable for use in a borehole, the small diameter d being matched to the size of the casing in the borehole. The larger diameter D may be only 10% greater than the smaller diameter d and be capable of accommodation within the borehole. In an alternative, shown schematically in Figure 3, the venturi is shown changing from a large diameter to a minimum then back to the large diameter, which corresponds to the diameter of the casing in the borehole. There is no portion of the meter with a diameter exceeding the casing diameter. Although there is some constriction of the pipe cross-section in the embodiment of Fig.3, in all embodiments there is an unimpeded channel right through the flowmeter. If this is installed down a borehole it remains possible to drop tools through the flowmeter to perform logging and other operations at lower levels. In all embodiments the Gradiomanometer is shown immediately upstream of the venturi where the pipe diameter is a maximum because this means that the errors caused by frictional pressure drop are minimised. This does not preclude any other position, although it is desirable to have the Gradiomanometer as close to the venturi throat as is possible. A complete system for obtaining real time values for v ls , v gs and y g can comprise the device shown in fig. 1, 2 or 3 with the transducers 3, 4 and 5 providing data to a computer programmed to implement the equations (1) to (9). In the case of a flowmter down a borehole, conventional telemetry techniques can be used to convey raw data to a computer at the surface or to convey results data to the surface from a computer down the bore hole. N OTATION S ymbols C constant in bubble slip relationship c o constant in bubble slip relationship d diameter h distance between transducer points 3, 4, 5 f friction factor (non-dimensional) F friction correction term (units of pressure) g acceleration due to gravity k constant in bubble slip relationship K constant in venturi equation N Re Reynolds Number P pressure v velocity y holdup (sum of all holdups is equal to 1) Δ difference ρ density σ surface tension S ubscripts 3 point 3 in Gradiomanometer 4 point 4 in Gradiomanometer 5 point 5 in venturi b bubble in standing liquid g gas phase l liquid phase m Gradiomanometer s superficial (averaged over entire pipe area) t fluid in the lines to the pressure transducer v venturi

Claims: 1. A flow meter comprising a venturi meter in a pipe, characterized by further comprising a differential-pressure measuring device having a tubular section of uniform internal diameter and means for measuring the pressure difference between two longitudinally-spaced locations in the tubular section, said device being in series with said venturi meter in the pipe, a value for density of the fluid flowing through the venturi meter being obtainable from a first differential pressure measurement in said device and a flow rate being obtainable from the density value and a second differential pressure measurement in the venturi. 2. A flow meter according to Claim 1, comprising three pressure transducers spaced along the pipe so that the first differential pressure measurement is obtainable from a common one of the transducers between said venturi meter and said device and from a second one of the transducers, while the second differential pressure measurement is obtainable from the common one of the transducers between said venturi and said device and from the third one of the transducers. 3. A flow meter according to Claim 1 or 2, in series with an upstream flow homogenizer. 4. A flow meter according to Claim 3 wherein the homogenizer is a non-obstructive homogenizer consisting of a pipe section which has an abrupt change in cross-section for creating turbulence. 5. A method of measuring the flow rate of a two-phase fluid comprising a lighter and a heavier phase, using a venturi meter in series in a pipe with a differential pressure measuring device having a tubular section of uniform internal diameter and means for measuring the pressure difference between two longitudinally-spaced locations in the tubular section, said method comprising the steps of: a) measuring a first differential pressure with said device; b) measuring a second differential pressure in the venturi; c) calculating an estimated value of the mean flow density on the basis of the first differential pressure measurement; d) calculating an estimated value of the flow rate of said heavier phase on the basis of the second differential pressure; e) correcting the estimated value of the mean flow density for friction loss between the fluid and said device from the second differential pressure measured in the venturi; and f) correcting the estimated value of the heavier phase flow rate for the velocity differences between the component phases of the two phase fluid from the first differential pressure measured in said device. 6. A method according to Claim 5, wherein the correcting steps comprise: a) calculating the proportion of the lighter phase in said two-phase fluid from the estimated value of the mean flow density; b) calculating the flow rate of said lighter phase from a predetermined velocity difference relationship of the component phases of the two phase fluid and in accordance with the calculated proportion of step a; c) calculating the frictional component of the pressure drop in said device using the flow rate calculated in step b; d) calculating a corrected value of the mean flow density and said proportion of said lighter phase from the first differential pressure and from the frictional component of the pressure drop in said device; and e) re-iterating the above steps until convergence is reached

Inventors: BRADBURY, LESLIE, HUNT, ANDREW
Applicants: SCHLUMBERGER LIMITED, SOCIETE DE PROSPECTION ELECTRIQUE  SCHLUMBERGER
Application year: 1987
Main classification: G01F1
IPC codes: G01F1, G01N9, E21B47