Cone Meters for Liquid and Gas MeasurementClass 8210.1 – May 2010

PHILIP A LAWRENCEDIRECTOR OF BUSINESS DEVELOPMENTCAMERON’S MEASUREMENT SYSTEMS

HOUSTON TEXASUSA.

Abstract

This technical paper will describe how generic differential pressure cone meters whilst similar in principle differoperationally from other differential pressure meters and how they are used for the measurement of liquid andgas.

The cone meter has become synonymous with specialist metering applications over many years due to specialtraits that are inherent in this type of meter design.

The original cone meter concept was taken from the “Venturi” original design in 1791 by Hershel and othervariants like Burton Dunlingson’s Inverse Venturi (which was Patented in the UK ,in 1935).

Generic Differential Pressure (DP) Cone Meters have been used to meter many fluids such as Steam, Wet Gas ,Liquids that have trash, asphaltenes and wax in pipes together with applications that have pipeline installationissues such as short meter runs lengths (usually off-shore).

They have also been used for custody transfer with user-party agreements and have been quite successfulthrough the years in other industrial applications such as water measurement, some of the key ideas that enabledthese concepts will be shown in this paper. Trade Marks, or Meter Trade Names will not be mentioned in thispaper.

History

The original inventor of the meter, Mr. Floyd McCall of Hemet California conceived the design in the form of aflow conditioning device / static mixer or fluid dispersing devices and also in the form of a differential pressureflow meter in the early 90’s with a patent being issued in 1986 European Patent No. 0 277 121 which expired inAugust 2006,and a US based patent issued in 1985 which USA patent numbers 4638,672.. 4812,049 which arenow expired.

This original design of cone meter was patented with up and down-stream cone angles that were steeper thansubsequent manufactured models. Cones for the meter are usually made from solid bar stock or fabricated sheetsformed to the required cone shape.

There have been many successful research and development papers on the cone meter and much new test workdone by various companies which are making the cone meter more accepted into the market place, there is alsoan API standard in which the device is mentioned.

The Metering Device

All Cone Meters (non wall tap design) consist of a conically shaped differential pressure producer fixedconcentrically in the center of a pressure retaining pipe, by which a differential pressure can be obtained acrossthe interface of two cone frustums via an internal port-way system.

This allows the downstream pressure P2 to be measured in the center of the closed conduit.

The fluid is linearized through the meter throat within a region defined by the differential producer and the interiorsurface of the closed conduit, whilst flattening the velocity profile in the throat region of the device.The upstream pressure P1, being measured at the pipe wall. (See Fig 1.0 CFD Image)

2

2

1D

d

Fig 1.0

The concept of using the center of the cone above to read the differential pressure downstream has showncertain benefits compared to conventional differential pressure meters such as the following :-

a) Flow Conditioning.b) Larger Turndownc) Static Mixingd) Wet Gas Applicationse) Steam.

Geometrical Considerations (P meters)

Manufacturing tolerances are important when making a differential meter that uses an iterative process todetermine its coefficient of discharge by calculation or lookup table. The method assumes a constant geometrysubject to a predetermined manufacturing tolerance i.e. orifice plates with machined holes.

In the case of a cone meter each device is usually calibrated against a traceable standard to determine theCoefficient of Discharge C.d. This makes sure that the correct C.d. is implemented per each meter manufactured.Some research work is being done to obtain repeatable C.d.’s per the same pipe diameter between subsequentmeters to reduce the need to calibrate each device and therefore allow the C.d. to be iterated or determined froma look up table, this method would depend on meter manufacturing tolerances being very close between eachmeter produced.

Manufacturing Concerns and Requirements

When producing a differential cone type meter there are various important issues to take care of:

A) Concentricity of the cone

B) Alignment and cone support robustness and stability

C) Assembly of the Differential Producer and tap location (Tap design)

D) Cone Angle ( both upstream and downstream)

The usual method for Beta Ratio determination of “annulus type meters” is known as being the ratio of the rootof the square of the displacement member annulus area versus the root of the square of the pipe area and thisreduces to the following universal equation shown in (e.q.1) .

………………..………………………………………………………..……….. (1)

50% X-Section. separation region

Computational Fluid Dynamics Image

Meter Throat

FLOW

P2

Meter Tube Wall

The Y factor equation (expansibility coefficient for gasses) usually is per the Reader-Harris-Peters,(NEL-U.K.)generated equation thus (e.q.2) ;-

Y = 1- (0.649+0.696 ^4) …………………………………………………………….. (2)

Cone GeometryThe drawing in fig 2 below shows typical generic differential pressure cone geometry as used in somecommercially made meter designs.

Cone meter area ratio’s (’s) are varied to accommodate the measurement of different flow rates by changing the cone length and thus the cone diameter (fig 2.0).

This changes the effective diameter of the cone in relation to the pipe diameter and thus the beta or effective arearatio and ultimately the velocity across the Beta Edge Boundary.

Commercially made cone meters operate generally in ratios from 0.45 - 0.85. It must be noted that as the beta

ratio becomes larger (approaching 0.8 - a smaller cone diameter) the meter performance changes and themeasurement uncertainty can become larger where disturbed flow profiles are evident.

This “performance” effect is caused by the reduced interaction between the cone area and the fluid, i.e. a smallercone does less work on the fluid so the flow linearization aspect of the meter is reduced.

Care must be taken when using smaller cones where valves or other flow disturbance generators are in line andupstream of differential pressure cone device. The cone meter manufacturer should be able to advise of theminimum straight lengths per beta ratio and diameter versus Reynolds Number per Diameter (ReD) regardingthis effect.

The mass flow rate equation for Generic D.P. Cone Meters is exactly the same as per any standard DP device(Orifice, Venturi meters) with the exception of the C.d. implementation which is usually derived from empiricaltesting by the manufacturer or other independent labs and not generally by mathematical iteration.The beta ratio determination as shown in equation(1) is slightly different than for the other standard DP devicesdue to the external annulus being used to determine beta ratio.

The fundamental (universal) DP equation for a cone meter is as follows and shown in Appendix #1.

Beta Edge Boundary

Taps: Static Low PressureP

Fig 2

Applications and uses for the Generic D.P. Cone Meters

1) Usage in a Bi-directional Flow Regime.

The use of differential pressure type meters to measure accurately a bi-directional gas flow in a pipelinecan have major measurement uncertainty issues due to the geometric difference in the differential producerelement shape when used in the reverse direction

Meter discharge coefficient’s may be different in these particular cases for geometric devices such as concentric,square edged and flange tapped orifice flow meters and venturi meters.

Current national and international measurement standards state that bi-directional flow measurement is notpermitted using orifice plate type flow meters for a “good measurement uncertainty” and that meter runs dedicatedfor each direction must be used in this application. Data from testing of cone meters on liquids and gas areincluded in this paper next regarding bi-directional usage thus;

The Concept & Preliminary Testing

Two 80 mm (3inch)diameter 0.75 Beta ratio cone meters were tested in 4 ways as per figs 3.0 through7.0, to see if there was any influence or interference between the meters due to the close proximity of the rearcone frustums , since the rear of each cone would be directly in each of the meters pressure recovery regionin either direction.

This recovery length is estimated at about 5-6 cone D’s according to wake theory (fig 3.0).The 0.75 beta range meters were chosen because these were nearer to a field application meters at 0.65 betathan other meters that were available at that time for which this test was used.

Methodology (Water Test) Single Meter

3 repeat runs of 4 Flow rates from around 38 m3/hr to 122 M3/hr of water were passed through the meters. Firstmeter (A) in direction A1 and each coefficient of discharge per rate calculated at a 95% confidence level.The R-G equation was used to verify the laboratory using an orifice plate (information regarding this method islisted in API 14.3 and ISO 5167)

Sufficient pre-straight length was used to obtain fully developed flow conditions, although it is known that genericcone meters exhibit a flow conditioning effect due to a velocity profile re-distribution or linearization in the meterthroat region.

The meter (A) was replaced by meter (B) and the same test method was used for meter B with similar flow rates,an average was taken for each block of 3 flows and an average C.d. determined from each block also.

The density of the water was 999.27 kg/m3 at a temperature of 24.06 degrees Celsius from a probe (T)upstream of the flow meter , this produced an average discharge coefficient of 0.7984 for meter “A” and 0.7915for meter “B”. Plots of CD versus flow rates are shown in figs 4.0 – 7.0.

Section X--X separation region

Fig-3Approximately 5-6 Cone Diameters

Near-Wake (Gas)

Computational Fluid Dynamics Image

Bi-Directional Methodology (Multiple Meters)

Both the Meters A and B were bolted together and Bi-Directional testing was done firstly in the direction ofmeter (A)using flow stream A2 and subsequently meter (B) by reversing the meter spool from right to left as perthe layout drawings below.

As before 4 blocks of 3 repeat flow rates from circa 38 m3/hr to 122 M3/hr were passed through the meter (A)in direction A1 and the coefficient of discharge calculated at a 95% confidence level.

A Straight length of 50 D’s was used upstream of the cone meter this was to make sure that a fully developedprofile was seen at the meters during this test. A good repeatability for the meter was obtained and the Cd’sexhibited a repeatability of 0.1% excluding the uncertainty of the rig.

2) Compressor Anti Surge Control by a D.P. Cone Meter

The use of Turbine Compressors in the oil and gas and process industry is becoming a standard because of thelighter weight and more efficient power ratios than previous reciprocating piston designs.

One of the most important issues that can face an operator using a rotating compressor is the design andimplementation of a satisfactory anti-surge system.

The correct and proper operation of such an “anti-surge” system is paramount in saving the user highmaintenance and intervention costs whilst offering efficient through-put management.

What Is This Thing Called Surge?

“Surge” It’s produced when fluid flow into a compressor system is reduced to a set point where spasmodic andmomentary flow reversal occurs.

The result of this surge condition is immediately seen at the location by severe vibration and pulsation that can befelt in the pipe work and compressor casing.

If this condition is left unresolved severe damage can occur very quickly to the rotor parts, bearings, anddriveshaft train.

The usual method employed to resolve this condition is to detect that the surge is occurring quickly by someapproved procedure and to increase the flow through the said compressor by opening a quick responding blowoff valve.

Where environmental conditions exist of the hazardous nature or were the fluid being compressed has inherentfinancial value.

It may be necessary to use a recirculation valve system (see below control schematic fig 8.0).

Response Time

A major issue in compressor anti-surge control operations is the “control valve response time”

When a surge happens the primary metering device has to detect the DP change seen at the transmitter.

The DCS has to calculate the nominal flow rate which also has to be repeatable and then output a position controlsignal to the control valve to produce the right amount of blow off or recirculation.

This requires a quick response time and calculation time to enable the valve to be moved and stabilized in usually0.5 seconds or less.

The normal use of dampening (averaging) the transmitter can build in to the control system a delay, thisdampening depends upon the type of primary device used and its downstream response or noise.

DCS

Gas flowCompressor

Recirculation or Blow Off

Fig 8.0

Valve

Meter

In the case of a standard orifice the downstream vortex street can affect the valve control loop because ofenhanced delay or noise caused by the plate, a parameter we need to keep to a minimum.

Frequently having the compressor in a surge condition can cause the device to produce variation of outputpressure, compressor wear and poor efficiency and higher maintenance costs.

System Design

There are various types of systems in use today, some using “incipient” temperature control of flow instability andpressure measurements across the compressor.

By far the best method is to use a real flow meter in series with the compressor rather than just pressure acrossan elbow or other pipe fixture.

Generally differential pressure type meters are used the cost of reliability and no moving parts cone meters are afavored choice due to the following traits:

A) A Generic Cone Meter is Low Noise !- (downstream wake generated produces a smoother response)B) Available Space - usually there is no room for a long meter run on a compressor skid.

The ability to generate this low noise signal is key in being able to operate at low Dp’s and low pressures (CBMmeasurement) and with quick response times (compressor control).Generally in some applications like coal bed methane, CBM wells only generate 5 PSI at the well head on a well@ 400 feet deep. This means that there may be < 15-20 “ W.C usable across the meter taps.

The fact that a cone meter generates a very small signal wake noise superimposed on the D.P. allows themetering of gas flows with less dampening (averaging) of the transmitter and is ideal were compressor controlapplications are needed because the D.P signal is cleaner and can update quicker. Figs-9 &10

Fig 9 - Generic Cone Showing Wake Distribution (rear view) Fig 10-Orifice Plate Vortex Disturbance (plate rear)

From research by Ifft during the 90’s it was found that an “OFU” (fig12.0) can generate a superimposed signal onthe D.P of up to and as much as 1 inch W.C. whilst cone meter noise levels generated be up to 10 times less(Awhite paper mentioning this OFU phenomenon was also published by George and La Nasa in 2002 ) This noisemay be as much as the useable D.P. on some CBM wells that are shallow and are nearing completion see figs11.0 &12.0

BBaacckk ooff ccoonnee

WWaakkee

WWaakkee

WWaakkee

CantileverSupport through Body

WWaakkee

FFllooww

WWaakkee

WWaakkee

Fig 11 Cone Meter Noise Downstream Fig 12 Orifice Meter Noise Downstream

Vortices superimposed on the P. Large Amplitude Vortices superimposed on the P.

Surge Control ChartUsually a system is custom designed to a certain type of machine and compression system these systems tend tobe safe and reliable over the range of test conditions used at the inception of the design.

This results in the user operating from a generated compressor “surge” line.(See fig 13.0).

Typical Surge Control Chart

The surge line is the minimum flow necessary for each given pressure to avoid surged condition points on thesurgical line are typically determined experimentally - fig 13

If the compressor is operating in a safe condition (position A), and then suddenly the flow decreases thecompressor can move into surge condition (position B).

It is necessary for the blow off valve or recirculation valve to be opened to increase all the flow (position C).

Two little blow-off can result in a surge condition whilst to much blow-off results in wasting fuel, and compressorenergy into the atmosphere.(Position D)

When the gas it is re-circulated during the compression cycle heat most be removed by a cooling method orcompressor overheat may occur which is a large issue.

3) Cone Meter Traits (space saving)

It has been long known that these devices can be installed in shorter runs this is due to the cone acting as its ownflow conditioner. Various research bodies have confirmed this useful quality

Using a cone device for gas metering on say an offshore platform can save money in real estate terms is veryinteresting to end users whom wish to keep CAPEX down in the jacket design stage. Linearities up to +/- 0.5%and repeatability at 0.1 is claimed by various manufacturers at Reynolds numbers larger than 10,000ReD

1/10”WC

DP

Flow

Margin of Safety

Surge region

B C D ASafeRegion

Fig13

1”WC

2 inch diameter 0.45 Test on Air at CEESI Colorado

A 2 inch meter was tested at the CEESI facility as part of the API 22.2 testing for the results are shown below inFig 10 which demonstrates the good linearity available for this meter type based on both baseline and fulldisturbance tests including a ½ moon orifice at 3 D’s.

Results are shown from 40,000 – 400,000ReD at about a 10-1 turndown – note only 0.5 % data spread in Fig14

Fig 14

Flow Conditioning Effect (Cone Meters)

It is known that the use of a cone shape concentrically mounted in a closed conduit (pipe) can facilitate a flowconditioning effect by “velocity profile re-distribution”. This effect seems to occur over quite a wide ReD range andappears to be more pronounced farther away from the transition region were changing flow patterns occur.(ReD: 8000-10,000)

4) Short Length Installations

Similar Field Installations as shown here – “90 deg bends” (fig 15.0) are usable with a good level of confidence ;

Fig 15

Flow

Weight Penalty in Platform Design

Cost savings for a “jacket design” or FPSO can be large if the real estate can be reduced considering it costsbetween 30 to 90$ per each lb weight for an item to be placed on a platform or FPSO.

Short meter runs are most necessary in today’s offshore marketplace to keep Capex down

Allocation Systems

The use of this technology with onshore systems also can enhance the overall cost savings with regard to theseinstallation types.

Areas were this has been seen in the recent past is in the CBM (coal bed methane) fields of Wyoming USA, andland based allocation in the same region together with other world areas such as Canada, India ,Russia andAustralia.

5) Typical Allocation System Using Cone Meters (full well-stream type)

The system is designed to enable a meter factor to be developed by well testing on the full well stream meter thismeter will operate as the back allocation point in the system once calibrated.

Devices that are less susceptible to wet gas and trash is necessary for a good allocation to be produced. Variousoperators have moved to this philosophy because of the inherent advantages the cone meter has shownthroughout the years.

A typical schematic is shown below the OFU separator meters in the diagram can also be changed to genericcone meters if separator carry over is present. Fig 16

Fig 16

Lease-level Pointsof Measurement.

M

M

M

MWell TestSeparator

BulkSeparation

M

M

M

M

LiquidsGathering &Stabilization

System

M

M

To GasGathering System.

Condensate to SalesExport.

Water to Disposal and/ or

Water Recycling.

Field-wide Allocation Meters.

Flash Gas.

Cone Meter.

Orifice Plate.

Turbine Meter.

Turbine Meter.

Orifice Plate.Orifice Plate.Custody Meter.

Turbine Meter.

Individual Well Measurements.

Turbine Meter.

Turbine Meter.

Full Wellstream.

Gas.

Condensate.

Water.

Gas.

Condensate.

Water.

6) Test Separator Usage for D.P. Cone Meters

Current design of multiphase separators can allow overall uncertainty (on all three phases) of may be up to 15% -20% according to past API discussions.

This can be due to operator control, time delay in stabilization of the vessel, incorrect design involving future fluidlevels, position of vessel in respect to the pressure head requirement (on the liquid side) and also the main crudeoil measurement uncertainty.

In particular where orifice meters are used it is necessary to perform, plate changes to facilitate larger turndownsotherwise the performance of the system could be compromised, and also its necessary to use upstream flowconditioners or velocity profile devices which add cost to a system.

Long-term vulnerability using orifice plates in production separators can be demonstrated by examining publicdocuments in the measurement field. (Example Cited above from “Phillips Petroleum Embla Platform North SeaNSFMW Paper Early 90’s Dalstrom.)

Research in this field by Chevron (Ting) and others also indicates a Cd movement circa 2% - 3% outside of thepredicted AGA requirements due to wet gas with small liquid loads of 0.33bbl/MMscf as indicated in this wet gasresearch.

Installations and Wet Gas

Generally it is known that cone meter installations may be short (fig 9.0) and issues are that the meter run can bein a constant state of wetness due to the well or separator carry over., which can cause problems with OFU’s dueto water build up in front of the plate, it has been noted that liquid slugging may occur on the rear side of the plateby the LP ports which can cause errors.

Previous research has verified that a cone meter does not have this negative attribute, and can sit there working inliquid mass fractions of > 5% with a minimum affect on the C.d. smaller cone diameters are less prone to liquidcontact and error. (Fig 17)

Fig 17 – OFU - ( ISHM WET GAS 2007)

Fig 18 - Cone Meter Wet Gas ( ISHM WET GAS 2007)

The lack of hold up effect by a cone meter is a key factor in helping keep accurate measurement in wet gasapplications (5% liquid mass fraction test at various betas in Fig 18 ,( Sveedman and Ifft SWRI Test 96-97)The well is also less likely to choke particularly in early the early stages of production if on a low pressure type.(ISHM Class paper 1320.1:Wet Gas Measurement 2009 has more in depth content regarding these parameters.)

7) Heavy Oil Metering and Low Reynolds Number Effects

Generic cone meters with beta ratios of both 0.65 and 0.75 were recently tested at the Caldon facility in Pittsburgon both 15 and 170 cst oils both installed in straight runs to allow Reynolds number flow ranges to be generateddown to 580 ReD for the 0.75 beta meter and 450ReD for the 0.65 beta meter.

Usually the minimum ReD range lower limit shown for this type of meter on commercial data sheets is 10,000ReDafter which most manufacturers recommend that the meter should be calibrated over an in-field operational ReDon similar product types.

The opportunity to test down to below 500 ReD was very useful in determining this genre of meters response toviscous fluids and its response to boundary layer effects.

Cone Meter Installation and Data Recording

The cone meters where installed fitted with a Scanner 2000 type flow computer which is designed to read staticpressure , differential pressure, and temperature and also perform integral liquid hydrocarbon flow calculationsbased on API algorithms, schematic as seen in Fig.19.

Fig.19 - Generic D.P. Cone & Fiscal Flow Computer Assembly

Test Procedure

Hydrocarbon fluid was passed through the prover loop for a set pre-run time and some provisional data collected ,after some quick calculations and flow comparisons it was deemed that the method being used was acceptablefor the test. Calculated data from the scanner was converted to a 4-20 mA flow rate signal then this data wastransmitted to the laboratory data acquisition system via the analogue to digital converter.

The Scanner 2000 was pre programmed with the fluid density and meter dimensions (to calculate the beta ratio)with the discharge coefficient set to 1.0000 so that the C.d could easily be determined without extra calculation bycomparison with the rig meter factor.

The analogue output was configured from 0 to 300 m3/hr and the analogue output was feed into the ACROMAG

895M-0800 analogue to pulse converter. The converter was configured such that 20 mA equaled 1000 Hz. As isthe DAS requirement. The SVP electronics were configured for a time constant of 1.5 seconds (1 second forscanner 2000 and 0.5 seconds for the analogue to frequency converter.

It is known that most DP meters exhibit non linear results when tested on low Reynolds number( ReD)ranges (i.e.have poor linearity) but can be repeatable according to some manufacturers claims.

These particular test’s where performed with 5 minute (SVP) proves per flow rate the average of the flow ratescollected and used to calculate the average coefficient of discharge (C.d.) per flow point this was then plottedagainst averaged Reynolds Numbers over the same time period per run and shows some interesting results inthe following graphs .

The fall off of the linearity for D.P. devices is well known and it was expected that there would be a similarresponse for D.P. Generic Cone meter types also.

Meter Test Configuration

The 0.65 and 0.75 beta ratio meters were tested first on the 15cSt, range liquid hydrocarbon giving ReD rangesfrom; 32950 to 3200ReD for the 0.65beta unit and then 47200 to 4700ReD for the 0.75 beta unit.

Meters where then tested with the 170cSt, hydrocarbon fluid giving ReD ranges from; 4,250 to 450 ReD for the0.65 beta unit and 5,973 to 583ReD,for the 0.75beta unit.

All data was recorded and calculations for C.d. for the meters produced in the Laboratory DAS (Digital Analoguesystem) Data was plotted to XL spreadsheets and is shown graphically in Figures 20-23

D.P Cone Meters High Viscous Oil Results

Fig20

Fig 21

Fig 21

Fig 22

Fig 23

Conclusions

Cone meters more readily accepted in the market place due to operational stability, robustness in the design andavailability. New allocation standards being written API chapter 20.2 and 20.3 will discuss their usage it isanticipated over the near future. Already companies are testing this technology to API 22.2 which is a good wayforward to acceptance worldwide for this genre of D.P. device.

The idea and concept pioneered by Mr. McCall in the 80’s was sound then as it is today and a good engineeringconcept.

A similar type of device that may have been used in the development of the Cone Meter using the InverseVenturi pioneered in the UK by Mr, Burton Dunglinson in 1935 for liquids application patent dated January 11

tth

1935 No 1028/35

It is hoped that these types of meter will be applied more in natural gas custody transfer applications when anISO or API standard for the device is produced or pushed by industry.

References

(1) Hayward A. “A Source Guide for Users” Edition Published 1978(2) Bagge, D.J., “Evaluation of Ketema, V-Cone Flowmeters” Test Report E 1705 S 92, SIREP, 1992.(3) Ifft, S. A and Mikkelsen, E.D - “Pipe Elbow Effects on the V-Cone Flowmeter” North Sea Flow

Measurement Workshop, Peebles, Scotland, 1992(4) B. K Lee, N.H. Cho and Y. D Choi, 1988 “ Analysis of periodically fully developed turbulent and heat

transfer by k- ε equation model in artificial roughened annulus”. Int J. Heat Mass Transfer, Vol,31, pp1797-1806

(5) B. H. Chang and A. F Mills, 1993, “Turbulent flow in a channel with transverse rib heat transferaugmentation”, Int J. Heat Mass Transfer. Vol 36, No, 6, pp 1459-1469

(6) B. E Launder and D. B Spalding, 1974, “The numerical computation of turbulent flows”, Comput MethAppl Mech Engng, Vol 3,pp 269-289

(7) C. K. G Lam and K. A Bremhorst, 1981, “Modified form of the k-w model for predicting wall turbulence”,Journal of Fluid Engineering, Vol 103, pp 456-460

(9) D.C Wilcox, 1993, Turbulence Modeling for CFD, DCW Industries, Inc(10) J.Y.Yoon, 1993, Numerical Analysis of flows in channels with sand dunes and ice covers, Ph.D Thesis,

Department of Mechanical Engineering, The University of Iowa.(11) D.C. Wilcox, 1988, “Reassessment of the Scale Determining Equation for Advanced Turbulence Models”

AIAA Journal, Vol 26, No 11, pp 1299-13(12) M. C. Richmond and V. C Patel, 1991, “ Convex and Concave Surface Curvature Effects in Wall-

Bounded Turbulent Flows”, AIAA Journal, Vol 29, pp 895-902(13) J.Tyndall, 1988, A Numerical Study of Flow over Wavy Walls, M. S. Thesis, Department of Mechanical

Eng. Univ. Iowa, Iowa City.(14) H. C Chen and V. C. Patel, 1988, “ Near-Wall Turbulence Models for Complex Flows Including

Separation” AIAA Journal, Vol 26, pp 641-648(15) Braid C Mr. (Barton Canada) first principle calculations for flow computers May 1999.(16) M. C. Richmond, 1987, Surface Curvature and pressure gradient effects on turbulence flow ; An

assessment based on numerical solution of Reynolds equation, Ph.D Thesis, Department of Civil andEnvironmental Engineering, Univ. of Iowa, Iowa City.

(17) D. D. Knight, 1982, “ Application of Curvilinear Coordinate Generation Technique to the computation ofInternal Flows”, Numerical Grid generation, Elsevier Science Publishing Company, pp 357-384

(18) Sveedmen SWRI Homogenous Model and OFU liquid effect( report)(19) Ifft Wet Gas Testing at SWRI 1997 - V-Cone Meter(20) D George & P La Nasa Avoiding Orifice Meter Differential Pressure Measurement Errors at Low D.P’s

SWRI) Pipeline Journal Jan ` 2002(21) Lawrence Wellhead Metering by V- Cone Technology NSFMW 2000 Gleneagles, Scotland,UK(22) Braid C Cameron Inc (Canada) Cone Equations for Flow Computers a Technical Document 2006(23) Lawrence CBM Measurement by D. P. Cone Meter CII Conference India February 2007(24) Lawrence ISHM Oklahoma Class 1320 Wet Gas May 2007(25) Davis .M.W. Shell Exploration and Production Allocation Methodology 2009(26) Lawrence South Asia Workshop-NEL-Forward and Reverse Flows in Closed Conduits Paper 7.1 March

2009 – Malaysia.(27) HOWS Conference Brazil 2009 – J. Hollister - The Effect of Temperature Gradients on the Differential

Pressure Measurement of Heavy Oils,(28)Flow Laboratory Data Set – Cameron - Caldon – Ultrasonics, Bobby Griffith - January 2010 – Pittsburgh

USA.(29) NEL South Asia Flow Measurement Workshop Malaysia March 2010 –Lawrence ; Challenges Using

Differential Pressure Cone Meters In Heavy Oil Measurement.

Appendix # 1.0