low pressure metering of natural gas

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Low Pressure Metering of Natural Gas Class# 1195.1 Philip A. Lawrence. Lead Engineer (Measurement). ENABLE™ Midstream Partners Oklahoma City, OK, USA. Abstract Many regions of the USA have many natural gas wells that are declining in both flow and pressure due to extensive exploitation and production over many years, horizontal drilling has brought new life to these regions however some production sites in a region may not be capable to be rejuvenated which leaves them in a state of low output. These traditional wells which are showing symptoms of reduced pressure and flow-rates, may need to change the scope and design criteria of the metering station or central receipt point (CRP) usually being designed around the API 14.3 - AGA 3 measurement standard for pipeline quality gas. The quality of gas now being seen at these upstream area stations generally is not meeting the requirements as dictated in these design standards. The situation gets worse and sometimes the issue can be passed downstream to the transporter were the BTU values of these wells are intermingled with newer or re-energized horizontally bored developments. Traditional energy supplies have also been enhanced in recent years by the addition of coal bed methane which has easy access in shallow and deep coal seams worldwide. Such places as Russia, India and Australia are all reviewing this efficient energy source as well as the USA In fact, major sources of this clean product “Natural Gas” has been discovered in all parts of the world. Some of the challenges that producers experience relate to providing cost effective accurate measurement at the wellhead whilst maintaining a low differential pressure across the gas transportation system whilst also dealing with wet gas issues in the meter run, which can be subsequently passed on to the gas transporter or midstream operator. This paper describes various pieces of experiential data from the writer’s involvement in this field over 30 years regarding allocation measurement of Natural Gas, particularly regarding the use of new types of differential pressure type meters as the primary differential pressure producer. Since the first natural gas wells drilled in the early 1900’s, the expansion of the world gas supply has been dramatic with US holdings controlling approximately 55% of the worlds O&G production and exploration. New hydrocarbon product finds are being forced to more costly world regions with smaller yield rates and return on investment. Changes in drilling methods and new ideas are being conceived to help produce the energy requirement we need, the move to compressed natural gas (CNG) as a clean energy source for automobiles is a natural and cost effective solution. Major Hydrocarbon supply companies are involved in both producing mineral wealth and energy wealth, the two being interlinked by a common factor Natural Gas whose main constituent is CH4 methane.

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This engineering paper was written and presented at the ISHM in OKLAHOMA CITY IN May 2014 Low Pressure Metering of Natural Gas Class# 1195.1by Philip A Lawrence

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Page 1: Low Pressure Metering of Natural Gas

Low Pressure Metering of Natural Gas

Class# 1195.1

Philip A. Lawrence. Lead Engineer (Measurement). ENABLE™ Midstream Partners

Oklahoma City, OK, USA.

Abstract

Many regions of the USA have many natural gas wells that are declining in both flow and pressure due to extensive exploitation and production over many years, horizontal drilling has brought new life to these regions however some production sites in a region may not be capable to be rejuvenated which leaves them in a state of low output. These traditional wells which are showing symptoms of reduced pressure and flow-rates, may need to change the scope and design criteria of the metering station or central receipt point (CRP) usually being designed around the API 14.3 - AGA 3 measurement standard for pipeline quality gas. The quality of gas now being seen at these upstream area stations generally is not meeting the requirements as dictated in these design standards. The situation gets worse and sometimes the issue can be passed downstream to the transporter were the BTU values of these wells are intermingled with newer or re-energized horizontally bored developments. Traditional energy supplies have also been enhanced in recent years by the addition of coal bed methane which has easy access in shallow and deep coal seams worldwide. Such places as Russia, India and Australia are all reviewing this efficient energy source as well as the USA In fact, major sources of this clean product “Natural Gas” has been discovered in all parts of the world. Some of the challenges that producers experience relate to providing cost effective accurate measurement at the wellhead whilst maintaining a low differential pressure across the gas transportation system whilst also dealing with wet gas issues in the meter run, which can be subsequently passed on to the gas transporter or midstream operator. This paper describes various pieces of experiential data from the writer’s involvement in this field over 30 years regarding allocation measurement of Natural Gas, particularly regarding the use of new types of differential pressure type meters as the primary differential pressure producer. Since the first natural gas wells drilled in the early 1900’s, the expansion of the world gas supply has been dramatic with US holdings controlling approximately 55% of the worlds O&G production and exploration. New hydrocarbon product finds are being forced to more costly world regions with smaller yield rates and return on investment. Changes in drilling methods and new ideas are being conceived to help produce the energy requirement we need, the move to compressed natural gas (CNG) as a clean energy source for automobiles is a natural and cost effective solution. Major Hydrocarbon supply companies are involved in both producing mineral wealth and energy wealth, the two being interlinked by a common factor Natural Gas whose main constituent is CH4 methane.

Page 2: Low Pressure Metering of Natural Gas

Coal Bed Methane

The primary energy source of natural gas is a substance called methane (CH4). Coal bed methane (CBM) or coal seam gas as described in other world areas is simply methane found in coal seams. It is produced by non-traditional means, and therefore, while it is sold and used the same as traditional natural gas, its production is different and has issues of low pressure output at the well head. CBM is generated either from a biological process as a result of microbial action or from a thermal process as a result of increasing heat with depth of the coal. Often a coal seam is saturated with water, with methane is held in the coal by water pressure. Currently, natural gas from coal and coal beds account for approximately 8-10% of total natural gas production in the USA Where is CBM located? Information from the CBM Association of Alabama states that 13% of the land in the lower 48 United States has coal under it, and some of this coal contains methane - either in the form we know as traditional natural gas or as CBM. According to the United States Geological Survey, the Rocky Mountain Region has extensive coal deposits bearing an estimated 30-58 trillion cubic feet (TCF) of recoverable CBM. While impressive, this represents only one third of the total 184 TCF of natural gas in the Rocky Mountain Region (Decker, 2001). Within the Rocky Mountain Region, untapped sources of CBM exist in the Powder River Basin of Wyoming and Montana, the Greater Green River Basin of Wyoming, Colorado, and Utah. The “Utah-Piceance” Basin of Colorado and Utah, and the Raton and San Juan Basins of Colorado and New Mexico being other regions of interest. An estimated 24 TCF (Trillion Cu ft) of recoverable CBM resources may lie below the Powder River basin of Montana and Wyoming (Decker, 2001). It is estimated that in the rocky mountain region alone 30,000 coal bed wells will be drilled over the next 8-10 years. The Environmental Impact Statement for coal bed methane development in the Powder River Basin of Montana reports 2.5 TCF of recoverable gas. The major term in the equation is “recoverable” investments in drilling and well completion do not necessarily mean big returns as sometimes the wells do not perform as expected. However if correct well spacing is maintained and some thought is put into piping layouts wells that come up short in production seem to have a better chance at making some reasonable returns.

Page 3: Low Pressure Metering of Natural Gas

Map Showing Major Coal Bed Methane Reserve Locations in the USA.

(Shown in red block ins fig 1.0)

Figure 1.0. How much do we have?

Bureau of Mines and Geology estimated the amount of recoverable CBM in the Powder River Basin using the following information:

If a coal seam has favorable reserves if it produces 50-70 ft3 per ton of coal.

If CBM extraction is economical at 50 ft3 per ton of coal when a coal seam is 20 feet thick or more.

If Coal bed methane exists only in areas where the dominant chemistry of the water in the coal seam is sodium bicarbonate and where the coal seam is buried deeply enough to maintain sufficient water pressure to hold the gas in place. This type of well can have measurement issues.

The Environmental Impact Statement for CBM development in the Powder River Basin estimated the amount of coal in the region based on the total reported tonnage of coal in the region multiplied by 50 ft3 of methane per ton of coal, regardless of seam thickness, depth or proximity to outcrop. How is the Methane Extracted. Since CBM travels with ground water in coal seams, extraction of CBM involves pumping available water from the seam in order to reduce the water pressure that holds gas in the seam. CBM has very low solubility in water and readily separates as pressure decreases, allowing it to be piped out of the well separately from the water. Water moving from the coal seam to the well bore encourages gas migration toward the well. Producers try not to dewater the coal seam, in a non controlled way but rather seek to decrease the

Page 4: Low Pressure Metering of Natural Gas

water pressure (or head of water) in the coal seam to just above the top of the seam. However, sometimes the water level drops into the coal seam the method is a compromise of obtaining maximum production versus de-watering the well to a stage where production falls off! Other areas have high quantities of impurities which can cause the environmental issues. Typical Well Methodology

A simple well is drilled using a truck mounted drill assembly (potable water drill equipment has been utilized in the past).Figure 2.0. This allows a quick turn-around/completion and easy movement of the equipment at low cost. This being circa: $45,000.00 per drilling with completion cost for a fully functional gas producing well at about $95,000.00 -$110,000 The depth of the wells may vary from 400 - 1000 feet depending on the geology.

Figure 2.0 Typical Coal Bed Methane Well Philosophy (Wyoming Region)

A wellhead manifold is fitted at the surface with twin piping return systems comprising:- a) Water Extraction Line with topside metering and submersible vari-speed water pump. b) Gas Emission Line with either local single wellhead meter or a lateral line to a multiple Meter system (pod) and pod building. Creating a partial pressure drop above a water column down whole generates CBM gas production. By pumping water from the well column, gas is released into the well cavity which then is piped through a meter system or single wellhead meter. The water drains into the column naturally from the local ground aquifer into the well. Advancement in small P.L.C. controllers has allowed the method to be successful with monitoring and control of fluid level using a down-hole variable speed drive pump and liquid level sensing technology. Some RTU/Flow Computers have adopted this philosophy also to provide the pump and measurement management.

400 to 1000 ft

Page 5: Low Pressure Metering of Natural Gas

Measurement Philosophy Two metering methods are currently used and approved locally by the BLM, a single well approach with Small Housing / Frost Box or a Multi-Stream system with larger pod building and multiple meter runs. Why measure at the well head ? Allocation metering or back allocation, as some people call it, can be very beneficial in maintaining security and minimizing system risk and losses due to leaks. Independents sometimes question the reason for a meter at the well-head when downstream there is a sales meter doing the measurement to the pipeline. Particularly when the independent owns all the wells ! This question is answered in many parts of the USA by the custodian responsible for collecting hydrocarbon tax revenue, in fact he usually imposes rules and regulations on the producer to protect his revenue stream and may be but not limited to one of the following BLM (Bureau of Land

Management), Texas Railroad Commission.

General Gas Measurement Philosophy for CBM The following is an overview of the measurement philosophy as being operated in the Wyoming and Colorado - Meters used 2 and 3-inch diameter, Cone type meters or Orifice (OFU pod style only). Gas volume outputs at around 250-1000MSCF/ day / well. BLM system approval or permits/waivers are needed for around 65% of the USA CBM areas. Cone type meters and orifice have been used in these areas The measurement is wellhead allocation for the gas fraction although water and liquid hydrocarbon (gas condensate) can be present. Usually the accuracy requirement is defined as being in the range of +/- 1.5% with +/- 0.1 % repeatability. Well production life is limited to about 5-10 years (from start-up) with pressures starting at around 30psig and dropping to below 5psig after a certain period of time based on de-watering, geology etc.

Figure 3 Pod Building Design Showing 7 Orifice Plate Units.

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Piping Concepts and Pressure Drop With low well head pressures declined to below 5 psi it is critical that pressure drop and meter DP – recovery is optimized. There is a fine balance in obtaining optimized production due to meter and pipeline hold caused by friction and DP losses in the system. Current thinking utilizes a method called telescoping piping to facilitate maximum production, whilst helping to prevent well cross over or gas being re-injected into an adjacent well usually because of a check valve failure.(Figure 17 later shows a piping layout concept). The advantage to using cone type meters is the recovery is high usually 20% better than a typical orifice unit for the same DP and also its ability to operate with good accuracy at low DP’s. During performance trials in Wyoming with similar geological areas and over multiple wells it was noticed that single well head systems produced more gas than multiple pod systems in the same geological region, approximately 15 - 20% higher, in some cases. Major operational issues that cone type meters can overcome are –

a) Conditioning/realigning the flow b) Does not need 30d’s upstream straight run as OFU devices. c) Passes liquid rather than holds it in the throat of the meter. d) Is economical and has low noise stability. (Can operate to 0.5” ‘W.C.) e) Can be fitted in a small space with small enclosure or frost box

How a Cone Type Meter Condition the Flow?

The meter consists of a differential producer fixed concentrically in the center of the pressure retaining pipe by which a differential pressure can be obtained across the interface of two cone frustums via an internal port-way system. The cone re-distributes the velocity profile across the throat of the meter (see fig 7a) This allows a downstream pressure P2 to be measured in the center of the closed conduit. Some compact units have wall taps instead. The upstream pressure P1, being measured at the pipe wall.(See fig 4.0)

The concept of using the center of the cone above to collect the downstream pressure has certain advantages over conventional differential pressure devices such as the following points: a) Flow Conditioning. b) Large Turndown (circa 10-1 if sufficient line pressure is available) c) Static Mixing d) Wet Gas

Fig 4.0 - Typical Cone Meter Geometry

Page 7: Low Pressure Metering of Natural Gas

Mathematical Constants.

The general mass continuity equation applies to this differential pressure device as (Equation.1.0) The fact that geometric similitude will be apparent in the design allows the use of a proven cone equation provided that :- a) The angles and lengths of the frustums are similar to the original device. b) The ratio sets are the same as the original with good concentricity of cone.

PEAtCdQv

2

……………………………………………………………Eq. 1.0

Figure 6 Generic Cone Meter The expansibility coefficient or Y Factor equation for gas density correction, has been derived from some work done at the national engineering laboratory in the U.K.(NEL) by Dr. M Reader-Harris, Dr Robert Peters and is as follows : (Equation … 2)

kP

PY

g))696.0(649.0(1 4

……………………………………………Eq. 2.0

This equation is used in many flow computers and is a standard featured in many off the shelf Flow Computers and RTU’s.

Flow Conditioning Effect

It is known that the use of a cone shape concentrically mounted in a closed conduit (pipe) can facilitate a flow conditioning effect by “velocity profile re-distribution”. This effect seems to occur over quite a wide Reynolds Number (ReD) range and appears to be more pronounced farther away from the transition region were changing flow patterns occur. (usually at ReD,8000 -10,000 transition area ) In 2005 testing was completed at SWRI in San Antonio on a 4 inch meter supplied by Cameron to demonstrate the insensitivity to flow disturbance by using out of plane elbows fitted upstream and downstream of the meter and the effect to a baseline compared (test data results shown in figure 7.0).

Page 8: Low Pressure Metering of Natural Gas

Figure 7.0 - Out of plane elbow testing on a cone type meter

A cone meter generates a wake however the vortices that are quite large in length and are of a high quantity per cone circumference length and it is thought that the low noise signal that is seen on the differential pressure signal (DP) may be due to phase cancellation at the interface of the centre line of the port.

Figure 8.0

A wake is a highly turbulent area of flow, located directly behind a body immersed in a fluid flow deficient in momentum.

The ability to generate a low noise signal is key in being able to operate a CBM well at low differential pressures because generally CBM wells generate 5 PSI at the well head on a well at around 400 feet deep. This means that there may be only app. 15-20 “ W.C usable across the ports the fact that the cone meter generates a very small signal superimposed on the D.P. allows metering of gas with generated D.P’s as low as <1 inch water column. See Figure 9.0

Figure 9.0 Low Noise Signal on D.P. Cone Meter Figure 10.0 Inherent Noise Signal on an OFU Meter Research by Mr.S Ifft. in the early 90’s found that an “OFU” generated a superimposed signal on the D.P of up to and as much as 1-2 inch W.C. on certain small size meters. This may be as much as is useable on some CBM wells that are shallow and are nearing completion - Figure 10.0.

Higher Pressure. CFD

Lower Pressure. CFD WAKE

Page 9: Low Pressure Metering of Natural Gas

Newer Designs of Cone Meters There have been new developments if the design of cone meters recently 2 manufacturers have designs both with patents that are of a flangeless type. In this variant the meter sits between flanges as a wafer and is installed using long bolts on the outside of the meter body usually supported by the force exerted by the pipe on the flange face and also on the initial stages of set up on some spacing rings that centralize the body with the pipe - Figure 11.0. The operating principle for this device is exactly the same as the previous generic cone meters mentioned however the big difference is the use of wall taps to read the static and differential pressure on one design of this device. The other type has a central cone port as the welded original versions but with no welding involved.

Figure 11.0 - Flangeless (wafer) Design

Artifact Calibrated Cone Meter

Calibration of the standardized orifice meter using the artifact compliance technique requires conformity and accuracy during manufacture of the plate and plate holder. Correct installation, seal ring integrity, correct DP tap communication, plate concentricity in manufacture and installation plus a meter tube manufacturing accuracy and surface roughness compliance as stated in the relevant standards(usually API MPMS Chapter 14.3 or ISO 5167- Part1) is required to satisfy the measurement need. This is why we do not need to test each orifice plate each time under kinematical flow conditions to obtain its (C.d.) coefficient of discharge, but just to make sure the artifact geometry (dimensions) are correct and the installation and operation is correct. The meter that will be shown next is for a new concept meter this meter uses artifact calibration techniques and has control of the following parameters in the design of the device ;-

1) Surface roughness control for the meter tube and cone

2) Robust cone support and body assembly using an investment casting with interchangeable

machined cone parts for different flow range-ability within the same body

3) Machine centering of the assembly after manufacture to maintain concentricity.

4) Accurate machining of the replaceable parts to CNC tolerances

5) API 22.2 -Test data set to show a signature per beta and per line size.

Page 10: Low Pressure Metering of Natural Gas

This type of meter is novel and has great promise since the concept to use artifact calibration and verification techniques allows minimal calibration relying on geometric similitude, a drawing of the device is shown in figure 17b and test curve 17 c next.

Figure 12.0 - API 22.2 Test Curve 0.6 beta Figure 13.0 -Artifact Calibrated Design Cone Meter Installations and Wet Gas as Seen in CBM Wells Generally it is known that cone meter installations can be short , some issues are that the meter run is in a constant state of wetness due to the CBM well water column, which can cause problems with OFU’s due to water build up in front of the plate, it has been noted that liquid slugging can occur on the rear side of the plate by the ports which can cause errors. Previous research has verified that a cone meter does not have this attribute, and appears to sit there working in liquid mass fractions of 5% with minimum affect on the C.d. smaller cone diameters being less prone to liquid contact (0.75 Beta usually).

Figure 14 – OFU - (Sveedman 97) Figure 15 - Cone Meter - (Sveedman 97)

The lack of hold up effect by a cone meter is a key factor in helping to keep accurate measurement at the well head. (5% liquid mass fraction test at various betas) The well is also less likely to choke particularly in early the early stages of production. Telescoping Piping Designs (lowering the pressure drop)

Using piping that changes diameter as it is laid to the compressor can have enormous benefits in CBM production. Starting with 3 inch diameter moving to 4, 6, and 8 over the length of the feed lines from each well reduces pressure drop in the system thus helping maintain a higher production level to the buyer.

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Using single well head approaches with cone meters plus this type of piping can improve production in the 15-20% range from using OFU’s and conventional single diameter pipe work also the benefit mentioned earlier in the area of wells feeding other wells locally due to check valve failure can be another reason to use this method.

Basically each well can be fed into is own group on similar diameter piping and as the field is developed use larger pipe diameters the further down-stream to facilitate lower system dP’s which can enhance the CBM production thus not having to fight the effect of friction and restriction caused by smaller diameters which reduce the available d.P. at the meter.(Figure 17.0)

Figure 16.0 - Artificial Gas Lift (Extraction) Blowers

Using centrifugal extraction fans (blowers) to pull CBM from wells has been used in the past, it is important to select the correct place for the meter usually upstream of the compressor using an absolute transmitter. This location / position is fixed to prevent the heat from the device converting the free water to steam or water vapor which will give the wrong d.P. and thus the wrong measurement.

Figure 17.0 - Telescoping Piping System (Lower Pressure Drop)

Page 12: Low Pressure Metering of Natural Gas

Ultrasonic Metering and Low Pressure / Atmospheric Pressure Conditions) It is difficult to transmit ultrasonic energy into a gas because of the mismatch of acoustic impedance between solid matter (transducer) and gas. This mismatch decreases as the gas pressure is increased (i.e. gas density increases). Air at ambient pressure can be a worst case scenario! Although all gases will attenuate the signal, the strength of the received signal is also dependent on the meter size (longer path lengths result in increased attenuation) and frequency of the transmitted signal. Signal to Noise Ratio (SNR) and Noise Limitations Consideration of the Signal to Noise ratio is imperative to understanding the limitations of ultrasonic meters. The signal quality (and therefore measurement accuracy) deteriorates once the SNR drops below a predetermined value. This value is predicated by the algorithm(s) utilized for the signal analysis. There are various potential sources for noise in a measurement facility. The most obvious and significant is that emanating from pressure regulators. Additional sources of noise are protrusions into the piping (i.e. Thermo-wells) and even the flowing gas itself. Therefore an ultrasonic meter must be able to deal with inherent noise in most applications. Basically, sound waves in a gaseous medium propagate in an omni-directional fashion from their source. The sound pressure level at a certain point is proportional to the amplitude of the sound-emitting source and distance from the source and decreases exponentially with the distance from the source of sound. During its propagation, the sound wave energy decreases as a result of interactions with the medium (attenuation ). Sound energy is transformed into thermal energy due to the viscosity of, and heat and conduction in the medium. Sound attenuation is very dependent on the properties of the fluid (gas) and the frequency f of the transmitted signal. Since, in the case under investigation, a similar medium is used all the time, this relation can be simplified as follows:

(eq. 3) If a sound wave hits an interface, its energy will be distributed into a different direction. The distribution will be the result of diffraction and reflection. The ratio of wavelength of the acoustic signal and the dimensions of the disturbing object play a major role here. Also, the ratio of reflector to transmitter surface area defines the resulting reflection signal loss. Fig. 1 illustrates this relationship using a 200 kHz ultrasonic sensor.

Figure 18.0 Signal level loss at a reflective surface versus

propagation directed over same distance

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Flow Testing of Chordal Ultrasonic Meters (various high pressures v low ambient pressure)

Many manufacturers have test data on various pressures covering various sizes the results below are from one manufacturers testing at an approved laboratory. Figure 19.0

Figure 19.0 Shift between the high pressure and ambient

Other Meter Types Coriolis force type meters inherently have high pressure drop and also require much higher pressure to develop the mass flow rate through the device and so are not suitable for low pressure applications. Root Meter Types Roots meters have a very good performance on dry gas types and also have minimum energy extraction from the gas fluid. (N.B.The metered gas must be clean filtered and dry).

Figure 20.0 Typical Roots Type Meter

These meters can operate over large turn-downs with low pressure inputs at circa 0.5” w.c. A typical set of units can offer the following ranges seen in figure 21.0 below.

Figure 21.0 – Typical Roots Type Meter High and Low Pressure Ranges.

High Pressure

1% shift between high and low pressure Low Pressure

Page 14: Low Pressure Metering of Natural Gas

References

(1) Bagge, D.J., “Evaluation of Ketema, V-Cone Flowmeters” Test Report E 1705 S 92, SIREP, 1992.

(2) Ifft, S. A and Mikkelsen, E.D - “Pipe Elbow Effects on the V-Cone Flowmeter” North Sea Flow Measurement Workshop, Peebles, Scotland, 1992

(3) Ifft, S. A “Installation Effects on the V-Cone Flowmeter” McCrometer Div. of Ketema 3255 West Stetson Avenue Hemet, California 92545 USA, 1995.

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

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

(6) 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) 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 and Environmental Engineering, Univ. of Iowa, Iowa City.

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

(17) H. C. Chen and V. C. Patel, 1985, Calculation of Trailing Edge, (18) Sveedman SWRI Homogenous Model and OFU liquid effect (19) Ifft Wet Gas Testing at SWRI 1997 on V-Cone Meter (20) Lawrence Wellhead Metering by V- Cone Technology NSFMW 2000 Gleneagles Scotland

UK (21) Kristin Keith and Jim Bauder, Montana State University-Bozeman John Wheaton, Montana

Bureau of Mines and Geology (2003) (22) BLM-Wyoming updated CBM Well-head drawing. (2005 Gillette) (23) Lawrence - AGMS 2010 Low Volume Metering Using Differential Pressure Cone

Technology (24) The Effect of Geometry on Differential Pressure Meter Performance Zanker- Lawrence, The 2011 Americas Flow Measurement Workshop Houston. (25) Roots Type meter data Dresser USA 2014 (26) USM Data – Sick - Low Pressure Gas Measurement -Ultrasonic Technology – ISHM 2013