Intro4u2u

Over the many years that I have been writing these articles in the Case Histories series, the one theme that re-occurs very frequently is problems encountered with valves. In recent years I have been told on quite a few occasions by people that their valve problems are over as they have now made the huge and expensive step forward by replacing all the positioners in their plants with smart positioners. I have also been told that the smart positioners completely eliminate hysteresis, and effectively cure all problems.

A smart positioner is one which contains a microcomputer, and as mentioned in other articles, another one of the fallacies I encounter is the common belief that computers are perfect, can do no wrong, and can sort out all problems.

Now, having been trained as an engineer around the time Noah came out of the arc, and having been brought up on relatively primitive devices like slide rules and log books, I am one of the biggest fans around when it comes to computers, and really love them. However, I do try and do this in a sensible fashion, and realise that whilst computers do good and at times wonderful things, they are only as good as the people who program them, and in fact they can and do introduce complications that may not have been present in the bad old ‘pre-computer’ era. Therefore, I was initially rather sceptical to hear these wonderful and possibly wild claims about smart positioners.

On talking to some very knowledgeable suppliers and manufacturers of various makes of smart positioners I learnt that there are smart positioners, and then there are really intelligent positioners, which apparently go a few steps further than just ’smart’. However, as the engineering world is a very competitive place where the hard headed accounting types who pay the bills, look very much at price as opposed to specifications, you do have to pay more for the extra intelligence. In other words you pay for what you get.

The main purpose of any positioner is to try and get the valve to the position as dictated by the controller as accurately as possible. Positioners were in fact introduced mainly to try and eliminate hysteresis effects. The old type of pneumatic positioners, which have been around for many decades, did a pretty good job, but like all pneumatic devices were relatively crude and inaccurate.

They only incorporated a P (proportional) control in positioning the valve. As mentioned in the Loop Signature series, P only control is likely to result in some offset, as it does not try and eliminate the actual error. The I (integral) term is needed to eliminate error completely.

Now, most people I have spoken to seem to think that their smart positioners definitely have a P + I controller in them. However, several of the smart positioner people I have spoken to, say that they only offer P + I at an additional price. I personally think that there would not be all that much added benefit in purchasing a smart positioner unless it did have a full P + I function.

However, one must be aware that the I term can also introduce problems, for if it cannot eliminate the error for any reason, it will tend to keep trying to move the valve in the direction needed to eliminate the error. If the valve is sticking too much, then a bad overshoot, or even continuous cycling (instability) can result. One must obviously also ensure that a positioner with a P + I controller in it, is correctly tuned for the particular valve/actuator combination.

However good a smart positioner may be, it still cannot eliminate problems caused by undersized (and hence underpowered) actuators. The actuator provides the motive power to the valve. The positioner’s function is to tell the actuator how much to move the valve. It cannot move the valve itself. Thus if the actuator has not got enough power in it to overcome valve stiction easily and move the valve properly, the positioner may push too much air into the actuator and cause overshoot and possibly instability. As mentioned above this will probably be made worse if the positioner has an I term in it.

To me, one of the best and probably most important features available, possibly at extra price on the ‘intelligent’ positioners, is the valve performance diagnostic ability that can be offered in these devices. At least one of the better-known makes actually can communicate information on the state of the valve over the Internet. It continually monitors the performance of the valve’s actual position and response dynamics, and can sound warnings if the valve’s performance starts deteriorating. Typically, it can advise of excessive stiction, hysteresis, overshoot, etc. As over 85% of all loop problems are generally valve related, this is a huge benefit, and if one is serious about optimisation, it is to me well worth the expense of the device.

Custody metering is an essential tool for the profitable operation of offshore platforms. In the light of Russia’s growing involvement in offshore production Barry Clark looks at the evolution of metering systems and their development to meet the exacting standards for accuracy, reliability and safety required for the operation of these increasingly sophisticated and automated platforms and given their extreme space constraints the need for compact, light equipment.

Why metering matters

There is an important cost saving. If a typical offshore oil production facility produces 150,000 bpd (barrels per day) and incurs a random $5 barrel extraction cost, an under-reading error of 0.5 % in flow can lose you $1.3m in a year assuming an oil price of $35 a barrel. As a custody metering station only costs around $1m, it will have paid for itself in a little over nine months. At $50 a barrel—the price at the time of writing—that loss, or potential saving, amounts to $2.25m.

However, the primary reason for offshore metering is security as you can only be sure of the output of a facility if you meter it at source. It is possible to offload crude by shuttle tanker to a shore terminal for custody metering. However, in practice this opens the way to disagreements with production partners and the tax authorities over issues such as ‘bill of lading’.

A little Offshore History

Although drilling over water began in Baku in the 1800s, the start of offshore drilling is usually traced back to the early 1930s. The Rincon California ‘Steel Island’ platform, constructed in 1932, was one of the first platforms to do away with ‘beach piers’, creating a recognisable offshore platform. But it was still within easy reach of the shore.

The first true offshore oilrig built out-of-sight of land was a fixed platform constructed by Kerr-McGee Corporation in the relatively warm and protected waters of the Gulf of Mexico in 1947. Nearly three decades elapsed before the industry was in a position to confront the challenges of deep-sea drilling in the inhospitable and treacherous waters of the North Sea—conditions that more accurately replicate the kind of challenges presented by the development of Russia’s Arctic offshore fields. Britain’s first North Sea oil was produced in 1975 from the Argyll Field platform 200 miles offshore in 2,700 metres of water.

Crude from the Argyll Field was processed on board and exported by a CALM (Catinary Anchor Leg Mooring) buoy to shuttle tankers for shipment to the BP’s ‘Isle of Grain’ refinery. In contrast, around 90% of offshore metering system requests nowadays are for FPSO (Floating Production, Storage and Offshore Loading) or other floating vessels, rather than for traditional platforms.

Fiscal, Custody and Allocation

In the metering business the terms ‘fiscal’ and ‘custody’ are essentially interchangeable, although fiscal means ‘concerned with government finance and policy’ and custody means ‘safekeeping or guardianship’.  Neither term defines a level of metering accuracy in itself, although both are taken to mean the best accuracy in normal oil field practice.

Metering performance is expressed as the total uncertainty of the flow rate measurement. In Russia, a mass based oil flow measurement is generally preferred; whereas in the UK volume metering is favoured.  Either is acceptable provided the necessary corrections for density, water and sediment quantity are properly addressed.

In the UK the Department of Trade and Industry (Dti) have supplied metering guidelines to offshore operators and licensees since the early 1970s, and define the following ‘measurement approaches’

Allocation measurement refers to continuous measurement by which a quantity of hydrocarbon, metered to Custody Transfer standard, is attributed to different sources.

For further information issue 7 of the UK’s DTi guidelines is available on its web link: http://www.og.dti.gov.uk/upstream/measurement/MeasGuidelines_V7.pdf, and is recommended for additional reading.

Space and Weight

Early offshore platforms were converted drilling rigs, where space and weight were severely constrained. The Argyll oil meter skid was typical of early offshore meter stations and was simply a cut-down version of its land-based predecessor.

The most significant change was to move away from PD (Positive Displacement) meters which, despite their excellent accuracy of ±0.15%, were too large, heavy, and susceptible to internal damage.

In the 1960s a certain Dr Potter patented a turbine principle meter to handle high fuel flowrates for the USA rocket propulsion programme. The ‘Pottermeter’ became the workhorse of offshore metering with a long-life low-drag hydrodynamic thrust bearing and linearity of ± 0.25%.  Later helical bladed rotor designs handled wider viscosity ranges with a premium linearity of ±0.15%.

These meters ‘infer’ the volume flowrate by removing a little kinetic energy from the liquid to spin the turbine in a fairly linear relationship to flowrate.  Whatever the design, they are to some degree susceptible to changes in the oil character (viscosity) and therefore require regular proving or calibration under real operating conditions.

Ball Provers

A ‘ball’ or ‘pipe prover’ is the conventional proving device for most turbine and PD meters.

The procedure involves a plastic sphere being inflated with water to create a close fit inside a pipe ‘loop’. This is then pushed along by the oil flow in series with the meter under test and passes ‘sphere detectors’ mounted in the pipe wall which initiate a timer with the start and finish of an accurately calibrated internal volume. Repeating the proving a number of times provides a highly accurate measurement of average flowrate that is used to calibrate the meter.

Early provers had the ball moving in only one direction through the loop. The physical size and weight of the early uni-provers became a problem for offshore service and the ‘bi-directional’ prover was developed.  Utilising a 4-way flow diverter valve it allows the ball to travel in both directions one after the other, combining the forward/reverse volumes to make a single proving ‘cycle’.   This reduces the overall calibrated length of the provers, and limits possible hysteresis errors by the sphere detectors.

In the mid 1980s, pulse interpolation techniques were developed for small volume piston provers. The procedure interpolates (estimates) the part of a full meter pulse that is inevitably ‘lost’ at the end of a displacer movement. This improvement is also now applied to ball provers.

Almost all new provers make use of pulse interpolation to reduce the necessary calibrated volume. However the reduction can only be made if the duty meters have a uniform pulse output per revolution. This is true of all turbine meters unless they have been damaged in a way that decreases their intra-rotational linearity.  It is not necessarily true for all PD meters, which have several different principles to achieve the swept volume per revolution.

‘New technology’ manufacturers are rightly proud of the inherent stability of coriolis and ultrasonic flowmeters.  However, the reality is that even a bad flowmeter may be calibrated to be accurate at a single instance in time, at a well-controlled test laboratory.  The real test is offshore under real operating conditions, 365 days a year.

The industry needs to prove to itself and government agencies that the meters remain consistently sound between onshore laboratory calibrations. Good practice demands a dedicated prover be installed for all offshore oil custody metering systems.

Ideally, a rotary inferred volume type meter should be proved by a different principle, such as a PD ball prover.  It is very unlikely that both devices would be affected in the same way by an external upset such as a sudden increase in product viscosity—this reduces the risks of so-called ‘common mode errors’ and is an important principle of good custody flow metering.

In ‘master metering’, the ball prover may be replaced with a transfer or master meter of equal or better accuracy than the duty meters.  To reduce its degradation, the master is normally kept isolated and protected from the main system. It is often the same type of meter as the duty, and is periodically returned to a laboratory for accurate recalibration.

As this method may suffer from the ‘common mode errors’ stated above, they are best suited to allocation or installations where the total rate of fluids metered is small.

Small Volume Piston Provers

These ‘small footprint’ units use machined solid pistons and cylinders, pulse interpolation, and optical position detectors to allow higher piston speeds, smaller swept volumes, and much greater turndown ratios than pipe provers.

They are perceived as more complex than bi-directional provers and require some de-rating for use with inferential pulse meters such as coriolis and ultrasonic flowmeters.  These meters have a pulse train generated electronically from a processor, based upon many instantaneous ‘snapshots’ of the flow.  This may lead to a ‘jumpy’ and over-responsive output, so that some de-rating of the prover is necessary. The amount depends on the size, configuration and manufacturing design of the prover and the meter under test.

‘New’ Meter Technologies - Coriolis Mass Meter

The first DTi approved mass metering system for the UK North Sea is believed to be the 1993 BP Forth Harding system, where there were potentially very high viscosity excursions up to 1800cP with wax and high acidity.

Extreme viscosity ruled out turbine meters and PD meters were considered vulnerable to the high acid content and local vibration. So the novel technique of coriolis mass metering was selected.  There were high pressure drops during high viscosity, but crucially the meters were not be damaged or degraded.

Good practice was observed by installing a permanent small volume piston prover on the package.

‘New’ Meter Technologies - Ultrasonic Flow Meters

Custody oil ultrasonic flow meters have been available since the mid 1990s and in less than ten years they have become as much a standard feature as turbines.

On the Canadian Husky Oil White Rose FPSO there was insufficient space for a conventional multi stream turbine and bi-di prover metering system, and a need to limit overall pressure drop.  After discussions with the consultant engineer Alderley arrived at the so-called ‘Z’ pattern arrangement.  It was essentially a duty and standby/master meter system – but with an unusually large capacity of 4000 m3/h.

The oil to be exported would be relatively stable after processing and storage in the FPSO’s tanks before batch offloading, reducing concerns over contaminants, viscosity swings and gassing.  The regulatory body was presented with the supporting design evidence for the propriety of this custody system and approved its use.

Orifice metering still continues to be the most commonly requested principle for gas flow measurement offshore.  Nonetheless, just as with ultrasonic oil metering, the pace of change to multi-path ultrasonic custody standard gas flow meters is increasing.

The primary benefits of orifice meters are their high acceptability, simplicity, low technology, ease of calibration, and ‘perceived’ robust nature. A reading of some sort is almost always available from an orifice meter and maintenance is simple, and can always be carried out offshore with limited tools. If the installation is properly designed to ISO5167/AGA3 and properly maintained the accuracy is deemed to be inherent,

Disadvantages are the inherent overall uncertainty (±0.65% at best), poor turndown (around 3:1) regular calibration of secondary instruments, and relatively large space requirements.

Ultrasonic gas flow meters have the benefits of relatively high accuracy (typically ±0.5%), high turndown (minimum 10:1), good reliability and comprehensive diagnostics.  Some operators are suspicious of the relatively short time, some 10-13 years, that custody metering has been practised, and consider the meters too complex.

Ultrasonic calibrations can also be a problem. The units need to be taken to onshore test laboratories where conditions are never identical to the real world installation.  Recently there have been pioneers in the Norwegian sector of the North Sea utilising ‘master meter’ type principles with two meters in series. The second meter checks, or perhaps even calibrates the first. But it is not yet clear how common mode errors will be identified in such systems.

Reliability/Availability

Maintenance offshore is never easy, and it might be tempting for an operator to continue to run a failing meter rather than to interrupt production. For this reason it is usually mandatory to duplicate one complete stream of metering equipment on a custody station.   This leads to the well known ‘N +1’ meter stream requirement.  In addition modern flow meters such as turbines are relatively compact and so a calibrated spare can be held offshore to allow failed units to be returned to base for repair.

Sphere detectors are duplicated at each end of offshore prover loops to give four effective calibrated volumes which produces considerable redundancy.

Offshore Computer systems

Most authorities insist upon ‘stand alone’ flowcomputers for each meter stream. This allows individual units to continue operating even if a neighbour is damaged.  A supervisory computer can ‘manage’ the disparate stream, as well as prover flowcomputers, alongside additional tasks such as flow scheduling and automatic flow sampler control. These are now most often ‘dual redundant’ arrangements rather than the earlier and arguably much more complex ‘hot standby’ systems.

Many now prefer a single station supervisory function since the primary metering data is retained in the separate flowcomputers.

Sampling & Analysis

As few offshore installations have comprehensive analytical laboratories all custody stations are offered with flow proportional automatic samplers.  In some cases smaller ‘sub samples’ are extracted and are more easily transferred to the shore base for analysis.  High pressure or volatile samples require special handling. It should be noted that restrictions are imposed on helicopter transfers of many sample canisters.

Conclusion

There are still many good examples of what we would term conventional oil and gas metering offshore. For gas a properly designed orifice metering station and for oil a turbine meter/bi-di prover system, is still considered to be an excellent, all round custody metering solution.  It is worth noting that few if any, field partners or government agencies will make a successful challenge to such a system on pure technical grounds.

Offshore production requires many systems and processes. A custody metering is almost universally regarded indispensable. Perhaps you could do without one, but you would lose the key to profitable offshore production.

The petroleum industry most commonly measures fluids in volume units. When volume is used as the measurement unit, a specific set of conditions of temperature and pressure are designated to be the standard or base conditions for the custody transfer of the fluid. Thus the measurement of volume requires that the gross volume metered be adjusted to an equivalent net volume at these base conditions. This correction requires knowledge of the relative density or specific gravity of the fluid in addition to the temperature and pressure at which the gross volume was determined.

Tables and equations are available for Certain fluids that will provide the user with the correction to net volume when the temperature, pressure, and relative density ere known. This empirical data predicts the change in density of the fluid with temperature and pressure, Crude oil, refined products, and pure compounds are predictable fluids that can be measured in volume units by Ibis method with very little uncertainty.

The physical behavior of mixtures of hydrocarbons is not very predictable. Different compositions can cause the density to vary differently with temperature and pressure, Another characteristic of mixed streams is known as volume shrinkage. The mixed stream has more volume due to its molecular structure than if all the components were measured by volume separately. However, a pound of one component added to a pound of another component always produces two pounds of the mixture. Custody transfer contracts for mixed streams are still written in volume units, however, the fluid is metered on a mass basis and then converted to volume by a ratio of weight per unit volume for each individual component in the stream.

There are some fluids with rapidly changing density at the temperature and pressure at which they are being measured. This region of rapidly changing density is known as the critical region. Such fluids as ethylene and carbon dioxide are often measured at conditions in this region, making it difficult to determine the net volume of these fluids. Contracts for custody transfer of these fluids are often written in mess units.

Mass measurement is utilized in the two Instances above to solve the problems related to determining the net volume. Mass measurement is also a desirable alternative to volume determination for inventory balance, as in underground storage, plant balance, and loading facilities. It can be argued that mass units are more logical units for custody transfer than volume units, since mass measurement does not require the measurement of temperature, pressure, and the use of empirical data to convert to e quantity that can be utilized for custody transfer. Mass units are a fundamental unit of measurement.

However, the metering technology for continuous mass measurement has only been available in the last thirty or so years, way after the petroleum industry had adopted standards for volume measurement. It has never been practical to weigh large quantities of fluid especially in a dynamic mode, though the weighing of tank trucks is often utilized for measurement of smaller quantities. Mass measurement also requires the use of electronics that again were not available in the earlier years.

This paper will now address the two methods of mass measurement. It will also identify areas where there are potential sources of error for mass measurement end will identify areas where this method has advantages over traditional volume measurement.

Inferred mass measurement is the utilization of a volumetric measuring device in conjunction with a densitometer and flow computer. This method utilizes the following flow equation:
M=VLDL
Where    M = mass flow
VL = volume flow at line conditions
DL = density at line conditions

The volume meter can be any one of several types, the choice being mainly dependent on the properties of the fluid to be measured end the flow rates. Turbine meters as well as orifice meters are common. The volume meter’s recommended installation for volume metering does not differ for inferred mass measurement and these guidelines can be found in the MPMS Chapter 5 for turbine meters and Chapter 14,3 for orifice meters published by the American Petroleum Institute.

Vibrating element technology is the most prevalent technology for density measurement in the petroleum Industry. It has no moving parts, thus requires little or no maintenance, and meets the accuracy requirement for custody transfer. The MPMS Chapter 14.6 published by the American Petroleum Institute contains the guidelines recommended for the densitometer when used for inferred mass measurement.

The most common problem in obtaining an accurate mass measurement by the inferred method is associated with the necessity to determine the volumetric flow and the density at exactly the same temperature and pressure. The most accurate densitometers require installation in a by-pass or slip stream, as they cannot typically handle the flow rate of the main pipeline. Thus this densitometer flow loop must be engineered such that the fluid in the loop is maintained at the same, or as near as possible to the temperature and pressure of the main line. It is always necessary 1o insulate the loop, Pressure differential is minimized by locating the densitometer as close as possible to the volume meter with as little as possible pressure drop between the two measurements.

Another important consideration is that the densitometer should see a representative sample of the fluid that is flowing in the main line. This makes it critical to consider the flow rate in the densitometer loop when determining the sampling method. It may also require consideration of where the sample is taken if the fluid does not stay adequately mixed in the flowing stream.

For inferred mess measurement it is necessary to prove both the volume meter and the densitometer. The volume meter is proven utilizing the same technology as In any other metering application. The MPMS Chapter 4 published by the American Petroleum Institute should be followed. For light hydrocarbons, a pycnometer is required to prove the densitometer. The method for proving a densitometer with a pycnometer is covered in the MPMS chapter 14.6 published by the American Petroleum Institute. A hydrometer is the acceptable method for proving a densitometer in crude oil service. The method for proving a densitometer with a hydrometer is covered in the MPMS Chapter 9 publishe3 by the American Petroleum Institute.

The second most common problem associated with Inferred mass measurement is the proving of the density measurement. Proving any device under field conditions requires time and care. The problem is similar to the one noted above regarding the requirement for temperature and pressure equalization between the volume meter and the densitometer. The pycnometer must be filled with the fluid at the same conditions of temperature and pressure as the densitometer is seeing. Once this is accomplished the pycnometer is weighed so that the density of the fluid can be determined. The knowledge of the correct tare weight of the pycnometer and the accuracy of the scale contribute to the accuracy of the proving technique. A correction factor for the densitometer is determined, much like the meter factor for the volume meter.

A flow computer handles the calculations for inferred max measurement. Signals are processed from the volume meter for gross volume, from the densitometer for density and with the meter factor and density correction factor, the mass is calculated. For contracts written in mass units, this is the final calculatlon for custody transfer. To determine the net volume for each component of a mixed stream, a chromatograph is utilized to analyze the weight fraction of each component. The weight per volume of these components at standard temperature is a known value. The flow computer can then use the total weight of the stream, the percentage of each component in the stream, and the known weight of these components at standard conditions to calculate the net volume of each component for custody transfer. The American Petroleum institute covers this procedure in the Manual of Petroleum Measurement Standards Chapter 14.7.

Coriolis flow meters are based on a principle of operation that relates the mater’s output directly to the mass flow rate of the fluid. The Coriolis meter utilizes vibrating element technology much like a densitometer. The vibrating tube(s) twist with flow. The amount of twist is proportional to the mass flow rate of the fluid.

This metering technology has revolutionized flow measurement across all industries. Their most distinct advantage over traditional metering devices is that they have no moving parts. This eliminates measurement errors due to wear on parts that create slippage and meter factor shifts over time and eliminates costly repairs.

For those applications where mass measurement is the preferred method over volume measurement, the determination of mass can be done with a single device. This not only reduces the cost of the metering equipment, but also reduces the overall cost of the piping end the installation by eliminating the sample loop. The errors associated with temperature end pressure differences between the volume meter and the densitometer are eliminated.

An obvious drawback for Coriolis meters is their limited flow rate. The maximum size available today in Coriolis meters limits flow rate through a single meter to about 5000 BPH or 25000 Ibs/min.

Another issue for the custody transfer of fluids on a mass basis utilizing a Coriolis meter is the technology for field proving on a mass basis. One approach is to install a densitometer on the volumetric prover, thus converting the volume of the prover to mass units. With this method, the result of the proving cremes a meter factor with the same technology and potential error as proving an inferred mass measurement installation.

Since the petroleum industry most often requires volume measurement, the Codicils meter offers the unique advantage of being either a mass or a volume meter. Vibrating element technology is used to determine the mass flow rate and the density of the fluid. With both measurements available from the same meter, the volume of the fluid is determined by using the same equation for inferred mass measurement, only rearranged
VL =M/DL

Where       M = mass flow
VL = volume flow at line conditions
DL = density at line conditions

With the ability of field mount electronics today, a Coriolis meter can basically act as a volume meter and produce a pulse output much like a turbine or positive displacement meter. With this pulse output, the Coriolis meter can be field proven by the same proving procedures associated with bi-directional or small volume provers.

The American Petroleum Institute is currently publishing a draft standard entitled, “Measurement of Single Phase, Intermediate, and Finished Hydrocarbons by Cot/oils Meters” and should complete the process dudn0 2000 to publish a standard for the use of Coriolis meters in crude oil service.

A compact bidirectional meter prover mechanism incorporates a straight calibration barrel having spaced detectors sensing passage of a fluid induced displacer piston. A four-way control valve is connected by flow conduits to the conduit containing the flow meter and is connected by a conduit system to respective extremities of the calibration barrel. Launch valves are interposed between the control valve and the calibration barrel and are selectively positioned to permit metering flow through the calibration barrel only after the control valve has been positioned for directional flow of fluid through the conduit system and the calibration barrel. Thus, the necessity for piston prerun is eliminated and minimum cycle time is permitted. The length of the calibration barrel is also minimized by elimination of piston prerun.

Compact or Piston (sometimes referred to as small volume) provers are similar to standard pipe provers with the noticeable difference that the displacer is not free, it is in fact a piston connected to a piston rod. The rod extends outside the barrel of the prover and is usually fitted with an indicator either of the micrometer type, or fully electronic using a displacement transducer and flags/proximity switches.

Due to the relatively small volume of product displaced by the pistons travel or stroke, a means had to be found to ensure compliance with the API’s recommended standard minimum of 10,000 pulses per run. The means employed was pulse interpolation.

There are several methods of employing pulse interpolation, but by far the most used is the dual chromometry (double clock) method (see API Chapter 6. Proving Systems - Pulse Interpolation). Essentially this method involves the use of two timers (T1 & T2) both driven by the same hi speed clock (>1 Megahertz) oscillator. The sequence employed is:

1. Start Timer 1 (T1) when first detector switch is activated.
2. Start Timer 2 (T2) at the leading edge of the next flow meter pulse following T1 start. (This is also where the pulse counter will start counting)
3. Stop Timer 1 (T1) when the final detector switch is activated.
4. Stop Timer 2 (T2) at the leading edge of the next flow meter pulse following T1 stop. (This is also where the pulse counter stops counting)

double chronometry pulse counting the formula to determine the number of full & partial pulses is then:

actual pulses = pulses counted [n+1] * T1/T2

or:

double chronometry formula
where:
K = proving K factor
T1 = time elapsed for Timer 1 over duration of run
T2 = time elapsed for Timer 2 over duration of run
n+1 = number of pulses counted during T1 timing
Vol = base volume of the prover

The other correction factors for Ctl, Cps & Cpl are made as for pipe provers above. However, the factor for Cts (Correction for Temperature Effects on the Steel) are made differently. The value for Em (cubical coefficient of expansion for prover material) must be changed to reflect the square coefficient of expansion for prover material (CCE/3 * 2) and a new variable for the linear coefficient of expansion of the prover rod must be added. Most prover rods are made of a nickel alloy called Invar. The linear coefficient of expansion of Invar is very low which means that the length of the rod changes little with temperature changes.