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Improve material balance by using proper flowmeter corrections

10.01.2011 | Peramanu, S., Canadian Natural Resources Ltd., Calgary, Canada; Wah, J. C. , Canadian NaturalResources Ltd., Calgary, Canada

Here are guidelines to increase accuracy for flow measurements

Keywords:

Process plants frequently encounter mass imbalances. These can be attributed to various factors, but often they lead back toinappropriate measuring devices, improper calibration, incorrect installation or incorrect interpretation of the measuredflows. There are well-established guidelines available to ensure appropriate flowmeter selection based on the processconditions and control requirements.

Instrument vendors follow the industry standards and approved procedures for flowmeter calibration, calculating thecalibration factors based on the data provided in the flowmeter specification datasheets. Engineering and constructionservice contractors often follow vendor guidelines and standard practices to correctly install the flowmeters. This means thatmost flowmeter installations, therefore, meet accepted project standards and specifications.

Whats the flowrate?

However, measured flow interpretation, normally a process or production engineers responsibility, is often done withoutproper directions or guidelines. Although it appears straightforward that the flowmeter measures the flowrate and theflowrate value is read from the display, significant error can be introduced if the flow measurement conditions are notunderstood and appropriate correction factors are not applied. Accurate stream flow interpretation and critical massbalance reconciliation require understanding flowmeter characteristics and their associated measurement uncertainties.This is of particular importance where mass balances may be used for highly sensitive process control operations,production accounting or government reporting on royalties and emissions.

This article provides a background on the importance of accurate measurements, a description of measurement errors andthe role of uncertainties in mass balance and reconciliation. Flowmeter correction equations are derived for differentialpressure flow, volumetric flow and mass flowmeters, and flow correction factors are provided for various units ofmeasurements (UOM). Flowmeter uncertainty equations are derived for differential pressure flow, volumetric flow and massflowmeters.

METERING APPLICATIONS

To achieve the most accurate flow measurement (minimum uncertainty), proper flow system operation and maintenancemust be practiced so that meter accuracy capabilities are realized. Periodic maintenance, testing and recalibration areessential because the calibration will shift over time due to wear, damage or contamination.

The maintenance may be only a secondary-equipment calibration, a complete system mechanical inspection, an actualthroughput test against some agreed-upon standards or any combination of these. The equipment used to test the meter,such as thermometers, dead-weight tests, pressure gauges, differential-pressure gauges, chromatographs and provers (usedfor throughput tests), must have accuracy certification and should be approved and agreed upon by the interested parties.Having operators who have had experience with similar metering systems also increases the calibration and test procedureconfidence levels. Test equipment itself should be recertified periodically by the agency or manufacturer that originallycertified the equipment.

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Custody transfer operations.

In custody-transfer measurement, the measurement furnishes quantity and quality information that can be used as the basisfor a change in ownership and/or a change in responsibility for materials.

Custody-transfer measurement is distinct from other measurement types because of the contractual nature of the meter.Custody-transfer metering may require accuracy of 0.1% or better, whereas control measurement may be accepted at a 2% accuracy and operational measurement may require a 5% accuracy. A high-integrity custody-transfer measurementsystem is a result of careful design based on the specific application requirements comprising fluid control, conditioning,metering, computation and a means of traceable site data validation.1, 2

Custody-transfer management involves the entire chain from the custody-transfer metering conceptualization to the finalproduction or sale data reporting. For example, in the upstream oil and gas sector, measurement includes all intermediatesteps such as measurement and sampling guidelines, operational procedures, data processing, data transmission andreconciliation, allocation or custody-transfer procedures. To solve the flow measurement equation, it is imperative that everyequation parameter be well understood and represented.

A primary custody-transfer measurement consideration is to minimize flow variations by maintaining better flow control.For situations where this may not be possible, a meter with a wide-ranging flow capacity is needed. If a single meter with therequired flow capacity to cover the intended operating range with minimum uncertainty does not exist, using multiplemeters with some type of meter-switching control is required. Most meters operate with a specified uncertainty within thestated flow capacity limits that is typically from 25% to 95% of the flowmeter maximum capacity. For custody-transfermetering and critical control measurement, it is important to maintain the meter operation within the stated flow capacitylimits.

Errors.

Other than some operating problems and poor maintenance that may affect the measurement, the main cause of error is thefluid characteristics and errors in fluid density calculation. For gases, mixtures are more accurately measured if the streamhas relatively constant composition. This allows specific PVT tests to be run, or data may be available for common mixturesfrom previous work. If the mixture is changing rapidly, a densitometer or a mass meter may be required to determine anaccurate measurement.

During times when a custody-transfer meter is out of service or registering inaccurately, a procedure must be in place formeasuring or estimating deliveries. This procedure may need to be in accordance with regulatory standards if the meter flowis used for regulatory reporting. An example of this is the recent USA EPA Greenhouse Gas Mandatory Reporting Ruleissued Sept. 22, 2009. A typical accuracy limit from 0.5% to 2% may be used, but may be set closer or wider dependingon the specific meter costs and measurement ability.

For custody-transfer meters, a prover system or master meter should be used for throughput testing and recalibration. Thebest throughput test can be run directly in series with a prover. The prover can come in many forms, but essentially itinvolves a basic volume that has been certified by a government or industrial group. Since most meters are not totally linear,tests may have to be run over the meters operating range to calculate the calibration factors dependent on the flow capacity.

Commercial mass balance software.

The characteristics and strengths of commercial mass-balance software may include:Graphically aided input that is user friendly and intuitiveInteractive diagnostics and feedback on input errorsFlexibility to select the measurement units desired by the userFlexibility for the user to select start and end times to perform the reconciliationFacility to construct mass-balance units based on plant configuration user inputReconciliation processes perform linear, nonlinear and inequality constraints on the measurement data to producereconciled measurements and unmeasured flow estimatesAlgorithm for efficient iteration and fast convergence to the solution. Some algorithms may include the Monte Carlo


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method to generate sets of random values for measurement errors within a prescribed range (%uncertainty) that are solvedand iterated in the reconciliation algorithmAlgorithm to ensure numerical robustness and prevent numerical runawayA reconciled mass balance at the processing unit level or group of processing units, progressing all the way up to the plantlevelAbility to reconcile total mass and selected component fractions at the same timeReporting tool to verify the present error in balance for each node and generate the customized reports.

Mass balance and reconciliation.

Data reconciliation3,4 improves process data accuracy by adjusting the measured values so that they satisfy the processconstraints. The amount of adjustment made to the measurements is minimized since the random errors are expected to besmall. Data reconciliation can be formulated by the following constrained weighted least-squares optimization problem:

Minimize the function (known as objective function):

Where n is the number of measurements, M is the difference between the reconciled and measured values ofmeasurements, i and si is the measurement i standard deviation. The value 1/s2 which is an inverse of variance (square ofstandard deviation) is the weight factor representing the accuracy of the respective measurements. Since a higher value ofstandard deviation implies that the measurement is less accurate, the above choice gives larger weights to more accuratemeasurements.

The above objective function minimization is subject to constraints:

fj(Mi 1 DMi) =0j = 1,....m

Where f is the balance equation for the measurements (i = 1,....n) and m is the number of balance equations.

During the reconciliation process, the measurements containing systematic bias or gross errors are detected by comparingthe difference between the reconciled and measured values to the measurement uncertainties.

If Abs(DMi/ Mi) > Uncertainty, measurement i has gross error.

The measurements containing gross errors are either eliminated or appropriately compensated for data reconciliation to beeffective, as shown in Fig. 1. In this example, the reconciliation involves:M1 = stream 1 cumulative measured mass flow over a period (a day, for example)M2 = stream 2 cumulative measured mass flow over a periodM3 = stream 3 cumulative measured mass flow over a periodM4 = measured mass inventory gain or depletion over the same period


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Fig. 1. Flow reconciliation example for a storage tank.

It is evident that because of measurement errors these measured quantities do not balance, namely:

M1 1 M2 fi M3 1 M4

Therefore, reconciliation is required; adjustments to each of the measured quantities need to be made to obtain a massbalance:

(M1 1 DM1) 1 (M2 1 DM2) = (M3 1 DM3) 1 (M4 1 DM4)

where Mi is an adjustment (+ve or ve) for the measured quantity Mi.It is evident that there are infinite sets of Mi, each of which will give the desired mass balance, i.e., they will satisfy theequation above. Of the infinite sets of Mi , the one particular set that corresponds to the least amount of total adjustmentis required. This suggests that the problem to find this particular set of Mi can be formulated as one that entailsminimizing a function (usually referred to as objective function) subject to some constraints (mass-balance equations). Forthe simple example here, the problem of finding that particular set of Mi can be formulated as:Minimize the objective function:

Subject to the constraint:

(M1 1 DM1) 1 (M2 1 DM2)

(M3 1 DM3) (M4 1 DM4) = 0

Where si is the uncertainty associated with the instrument that gives the measured quantity, Mi.

The use of uncertainties for reconciliation can be explained with this example. Assume that a flowmeter M1 with percentuncertainty at 95% confidence level (%U95) as 2% is reading 300 kg during a certain time period. Since the 95%confidence level corresponds to two standard deviations, 2s1, the standard deviation error, s1, for this measurement can becalculated as 3 kg as:

Therefore, the weight factor, (1/s12), for measurement M1 in the objective function above is 1/9. Suppose if the reconciledflowrate for M1 is 307 kg, then the reconciled error (difference between the reconciled value and the measured value) is 7 kg.This value is greater than the 6 kg error (95% confidence) calculated. This means that measurement M1 has a gross errorand should be eliminated or properly compensated for effective reconciliation.

FLOW CORRECTIONS

Process industry flowmeters can be classified into three broad categories that include differential-pressure meters, actualvolumetric flowmeters and mass flowmeters. The differential-pressure meters include orifice, venturi, nozzle, wedge, pitottube and annubar; volumetric flowmeters include vortex, turbine, ultrasonic and magnetic; and mass flowmeters includeCoriolis and thermal meters. The meter operating principles and flow equations are provided in Appendix A.


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For any of these flowmeters, the vendor should make sure that the flowmeters measured outputs are in the UOM requestedin the flowmeter specification datasheet. For this, the vendor calculates the conversion factor by using the design densitydata (or pressure, temperature and molecular weight data for gases) specified on the datasheet to output measured values inthe desired UOM.

During process operation, the measured density (or P, T, MW and z for gases) values may not be the same as the values onthe datasheet. Therefore, the measured flowrates should be corrected to account for the measured process conditions. Thecorrection factors for various flowmeters using different UOM are provided in Table 1. The details of the flowmetercorrection calculation are available in Appendix B.

Flow uncertainty equations. Uncertainty, U95, is a statistical statement of measurement accuracy that is useful in:Defining tolerances for reconciling measurements with concurrent gross-error detection and eliminationEstimating accuracies when reporting to government on measurements that impact royalties and emissionsEvaluating custody-transfer metering performance.

Uncertainty is a measurement process characteristic. It provides an estimate of the error band within which the true valuefor that measurement process must fall with high probability.5 It is based on the probability of 95% that is twice thestandard deviation, 2s. The 95% confidence level for the estimated flowmeter uncertainty is in accordance with prudentstatistical and engineering practice.

Flowmeter uncertainty is actually a function of both bias (systematic or gross error) and precision (random error), as shownin Fig. 2. Flowmeter part manufacturers follow rigorous testing and calibration to remove or randomize the measurementbiases. In Canada, they follow the standards by Measurements Canada, and in the US, the test method follows the NationalBureau of Standards (National Institute of Standards and Technology). The values used for the precision may be obtainedfrom manufacturers specifications for the respective equipment provided that the values are adjusted to reflect operatingconditions.


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Fig. 2. Bias and precision errors.

To calculate the uncertainty values, the significance of each variable (parameter) in the flow calculation equation isexamined and is related to flow measurement. It is assumed that the meter has been properly installed, operated andmaintained. It is also assumed that the systematic equipment biases are randomized within the database, which means thatvariations in the equipment and laboratories will not impose any bias in the equations ability to represent reality.

For practical considerations, the pertinent variables are assumed to be independent to enable simpler uncertaintycalculations. It was noted that the simplified uncertainty equations would provide very good uncertainty estimates.6 Themathematical relationships among the variables establish the sensitivity of the metered quantities to each of these variables.Each variable that influences the flow measurement uncertainty has a specific sensitivity coefficient. The uncertainty for ageneral equation Q = f(x1, x2,.....xN) can be derived analytically by partial differentiation based on propagation ofuncertainty by the Taylor series.

Refer to Appendix C for derivation using the Taylor series. The uncertainty in Q can be given as:

This can be represented in a simpler form as:

where dQ/Q is the uncertainty in Q, Sx is the sensitivity coefficient associated with the variable and Ux is the variableuncertainty. The uncertainty equations are derived for differential pressure, volumetric and mass flowmeters in Appendix Dusing the flow equations representing the basic operating principle.

FLOWMETER UNCERTAINTY

Uncertainty for orifice, venture or nozzle meter measuring in standard flow is given by:


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The same equation above can be used for a wedge meter; however, the deviation in the equivalent diameter, d, for a wedgemeter is calculated by using:

where:

Uncertainity equations for vortex, turbinem ultrasonic and coriolis flowmeters are in Appendix D.

Measured flowrate correction.

An orifice meter is used in a refinery to measure the flowrate of liquid hydrocarbons and it is calibrated to indicate(readout) flowrate in standard volumetric flows. For example, design stream conditions indicated on the flowmeterspecification datasheet are:TD = Design temperature = 300CPD = Design pressure = 1,500 kPaarD_Std = Design standard density = 950 kg/m3 (normally obtained from process simulation)rD = Design actual density = 750 kg/m3 (normally obtained from process simulation).

During actual operation, the measured conditions are:TM = Measured temperature = 310CPM = Measured pressure = 1,500 kPaarM_Std = Measured standard density = 960 kg/m3 (measured in the laboratory using the sample)rM = Measured actual density = 740 kg/m3 (measured, or calculated using an appropriate correlation).

For liquid flows, if the measured densities are not available at the actual operating conditions, the established correlationscan be used. It should be noted that these correlations may result in some error in the density predictions.

Actual liquid hydrocarbon stream density can be estimated using the equation by Yawas:7

For C20 and heavier alkanes, the densities can be obtained using the method by Fisher:8


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where SGm is specific gravity at measured temperatureSGr is the specific gravity at reference temperatureTm is measured temperature in KelvinTr is reference temperature in C.

A method for calculating actual density using liquid critical properties is given by Noor:9

where rm = Density at measured temperature in kg/m3,M = Molecular weight,VC = Critical volume in m3/kgTm = Measured temperature in KelvinTC = Critical temperature in Kelvin.

From Table 1, the correction factor for the orifice meter with indicated (readout) liquid flowrate at standard conditions isgiven by:

and the corrected flowrate at standard conditions is given by:

QStdVol_Corr = QStdVol_Meas 3 Correction Factor

If the flowmeter indicated (readout) flow is 600 std. m3/d, then the corrected flowrate at standard condition is:

= 589.8 Std m3/d ~ 590 std. m3/d

Uncertainty calculation.

A 3-in. orifice meter run with a b ratio of 0.6 is selected for the previous liquid hydrocarbon flow measurement example at astatic pressure of 1,500 kPaa and flowing temperature of 310C. Differential pressure recorded for the flow is 25 kPa and theflowrate is 590 std. m3/h.

The variable sensitivity coefficients can be calculated using the orifice uncertainty equation:


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The uncertainty values for the variables dx/x at 95% confidence level, U95, can be obtained from industry standards andprocedures (AGA, API, ASME, ASTM) and/or manufactures specifications for the equipment or parts. For each variable,the uncertainty listed in Table 2 represents random errors only, which are obtained from AGA RP-3-1.

Based on the calculations, the standard volumetric flow measurement uncertainty at 95% confidence level is 0.76%. Formass flow measurement uncertainty, the standard density variable, rStd, in the above equation is excluded, which gives the %U95 value of 0.58%.

APPENDIX A

The operating principles and flowmeter equations are listed in this appendix for the flowmeters as shown in Fig. 3.


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Fig. 3. Examples of various flowmeters used by industry.

Differential pressure flowmeters.

The flowmeters that measure differential pressure to calculate the flowrates can be classified as differential pressureflowmeters.

Orifice, venturi and nozzle flowmeters. For fluid flow in an orifice, venturi or nozzle flowmeter, the actual volumetricflowrate can be given as:10

where d is the orifice diameter for an orifice meter or throat diameter for venturi and nozzle meters,P1 = Pressure at the upstream pressure tap,P2 = Pressure at the downstream pressure tapr1 = Density at P1 pressure condition.Cd = Discharge coefficient to account for frictional losses (kinetic energy into heat) due to viscosity and turbulence effects.Eu is the velocity approach factor that relates the flowing fluid velocity in the meter approach section (upstream meter tube)to the orifice/throat fluid velocity:

where b = d / D is the orifice bore (or throat for the venturi and nozzle) to pipe inner-diameter ratio.

Y is the expansion factor to account for the gas compressibility that is given by:

where k is specific heat ratio CP/CV. For b less than 0.25, b4 value approaches zero in the equation.

Pitot tube or annubar flowmeters (for velocity less than 30% of sonic velocity). For fluid flow in a Pitot tubeflowmeter, the actual volumetric flowrate can be given as:

Where: K = Instrument coefficient that is usually determined through calibration,D = Pipe inside diameterP = Pressure drop measured by the Pitot tube, which is the difference between the total (stagnation) pressure, Pt, and thestatic pressure, Ps.

Wedge flowmeter (used for liquid flows only). For liquid flow in a wedge flowmeter, actual volumetric flowrate canbe calculated using the orifice equation:


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where d is equivalent orifice diameter that is calculated using equivalent beta ratio:

where H = wedge segment opening height,D = Pipe inside diameter,P = Pressure drop across the orificerAct = Liquid density at actual temperature and pressure conditions, T, P.Cd is the wedge meter discharge coefficient to account for frictional losses (kinetic energy into heat) due to viscosity andturbulence effects.Eu is the velocity approach factor that relates the flowing fluid velocity in the wedge meter approach section (upstreammeter tube) to the fluid velocity in the wedge section.

where b is d/D which is equivalent orifice to pipe inner diameter ratio.

Volumetric flowmeters.

The flowmeters that directly interpret the actual volumetric flow from other measured parameters are called volumetricflowmeters. To interpret the velocity, vortex meters use vortex shedding frequency; ultrasonic meters use sound transit time;and magnetic meters use voltage induced in the fluid (conductive) flowing through an imposed magnetic field.

Vortex flowmeter. A vortex flowmeter measures the volumetric flowrate by using the vortex shedding frequency caused bya flow barrier.11

Strouhal number, S, is related to vortex shedding frequency by S = fw / u

where f = Vortex shedding frequency that depends on flow velocity, fluid viscosity and flow barrier dimensions (bluff, whichis either a cylinder or a square column) used to create vortexw = Flow barrier width (bluff)u = Fluid velocity in the bluff section.

Actual volumetric flowrate can be given by:

where D is the pipe inner diameter

and B is the blockage factor that is defined as the pipe bore area less the bluff body blockage area, divided by the pipe fullbore area:


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where K factor is used to compensate for the pipe flow nonuniform profile in industrial applications. Combining the aboveequations the actual flowrate is given as:

The Strouhal number, S, is about constant across a wide Reynolds number range of (102107). The S value depends on thebluff width to the pipe inner diameter ratio. S = 0.18 for w/D = 0.1; S = 0.26 for w/D = 0.3; and S = 0.44 for w/D = 0.5.

Turbine flowmeter. A turbine flowmeter measures the volumetric flow by counting the rotor revolutions (rotor angularvelocity) that turns in proportion to the flow velocity.1214 The equation for a turbine meter can be given as:

utan(theta) = Kr(omega)

where u = Incoming flow velocity,Theta = Angle between the pipe axis (incoming flow direction) and the turbine blades,r = Root-mean-square value of the blade inner and outer radii to represent the average radius,K = Instrument factor to compensate velocity loss (nonidealities) due to rotor blade design and omega is the rotor angularvelocity.

where ro = Blade radius outer edge and ri = Radius blade root.

Actual volumetric flowrate can be given by:

Ultrasonic flowmeter. An ultrasonic flowmeter measures the volumetric flow by using sound pulse transit time in theflow medium caused by doplar effect.1517 A typical ultrasonic flowmeter (transit-time flow measurement) system utilizestwo ultrasonic transducers that function as both transmitter and receiver. The flowmeter operates by alternatelytransmitting and receiving a sound energy burst between the two transducers and measuring the transit time that it takesfor sound to travel between the two transducers. The difference in the transit time measured is directly and related to theliquid velocity in the pipe.

If tD is the sound pulse transit-time (or time-of-flight) traveling from the upstream transducer to the downstreamtransducer, and tU is the transit-time from the opposite direction, the equations can be given as:


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where theta = Angle between the transducer axis to the flow direction,c = Sound speed in the liquid,D = Pipe inside diameteru = Flow velocity averaged over the sound path. Solving the above equations leads to:

where tf = (tU tD) / (tUtD) is the transit-time function and K is the instrument factor determined through calibration.Therefore, by accurately measuring the upstream and downstream transit-times, tU and tD, the flow velocity, u, can beobtained.

Actual volumetric flowrate is calculated as:

where A is the pipe inner cross-section area.

Magnetic flowmeter. Magnetic flowmeter operation is based on Faradays Law that states that the voltage induced acrossany conductor as it moves at right angles through a magnetic field is proportional to the conductor velocity.18 To apply thisprinciple the fluid being measured must be electrically conductive.

The voltage, E, generated in a conductor is given by:

E (alpha) BLu

where:E = Voltage generated in a conductorB = Magnetic field strength perpendicular to the flow directionL = Distance between the electrodes (usually equal to pipe inside diameter in most construction)u = Conductor velocity.

The fluid velocity can be given by:

where K is the instrument coefficient that is usually determined through calibration.

Subsequently, the actual volumetric flow rate is calculated as:

where A is the pipe inner cross-section area and D is the pipe inside diameter.

Mass flowmeters.


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A coriolis flowmeter directly measures the mass flow based on the inertial forces exerted on the tube vibrations.1921 Whenan oscillating excitation force is applied to the tube, causing it to vibrate, the fluid flowing through the tube will induce atwist (or rotation) to the tube because of the Coriolis acceleration acting in opposite directions on either side of the appliedforce.

In a U-tube coriolis meter, the flow is guided into the U shaped tube that is vibrated using an actuator. The vibration iscommonly introduced by electric coils and measured by magnetic sensors. When the tube is moving upward during the firsthalf of a cycle, the fluid flowing into the meter resists being forced up by pushing down on the tube. On the opposite side, theliquid flowing out of the meter resists having its vertical motion decreased by pushing up on the tube. This action causes thetube to twist. When the tube is moving downward during the second half of the vibration cycle, it twists in the oppositedirection. The two vibrations are shifted in phase (time lag) with respect to each other, and the degree of phase-shift isdirectly affected by the mass passing through the tube.

A U-shaped Coriolis flowmeter mass flow is given as:

where Ku = Tube stiffness,K = A shape-dependent factorL = Width,t = Time lag, omega = Vibration frequencyIu = Tube inertia that includes the tube fluid mass. The expression can be simplified as:

where:

is the natural frequency of the U-shaped tube system.

Thermal flowmeter.

A thermal flowmeter measures the mass flow based on heat absorption. As molecules of a moving fluid come into contactwith a heat source, they absorb heat and cool the source. At increased flowrates, more molecules come into contact with theheat source absorbing even more heat. The heat dissipated from the source in this manner is proportional to the number ofmolecules of a particular gas (its mass), the gas thermal characteristics, and its flow characteristics. The mass flow of athermal mass flowmeter can be given as:

QMass = K Hwhere K is the instrument coefficient which is usually determined through calibration, and H is the amount of heatdissipated from the heat source.

APPENDIX B: FLOWMETER CORRECTION CALCULATIONS


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Flow correction for differential pressure flowmeters.

Actual flow for differential pressure meters is calculated using:

Assuming incompressible fluid in the range of interest (constant fluid density between the flowmeter pressure taps) theactual flowrate measured by the flowmeter can be given as:

Liquid flowmeter (actual volumetric flow measurementact. m3/h). The equation for corrected flow is:

Liquid flowmeter (standard volumetric flow measurementstd. m3/h). Standard volumetric flow is calculated using:

The equation for corrected flow is:

Liquid flowmeter (mass flow measurementkg/h). Mass flow is calculated using:

The equation for corrected flow is given by:


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Gas flowmeter (actual volumetric flow measurementact. m3/h). The equation for corrected flow is:

Gas flowmeter (standard volumetric flow measurementstd. m3/h). Standard flowrate is:

The equation for corrected flow is given by:

Gas/steam flowmeter (mass flow measurementkg/h). The equation for mass flow is:


Flow correction for volumetric flowmeters.

Actual flow measured by the volumetric flow is:Vortex meter: QActVol fvTurbine meter: QActVol omegaUltrasonic meter: QActVol f (TUP, TDown)Magnetic meter: QActVol E

Liquid flowmeter (actual volumetric flow measurementact. m3/h). The equation for corrected flow is:

Liquid flowmeter (standard volumetric flow measurementstd. m3/h). Standard volumetric flow is calculated using:


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Liquid flowmeter (mass flow measurementkg/h). Mass flow is calculated using:


Gas flowmeter (actual volumetric flow measurementact. m3/h). The equation for corrected flow is:

Gas flowmeter (standard volumetric flow measurementstd. m3/h). Standard volumetric flow is calculated using:


Gas/steam flowmeter (mass flow measurementkg/h). The equation for mass flow is:


Flow correction for mass flowmeters.


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Mass flowrates for the mass flowmeters is:Coriolis meter: QMass tThermal meter: QMass DH

Liquid flowmeter (actual volumetric flowact. m3/h). Actual volumetric flow is calculated using:


If the coriolis meter has an integral density measurement and uses the operating density (or flowing density) instead ofdesign density, rD , in the above equations, then correction factor is equal to 1.

Liquid flowmeter (standard volumetric flowstd. m3/h). Standard volumetric flow is calculated using:


Liquid flowmeter (mass flowmeterkg/h). Equation for corrected flow is:

QMass_Corr = QMass_Meas

The correction factor required for correcting the flowmeter reading is equal to 1.

Gas flowmeter (actual volumetric flow measurementact. m3/h). Actual volumetric flow is calculated using:


If the coriolis meter has an integral density measurement and uses the operating density (or flowing density) in the aboveequations instead of design density, then correction factor is equal to 1.

Gas flowmeter (standard volumetric flow measurementstd. m3/h). Standard volumetric flow is:


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Gas flowmeter (mass flowmeterkg/h). The equation for corrected flow is:

QMass_Corr = QMass_Meas

APPENDIX C: PROPAGATION OF UNCERTAINTY BY TAYLOR SERIES

The sensitivity coefficient associated with each flow variable is derived analytically by partial differentiation based onuncertainty propagation by the Taylor series [ASME-MFC-2M, 1983]. The relationship of dependent variable Q withindependent variables x1, x2,..., xN can be expressed in a general form as:

Q = f (x1, x2,..., xN)

Using the Taylor series the uncertainty in Q can be expressed as:

Squaring on both sides, the equation can be written as:

Given that the variables are uncorrelated (independent), i.e., (delta)xi (delta)xj = 0 (i j), all the values of the summation inthe above equation will be zero. Therefore, the uncertainty in Q can be given as:

which can be represented in a simpler form as:


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where (delta)Q/Q is the uncertainty in Q, Sx is the sensitivity coefficient associated with the variable, and Ux is theuncertainty of the variable.

APPENDIX D: UNCERTAINITY EQUATIONS FOR VORTEX, TURBINE, ULTRA SONIC ANDCORIOLIS

Vortex flowmeter uncertainty is:

Turbine flowmeter uncertainty is:

Ultrasonic flowmeter uncertainty is:

Coriolis flowmeter uncertainty is:


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NOMENCLATURE

Subscript DDesign values from flowmeter specification datasheetSubscript MMeasured values during plant operationMMolecular weightPPressure, kPaaPPressure drop, kPaQFlowrateQMassMass flowrate, kg/hQActVol Volumetric flowrate at actual operating conditions, act. m3/hQStdVol Volumetric flowrate at standard conditions (15C and 1 atm.), std. m3/hQMass_MeasMeasured (readout) mass flowrate from the flowmeter, kg/hQActVol_MeasMeasured actual volumetric flowrate (readout) from the flowmeter, act. m3/hQStdVol_MeasMeasured standard volumetric flowrate (readout) from the flowmeter, std. m3/hQMass_Corr Corrected mass flowrate for the flowmeter, kg/hQActVol_Corr Corrected actual volumetric flowrate for the flowmeter, act. m3/hQStdVol_Corr Corrected standard volumetric flowrate for the flowmeter, std. m3/hRUniversal gas constant (R = 8.3145 kPaa m3/kmol K)SSensitivity coefficientTTemperature, KUUncertaintyU95 Uncertainty at 95% confidence levelZCompressibility factor for gases (Z = 1 for ideal gas)sStandard deviationrMass density, kg/m3

rD Design density at actual conditions from flowmeter specification datasheetrM Measured (or calculated) density at actual conditions during operationrD_Std Design density at standard conditions from flowmeter specification datasheetrM_Std Measured density at standard conditions during operation

Acknowledgments

The authors thank their colleague Ken Fernie, P.Eng., for review and valuable comments on custody transfer metering, andAndrew Nelson, Production management manager from Matrikon Inc., his for review and valuable input on flow meteruncertainties.

LITERATURE CITED

1 Spitzer, D. W., Flow Measurement: Practical Guides for Measurement and Control, 2nd Edition, Research Triangle Park,NC: ISA, 2001.2 Upp, E. L. and P. J. LaNasa, Fluid Flow Measurement: A Practical Guide to Accurate Flow Measurement, GulfProfessional Publishing, 2nd Edition, 2002.3 Romagnoli, J. A. and M. C. Sanchez, Data Processing and Reconciliation for Chemical Process Operations, ProcessSystems Engineering, Vol. 2, Academic Press, 1st Edition, 1999.4 Ozyurt, D. B. and R. W. Pike, Theory and Practices of Simultaneous Data Reconciliation and Gross Error Detection for


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Chemical Processes, Computers and Chemical Engineering, 28, pp. 381402, 2004.5 ASME MFC-2M, Measurement Uncertainty for Fluid Flow in Closed Conduits, American National Standard, 1983(Revised 2006).6 AGA RP-3-1, Orifice Metering of Natural Gas and Other Related Hydrocarbon Fluids Part 1General Equations andUncertainty Guidelines, American Gas Association, June 2003. (API MPMS 14.3-1; ANSI/API 2530-91 Part 1; GasProcessors Association GPA 8185 Part 1).7 Yawas, C. L., et al, Equation for Liquid Density, Hydrocarbon Processing, Vol. 70, No 1, January 1991, pp. 103106.8 Fisher, C. H., How to Predict n-Alkane Densities, Chemical Engineering, Vol. 96, No 10, pp. 195, October 1989.9 Noor, A., Quick Estimate of Liquid Densities, Chemical Engineering, Vol. 88, No. 7, pp. 111, 6th April 1981.10 ASME MFC-3M, Measurement of Fluid Flow in Pipes Using Orifice, Nozzle and Venturi, American National Standard,2004.11 ASME MFC-6M, Measurement of Fluid Flow in Pipes using Vortex Flowmeters, American National Standard, 1998(Revised 2005).12 AGA RP-7, Measurement of Natural Gas by Turbine Meters, American Gas Association, February 2006.13 API MPMS-5.3, Measurement of Liquid Hydrocarbons by Turbine Meters, American Petroleum Institute, September2000.14 ASME MFC-4M, Measurement of Gas Flow by Turbine Meters, American National Standard, 1986 (Revised 2008).15 AGA RP-9, Measurement of Gas by Multipath Ultrasonic Meters, American Gas Association, April 2007.16 API MPMS-5.8, Measurement of Liquid Hydrocarbons by Ultrasonic Flow Meters Using Transit Time Technology,American Petroleum Institute, February 2005.17 ASME MFC-5M, Measurement of Liquid Flow in Closed Conduits Using Transit-Time Ultrasonic Flowmeters, AmericanNational Standard, 1985 (Revised 2006).18 ASME MFC-16M, Measurement of Liquid Flow in Closed Conduits with Electromagnetic Flowmeters, American NationalStandard, 1995 (Revised 2006).19 AGA RP-11, Measurement of Natural Gas by Coriolis Meter, American Gas Association, January 2003.20 API MPMS-5.6, Measurement of Liquid Hydrocarbons by Coriolis Meters, American Petroleum Institute, October 2002.21 ASME MFC-11M, Measurement of Fluid Flow by Means of Coriolis Mass Flowmeters, American National Standard, 1989(Revised 2003).

The authors

Subodhsen Peramanu has more than 15 years of experience in conceptual, front-end design and detailedengineering of upgrading and refining processes. He has authored papers on topics including hydrogenseparation and economics, bitumen characterization, and asphaltene solubility and reversibility. Dr.Peramanu was involved in commissioning and start-up of CNRL Horizon Upgrader and is working with CNRLThermal Team as a senior engineering specialist on in-situ oil recovery. He holds a BChemEng degree inchemical engineering from Institute of Chemical Technology (formerly UDCT), Mumbai, MTech degree fromIndian Institute Technology, Kanpur and PhD from University of Calgary.

Juon Wahs career in process engineering spans more than 30 years and covers conceptual design, FEED,EPC and detailed process and equipment design of major projects in refining, bitumen upgrading and oil andgas production facilities. At present, Mr. Wah is a consultant on process design and plant operations. At thetime of writing, he was working on an expansion project for the Horizon Upgrading complex of CNRL. Mr.Wah holds a BSc degree in chemical engineering from the University of Birmingham, UK, and a DiplmedIngnieur in chemical engineering and petroleum refining from the IFP, France.


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Richard von Brecht01.20.2013

This is an amazing article. to me. I'm unfamiliar with some of the nomenclature. I'd be interested seeing an expandedversion of your paper.

Muhammad FarhatUllah12.19.2011

It is really handy and valuable article.Thanks

William Blanco12.07.2011

To both of you, excellent and valuable work


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