Impact of entrained water on natural gas measurement

Material Information

Impact of entrained water on natural gas measurement
Simpson, David A
Publication Date:
Physical Description:
vi, 32 leaves : illustrations ; 29 cm

Thesis/Dissertation Information

Master's ( Master of Science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Mechanical Engineering, CU Denver
Degree Disciplines:
Mechanical engineering


Subjects / Keywords:
Natural gas ( lcsh )
Gas reservoirs -- Measurement ( lcsh )
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )


Includes bibliographical references (leaves 31-32).
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Science, Mechanical Engineering.
General Note:
Department of Mechanical Engineering
Statement of Responsibility:
by David A. Simpson.

Record Information

Source Institution:
University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
30674330 ( OCLC )

Full Text
David A. Simpson
B. S I.M., University of Arkansas, 1980
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado at Denver
in partial fulfillment of
the requirements for the degree of
Master of Science
Mechanical Engineering

This thesis for the Master of Science
degree by
David A. Simpson
has been approved for the
Department of Mechanical Engineering
' Date

Simpson, David A. (M.S., Mechanical Engineering)
Impact of Entrained Water on Natural Gas Measurement
Thesis directed by Associate Professor Richard S. Passamaneck
This paper discusses a method to quantify the error that entrained liquids
inteiject into field measurement of natural gas. This method is based on experiments
conducted on gas wells in the San Juan Basin of northern New Mexico and on a
review of the existing literature on the subject. The conclusion of this paper is that at
saturated conditions, a significant error occurs in measurement which is not
accounted for by standard correction factors. These errors are a function of fluid
properties and piping configuration. They can be quantified using flow parameters
that are normally captured (i.e., meter tube diameter, orifice diameter, differential
pressure across the orifice plate, and indicated volume flow rate).
This abstract accurately represents the content of the candidate's thesis. I recommend
its publication.
Richard S. Passamaneck

I would like to thank Amoco Production Company for providing the
opportunity to work on this project, the resources it required, and the people that
made it possible.
I would like to specifically thank Mr. Jimmie Penrod for providing invaluable
help with what can be done with oil-field equipment and expertise in making it
I would also like to thank my thesis committee members Dr. Richard S.
Passamaneck, Dr. William H. Clohessy, and Dr. R. Wayne Adkins.

1 INTRODUCTION.................................................1
Purpose of Investigation..................................3
Review of Literature......................................4
Calculation Methodology...................................7
Fluid Characteristics....................................10
Test Trailers............................................12
EFM Unit.................................................13
Moisture Analyzer........................................15
Dehydration Unit.........................................16
3 EXPERIMENTAL PROCEDURE......................................18
Heat Transfer Analysis...................................18
Data Collection..........................................20
Data Analysis............................................20
4 DISCUSSION OF RESULTS.......................................24
Verification of Results..................................25
5 CONCLUSION..................................................27
APPENDIX 1-COMPONENTS OF FLOW EQUATIONS.........................28
APPENDIX 2STATISTICAL ANALYSIS.................................30

1.1 Well Site..............................................................2
2.1 Site Schematic.........................................................6
2.2 Typical Orifice Meter Configuration....................................8
2.3 Test Trailers.........................................................12
2.4 Barton EFM Unit.......................................................13
2.5 Moisture Analyzer.....................................................15
2.6 Dehydration Unit......................................................17
3.1 Thermal Entry Length..................................................18
4.1 Project Results.......................................................24

Measurement of natural gas using a square-edged orifice meter depends on
many assumptions and empirical constants. One of the primary assumptions is that
the gas is dry, homogeneous, and that there is no liquid being carried by the gas. This
assumption is seldom accurate in wellhead measurement, and we do not understand
the effect of this inaccuracy at low gas-liquid ratios very well. One school of thought
(based on the work of Mr. Roy Schuster [1, pg 19] in 1958) suggests that errors will
be in favor of the seller by as much as 14% for very wet gas (i.e., 30,000 pounds of
liquid per million cubic feet of gas), and that the mechanism of the error is related to
"coning" of the liquid downstream of the meter which makes the meter plate
effectively thicker and effectively smaller. "Coning" is a phenomenon where the
pressure drop through the orifice plate causes the mixture to become locally super-
saturated and allows some of the excess liquid to drop out of the gas. Mr. Schuster's
theory goes on to say that the error is a linear function of the actual volume of fluid
passing through the plate and is independent of both fluid properties, system pressure,
and temperature.
An analysis by Mr. J.R. Wright [2, pg 39] in 1962, suggested that while liquids
in the gas stream (still in very large quantities) favor the seller, the error is strongly
dependent on both fluid characteristics and operating pressure. This data also
suggests that the slope of the Error vs. Liquid Content curve is much flatter than
Schuster calculated.
The current report deals with much lower liquid contentabout 20-100 pound
mass of liquid per million cubic feet of gas. The information in this report was

assembled using standard Electronic Flow Measurement (EFM) equipment (Barton
Industries model 1130) using the current calculation methods (i.e., AGA 3, Third
Edition [3] and NX-19 compressibility calculations), in-line continuous reading
moisture analyzers (Accupoint model FI 110, from MEECO, Inc.), Triethylene
Glycol (TEG) dehydration units (adjusted to dry the gas stream to about 7 pound
mass per million cubic feet of gas), and 2 inch (2.067 inch nominal inside diameter)
meter tubes mounted on test trailers. Figure 1.1 shows one of the well sites. This
photograph shows piping for the gas to flow through a fired separator to knock out
any free liquid hydrocarbons or free water, through a flexible hose to the first test
trailer, through a static mixer, past a moisture analyzer, through the test trailer's
mechanical separator,
down a meter tube,
through another
flexible hose, through a
second static mixer,
past a second moisture
analyzer, through the
TEG dehydration unit,
through a second test
trailer (identical to the
first, also with two moisture analyzers), and finally to the sales meter.
All data presented in this paper is in standard U.S. oil-field units where one
barrel (abbreviated "BBL") of liquid is 42 standard gallons, thousand cubic feet of gas
is abbreviated "MCF", and million cubic feet of gas is abbreviated "MMCF". Pound
mass will be indicated as "lbm" and pounds force will be "Ibf'. When a gas is referred

to as "wet" then it is a raw-gas stream that has not been processed through a
separator of any sort Gas out of a separator will be referred to as "saturated".
Purpose of Investigation
The intent of this project was to quantify the magnitude and nature of the
measurement error when an orifice meter is used to measure a saturated gas/water
mixture at the pressures, temperatures, and relative proportions of components
encountered in the San Juan Basin of northwestern New Mexico and southwestern
Colorado. This basin has the capacity to produce 3,000,000,000 standard cubic feet
of gas each day which (at March 1993, prices) is worth $4.5 million/day at the
wellhead. A systematic bias error of 0.5% would result in settlement errors of
$22,500/day (or over $8.2 million/year) at the wellhead.
Previous work in this field has evaluated much higher liquid content than is
found in the San Juan Basin. The gas-to-water ratios in the earlier tests have
approached the point where the analysis was looking at gas entrained in liquid instead
of a liquid in a gas (i.e., one MMCF of pure methane can weigh 50,000 lbm at
operating pressure and temperature, so an analysis of gas with water content of
30,000 lbm/MMCF is 3/8 water). At high water proportion, the effects are
mechanical (eg., the flowing fluid sees rougher pipe walls because of condensation on
the walls and more massive flow restriction because of coning) and this work has
shown that the mechanism of the induced error is a high differential pressure (hw in
Appendix 1) which results in a bias in favor of the seller. This high-liquid data has
tended to show a linear relationship between liquid content and error.

There are unpublished theories for low-liquid-content gas measurement which
shift the controlling mechanism from hw to the compressibility (Z/; in Appendix 1)
which could change the nature of the bias to favor the buyer.
The goals of this investigation are to:
1. Determine the controlling mechanism and nature of saturated-gas flow-
measurement error.
2. Develop methods to compensate for any bias.
3. Determine if coning of fluid downstream of the orifice plate is a factor
in low-water measurement error.
Review of Literature
Information on measuring gas with entrained fluids is included in publications
from the American Gas Association [3,4,6], the Society of Petroleum Engineers [5,7],
American School of Gas Measurement Technology [8], industry sources [9], and
previous Master's Theses [1,2,10],
These sources have reached the conclusions that at high water [5, pg 657]:
1. Free-liquid will accumulate downstream of the orifice plate.
2. Gas will lose energy due to the free-liquid surface being rougher than
the expected tube walls.
3. Energy will be lost by the gas in re-acquiring the liquid.
There is considerable disagreement among the earlier research as to whether the
error has a pressure dependency [2,10] or not [1], or a dependency on fluid
characteristics [10] or not [1], All researchers have seen a linear relationship between
percentage error and liquid content, but the slope of this relationship has varied
widely. Wichert [7] has presented a method of determining the slope of the line based
on liquid specific gravity (at both standard temperature and flowing temperature), the
molar density of the fluid, and the gas specific gravity.

I have been unable to locate any previous research that looked at water-content
data within an order of magnitude of the saturated conditions analyzed in this study.

Figure 2.1 shows the test apparatus schematically. This configuration provided
consistent measurement of both the saturated and dehydrated streams for comparison.
The measurement devices on
both of the test trailers and on
the sales meters are square
edged orifice meters which are
described in the next section.
The Barton EFM units on
the trailers were carefully
calibrated in Farmington, NM,
under the same ambient conditions of temperature, pressure, and humidity. The two
test trailers were carefully alternated between upstream and downstream from one
well to the next to minimize any bias errors. All of the parameters that go into the
flow calculation were determined independently for each test trailer on each well, so it
was possible to compute each of the various parameters' impacts on the calculation to
find the controlling mechanism.
Control runs were made with the dehydrator out of service on each wellthe
difference in volume between the two trailers was random and within the expected
0.5% error. We verified the readings from the moisture analyzers using a "stain
gauge," a portable electronic device, and shifting the Accupoint devices among the
sample points The readings were consistent within expected accuracy for all devices.
Figure 2.1 Site Schematic

When a fluid is coning, some of the free liquid will be trapped in the turbulent
region just downstream of the orifice plateeffectively reducing the orifice throat
diameter (d) and the P-ratio (i.e., the ratio of the orifice-plate throat diameter to the
tube diameter). This effect also makes the plate appear thicker (the calculations are
very sensitive to plate thickness since the underlying theory assumes an infinitely thin
plate). Mr. Nangea et. al. [5] suggested that the ability of the turbulent region to hold
liquid is limited by the energy of the turbulent region. When the energy increases to
some critical point, a slug of liquid is released into the flow. The downstream
moisture analyzer was intended to pick up these slugs. Short interval (i.e., each
minute) data was gathered to determine if slugs would show coning in this low-water
fluid. There was no evidence of coning on any of the wells tested.
Calculation Methodology
Volumetric flow measurement using a square-edged orifice plate is based on
Bernoulli's Equation along a streamline:
Y+rL+^=T+n ^+gZd
2 P0 2 p0
Where u is the average velocity (ql A),p is the pressure, p0 is the fluid density
(assumed to be constant in the derivation of Bernoulli's Equation), A is the cross-
sectional area, and q is the volume flow rate. Since all the meter runs in this test
were installed horizontally, the gz terms cancel, and the measurement is based on a
correlation that relates the pressure drop across a known change in diameter to
average fluid velocity by:
= pd ~pu
2 Po

The subscripts refer to upstream, or downstream of the orifice plate in figure
2.2. Since u=q/A, the left side of the equation above is:
u d _
' 4
^{d4 d4y
Assuming that the flow through an orifice plate is an adiabatic process (i.e., no
work is done on or by the system), then the pressure term above can be restated as:
Pd ~ Pu _
Po Pd P
If the expansion is isentropic, then an isentropic exponent (k) can be defined
such that: p{yPY is constant, and:
ip* p
pd U-i
Combining the right and left sides of Bernoulli's Equation.
8 q2 1 Mp, * ) 1 _ f Pul
7l2 W d4 J pd U-u ^Pd >
Bernoulli's Equation
assumes the flow is both
incompressible and
inviscid. For gas flow, the
inviscid assumption is a
reasonable first
approximation, but there is
significant change in
density (at normal operating velocities) as the gas goes through the orifice plate so the
Figure 2.2 Typical Orifice Meter Configuration

incompressible assumption is questionable. From this point, empirical and numerical
methods must be used to evaluate the terms of the equation to reach the
approximation that is commonly used today [6, pg 13]:
q = c'Jhpfnf
The c' factor (described in Appendix 1) has traditionally been assumed to be
relatively constant, and was seldom updated. Current EFM technology reduces the
effort required to update c', and it is corrected more often today than in past years.

Fluid Characteristics
A detailed gas analysis was performed to accurately determine the content of
various components of the gas. The range of these components was:
Minimum Mole % Average Mole % Maximum Mole %
Nitrogen (N2) 0.435 0.621 1.238
Carbon Dioxide (C02) 0.712 0.812 1.044
Methane (CH4) 78.236 84.746 86.944
Ethane (C2H6) 7.334 8.168 11.358
Propane (C3H8) 2.517 3.418 5.493
Iso-Butane (C4H10) 0.385 0.473 0.722
Butane (C4H10) 0.559 0.834 1.141
Iso-Pentane (C5H12) 0.206 0.284 0.361
Pentane (C5H12) 0.161 0.241 0.292
Hexane (C6H14) 0.154 0.239 0.316
Heptane (C7H16) 0.071 0.130 0.218
Octane (C8HI8) 0.012 0.032 0.066
Nonane (C9H2o) 0.000 0.003 0.015
Ideal Total 100.000
The fluid data was obtained using a portable gas chromatograph that gives a
mole percentage on a dry-gas basis. To find the mole fraction of water (xj, use the
relationship [11, Pg 272]:
106scf Y lb-molto } = xwMw _______________
v_ w/ KMMCF )\tt0.69scf ) 3.8069 x 10^(l -xj
The moisture content of the gas (Whc) is the reading from the moisture analyzer
(lbm/MMCF), the Mw term is the molecular weight of water (18.01534 lbm/lb-mole),
so the mole fraction of water can be determined by rearranging this equation to:
W =^
* fl-:


0^(3.8069 xHT*)
18.01534 + ^(3.8069x 10^)
The chromatograph output of each component (x,) can be corrected for water
content by (x, )coiiected = (1 xw )(x,)_,. The amount of water vapor that the gas
can carry is a function of fluid temperature and pressure. As fluid temperature
changes with ambient temperature, the amount of water in the gas also changes.
Consequently, during the course of this study it was necessary to recalculate the
relative mole fractions for each data point. Using the adjusted gas composition and
current flow conditions, I was able to recompute fluid density (p), compressibility
(Zy), and the super-compressibility factor (fpv) for each reading. Using AGA Report
Number 8 [4] calculations:
zf = 1 + ^ D £ Cj- + £ c;r' (i c,k,D- )z+ exp(-c£>*-)
A n=13 n=13
Where: 2f = Compressibility factor
B =
K =
D =

k =
Second virial coefficient
Mixture size parameter
Reduced density
Coefficients which are functions of composition
Constants from "Table 4" of AGA-8 [4, pp 22-23]
The super-compressibility can be calculated using [6, pg 15]:
The Zb term is the compressibility of the dehydrated gas at base conditions. The
molecular weight of a gas is the gas ideal specific gravity (G,) times the molecular
weight of dry air (28.9625 lbm/lb mol), so the flowing density is [6, pg 19]:

p =
( 28.9625lbmmr V144in2 Y G,
/Z> mol j

= 2.69881G,
f Pf )
Where Pf is the static pressure (in psia) of the gas, TJris the fluid temperature
(in Rankine), and R is the universal gas constant (1545.35 ft-lbf/lb mol-R).
Test Trailers
The test trailers have both 2 inch and 3 inch meter tubes with flange taps. This
test used the 2 inch tubes. Figure 2.3 shows one of the trailers. The meter tubes on
these trailers were cleaned and inspected before the test. The mechanical separator
on the trailers has a
positive displacement
liquid measurement
totalizer--no liquid
was measured on
these totalizers.
Considerable care
was taken to make
certain that any trace
liquid that might have
been in the separators was drained before the trailers were moved to the next
The test trailers were tested and certified for accuracy at the Colorado
Engineering Experiment Station, Inc. in November 1990. At that time the two inch

run was certified to be accurate to within 0.5% for 0.3024, 0.4838, and 0.6652 P-
EFM Unit
The data was collected on a Barton Model 1130 EFM Unit as shown in Figure
2.4. The Barton 1130 was selected because of its excellent ability to accept standard
4-20 mA input signals. In addition
to the upstream (static) pressure,
plate differential pressure, fluid
temperature, and gas composition,
the Barton was able to store
ambient temperature and the output
of the two moisture analyzers. The
EFM units looked at flowing
temperature, static pressure,
differential pressure, and calculated
volume flow rate each second.
They captured (and stored) a
cumulative volume, average fluid
temperature, average static pressure, and average differential pressure each hour.
A complete 11-point calibration of the differential pressure cell, a 5-point
calibration of the static pressure cell, and a 2-point temperature calibration was done
on both EFM units in the shop prior to the first well and then again at each well. The
calibration checked out (with very minor adjustments) at each well site. The linear

input from the moisture analyzers was calibrated in the shop, and no further
calibration was needed. The setup of the EFM units was:
Calculate flow as Volume and energy
Display unit system is US (inch-pound)
Primary device is Differential producer
Device type is Orifice meter
Configuration is Flange taps
Static pressure tap is Upstream
Differential pressure mode is Single dP
Gas data for Z-factor is Mole fractions
Compressibility method is NX-19 analysis
Mole fractions obtained from Manually input
Energy calculation based on Volume flow rate
Gas gravity is Manually entered
Volume heating value is Manually entered
Gas component logging is Off
Daily/hourly history is 35 days
Flow direction is Forward
The NX-19 calculation was used on the Barton because at the beginning of the
test the AGA-8 calculation was not approved by industry. Later analysis of the fluid
density and mass flow rate used the AGA-8 calculations. At the test conditions, the
difference between the results of these calculations is on the order of 0.1%, and any
error caused by these slight differences is outside the accuracy of the measuring

Moisture Analyzer
The MEECO, Inc. Accupoint in-line moisture analyzer (Figure 2.5) was
selected for this test because of: (1) its advertised ability to work in harsh
environments, (2) its ability to work with
a range of fluids; and (3) its ability to
output a linear 4-20 mA signal. These
units proved to be less robust than
advertised. During the course of the test,
over 150,000 data points were taken
4% of these had all four MEECO's
operating and only 41% had the
minimum of two MEECO's operating.
Foreign matter getting into the cell
caused the majority of the downtime.
The cell was not field-repairable.
Changes were made to both piping and to operating procedures to attempt to reduce
the incidence of these failures. The piping configuration changes were: (1) static
mixers were installed two pipe diameters upstream of the sample probe (which was in
the center 1/3 of the pipe); and (2) Genie membrane filter-separators were put in as
secondary filters. Operationally: (1) filter-element changes on the Balston coalescing
filters were increased to weekly; (2) the flow-rate of gas to the cell was verified with a
bubble-gage each day; and (3) the cells were dried with high-pressure nitrogen before
connecting. The cells still failed.

When the MEECO's were operating, they did exactly what was expectedthe
results were verifiable and repeatable. Using the Barton units, we were able to record
moisture and ambient temperature data on a one-minute cycle. A very desirable
feature of the Accupoint was that each time one failed, it gave consistent readings
up to the minute it failedthere was no unreliable period prior to failure.
The basis for the operation of the Accupoint [12] is Faraday's Law. The
sample gas enters the cell at a constant 10 cc/min. flow rate. In the cell, there is a
phosphorus pentoxide (P205) coating on a wire that absorbs all of the moisture
molecules in the flow. A voltage applied across the wire electrolyzes moisture in the
film. Each electrolyzed water molecule causes two electrons to move from the anode
to the cathode. The electrolysis current gives the electrical charge displaced per unit
time. The relationship between moisture content and charge is based on the ideal gas
law (at 1 atmosphere and 25C) by:
N =
PV {\atm){0.U)
~RT~ 0 0825^.^,(298.16K.)
= 4.085x10 3/wo/
This calculation is linear over all ranges, and is easily converted into the 4-20
mA output range that was used for the recording devices used in this test.
Dehydration Unit
Each well included in this test has a Triethylene Glycol (TEG) dehydrator
(figure 2.6) permanently installed at the well site. These units use a contactor tower
to flow the saturated gas through dried TEG. The TEG has a higher affinity for water
than the gas, so the gas leaving the contactor is quite dry and the TEG has the water
(which is removed in the reboiler). The concerns with using this device for this test
were: (1) would the TEG absorb some gas along with the water; (2) would some

TEG flow along with the gas (changing its density); and (3) would the reboiler fuel
consumption show up as a measurement error?
The fuel-gas tap on the test wells was downstream of the last trailer, so no error
was introduced by the dehydrator consuming the gas. Computer models of the
operation of TEG dehydrators are readily available, and they showed that the
the orifice plate of the downstream trailer, but the amount of TEG was very slight and
should not have affected measurement accuracy. There is a potential that this slight
TEG carryover contributed to the failure rate of the Accupoint units.

These experiments were conducted on six different wells over a three month
period. During this period, ambient temperature varied over a range from 20F to 80
F. Day-to-night temperature changes frequently ranged over 30F, so it was crucial
that all data points be referenced to a fluid temperature. Through the use of
temperature probes and Heat Transfer analysis, it was determined that in all flow
regimes the fluid at the outlet moisture sampler was at ambient temperature for both
trailers. The fluid temperature at the upstream moisture analyzer was unpredictable,
so this data could not be used.
Heat Transfer Analysis
The method used to compute flow error (see Data Analysis below) depends
upon moisture readings being taken at the same fluid temperature. Since the outlet
temperature of the separator is not necessarily the same as the outlet of the
dehydrator, the only chance
of consistent readings was
to allow heat transfer
through the pipe walls to
adjust fluid temperature to
ambient. This mechanism could only be trusted if the thermal entry length (LE) were
less than the length of exposed pipe upstream of the downstream moisture analyzer.
Figure 3.1 shows the nature of this entry length.

The fluid at the start of the pipe run is at a homogeneous temperature with an
average velocity from 30-150 ft/sec. Using computer fluid models, the heat capacity
(cp) of these fluids under these temperature conditions is in the range of 1.640-1.684
BTU/lbm-R. The thermal entry length is [13, pg 232]:
Le = -L In
£ kDh
( T T ^
A M*)
Where: m Mass flow rate (m puA)
D = Pipe inside diameter
h = Average convection coefficient
Ts = Pipe surface temperature (assumed to be constant)
Tnii) = Fluid average temperature at distance x
Tmii)= Fluid average temperature at x = 0
The Average Convection Coefficient can be calculated by:
- wc
h =-In
The average fluid temperature at the orifice plate (46 feet from either the
separator or the dehydrator) is recorded each hour, the ambient temperature (which is
also the pipe wall temperature) is monitored each minute, and the range of possible
fluid temperatures out of the well site equipment is 50-100F. The worst possible
scenario had an entrance length of 55 ft which is considerably less than the 72 ft of
exposed pipe upstream of the downstream moisture analyzer.

Data Collection
Each hour, the EFM units recorded:
Cumulative volume flow rate for previous hour.
Cumulative energy flow rate.
Cumulative extended flow (i.e., -JhwPf jTf from the c' term)
Average flowing pressure at the upstream tap.
Average differential pressure.
Average flowing temperature.
Average ambient temperature.
Average upstream (of the orifice plate) moisture.
Average downstream moisture.
Each minute, the EFM unit measured the following data from each trailer:
Ambient temperature.
Current upstream and downstream moisture reading.
This information was loaded into a database along with gas composition data
for analysis.
Data Analysis
Beginning with the assumption that the downstream trailer would register the
most accurate flow rates (because it was measuring dehydrated gas), the flow error
was computed by
1. Calculating the mass flow rate at standard conditions for both trailers.
2. Computing the mass of water that was removed by comparing the
readings from the moisture analyzers and converting the result to a mass
flow rate of water.
3. Determining the mass of fluid that was unaccounted for per unit time.
4. Returning the unaccounted-for mass to a volume flow rate.
5. Calculating the measurement error as a percent of upstream volume flow

The mass flow rate was:
p <7
v MCF f
If W is the reading on the moisture analyzer (Ibm/MCF), then the mass of water
removed was:
W -W ^
upstream downstream

The upstream volume flow rate was used in this equation because I was trying
to relate the water removed to normal field measurement. If the more accurate
downstream rate is used, the result is to flatten the flow error curve slightly. The
unaccounted-for fluid is:
^upstream ^downstream
This can be converted to a volume flow rate by:
/ P upstream
So the percent error is:
Flow Error = 100
( <7io ^
^ upstream ,
The Flow Error term was often positive (i.e., the saturated measurement read
low and a positive adjustment was required to get to accurate measurement and the
error favored the purchaser), but it was just as often negative which favored the
seller. The magnitude of the Flow Error term was 11%. This error was much
higher than expected.
The first step in the statistical analysis (see Appendix 2 for the basic equations
used) was to try to fit a flow parameter to a straight-line relationship with the flow

error. The standard error of the estimate for flow error vs. another data element
would have values in the range of the data (i.e., 11%) and a good result would be
less than 2.2% (which is 10% of the data range). The coefficient of determination
should be in the range of 0.8-1.0 if the relationship is linear.
The attempt to fit the data to a straight line showed that the flow error was
loosely related to P-ratio, but was unrelated to ambient (or fluid) temperature, volume
flow rate, water content, differential pressure, or static pressure. Further, it was
unrelated to the Coefficient of Discharge (CD in Appendix 1), super-compressibility
(fpv), or fluid density.
The energy lost across the orifice plate was a term that seemed to encompass all
of the expected contributors to the error (i.e., fluid density, compressibility, P-ratio,
super-compressibility, dynamic pressure, and pressure drop). This term was
designated as Eop and it is the product of the superficial throat velocity (i.e., the
velocity uncorrected for pressure effects) of the fluid and the permanent pressure drop
across the plate (see Chapter 4 for the development of this term).
The parameters analyzed and the results of the analysis (for a fit to a straight
line) were:

Parameter Standard Error of the estimate (flow error) Coefficient of Determination
Reynolds number 2.91% 0.0862
3-ratio 3.65% 0.1789
AP/P 3.00% 0.0227
Throat velocity 3.28% 0.3341
Permanent pressure loss 3.29% 0.3308
Eop 3.24% 0.3311
Fluid density 4.00% 0.0106
Super-compressibility 4.02% 0.0003
Ambient temperature 4.00% 0.0108
Saturated water content 4.00% 0.0125
Measured differential pressure 3.25% 0.3464
This data indicates that the flow error is not a linear function of any of the flow
variables. The same relationships were then compared to a second through ninth
order polynomial with the same negative results. Next they were compared to ratios
of polynomials in several combinations (e g., a seventh order polynomial over a third
order polynomial, and vice versa).
When flow error was plotted as a function of the ratio of two second order
polynomials of EOP, the standard error of the estimate fell to 1.42% (which is within
6% of the data range) with a correlation coefficient of 0.878. This was the best result

A portion of the pressure drop across an orifice plate is recovered by the fluid
due to the fluid's compressibility. The portion that is not recovered (i.e., the
permanent pressure loss) is described by [14, pg 6-36]:
h, =(l-0.24p-0.52p2-0.16p3)/tw
The superficial velocity of the fluid through the throat of the orifice is:
in2 hr
Energy Lost in the Orifice Plate
vs. Percent Error
The product of these two
terms is:
77 .. j W
EoP Mihrou A 97fioo-
^ 27.688 inh20 ^
Analysis of the data showed a
strong relationship between the flow
error and &0P- This relationship
shown is figure 4.1. This function
tends toward zero error as the flow goes to zero. The accuracy of the measured data
at very low Eop was quite erratic, so data below Eop =200 was disregarded.
The equation for the regression line through the data is:
Flow Error
1.6759 2.8098 x 10-2 EQp + 2.5620 x 10-5 £2 ^
-1.3120 + 7.9344 x 10EQp 3.1249 x 10_6£2

Verification of Results
This model was easily tested on readily available data. In the San Juan Basin,
there are several gathering systems that have little or no fuel consuming equipment,
no dehydration, and minimal volume lost to other sources. There are seven of these
systems that gather the gas from about 200 wells and consistently show a volume at
the central aggregation point that is greater than the sum of the wellhead volumes.
There is no way to determine the exact system loss on each of these systems, but it is
certain that the central volume cannot be made up of more molecules of gas than the
wells produced
On one property, the Northeast Blanco Unit (NEBU), there are three primary
segregated gathering systems: Simms Mesa (24 wells), Pump Mesa (17 wells), and
Middle Mesa (54 wells). All three of these systems consistently show a gathering
gain. Applying the individual meter data to this model yielded the following results:

Simms Mesa 4 (MCF/mo.) ^adjusted (MCF/mo.) Adjustment
Wellhead Measurement 2,367,054 2,376,352 9,298
CPD Measurement 2,363,615 2,352,451 (11,164)
Gain (Loss) (3,439) (23,900)
Gain(Loss) % (0.15%) (1.02%)
Pump Mesa
Wellhead Measurement 1,287,884 1,294,882 6,998
CPD Measurement 1,423,521 1,395,547 (27,974)
Gain (Loss) 135,637 100,665
Gain (Loss) % 9.53% 7.21%
Mic die Mesa
Wellhead Measurement 3,515,450 3,502,918 (12,532)
CPD Measurement 3,589,221 3,333,614 (255,607)
Gain (Loss) 73,771 (169,304)
Gain (Loss) % 2.06% (5.08%)
NE BU Total
Wellhead Measurement 7,170,388 7,174,152 3,764
CPD Measurement 7,376,357 7,081,612 (294,745)
Gain (Loss) 205,969 (92,540)
Gain (Loss) % 2.79% (1.31%)
While this data is far from conclusive, in every case the model moved the
measurement closer to a value that is possible (away from a value that is clearly
impossible). The NEBU data had several data points where the Eop was well beyond
the range of data used to build the model. This sort of extrapolation frequently
produces invalid and/or misleading results, and should be avoided. Additional testing
should be done at these high velocities/pressure drops, but that testing is beyond the
scope of this study

The measurement error caused by gas saturated with water can be significant,
and it can favor either the buyer of the gas or the seller. The equation:
1.6759 2.8098 x 10~2£op +2.5620x \0~s E\p
Flow Error =------------------------------------- -f-
-1.3120 + 7.9344 x 1 O'4 EOP 3.1249 x 1 O'6 E2op
describes the error as a function of the energy lost from the fluid in passing through
an orifice plate. If the Error is positive, then the indicated flow rate is less than the
accurate flow rate (so the adjustment is positive) and the error favors the purchaser.
If the Error is negative then it favors the seller.
This equation yields good results for Eop in the range 200-4,000 ft-lbf/sec.
When it was applied to data outside this range, the results were inconclusive.
Keeping EOP in the range of 1,000 to 1,200 ft-lbf/sec minimizes the error. You can
control this factor with the P-ratio (a smaller plate increases the throat velocity for the
same volume flow rate while it also increases the pressure drop).
Contractual, technical, and cultural considerations will prevent using this (or
any) model to retroactively correct previous data, but this model provides an
operating range that can serve to minimize future errors. The energy lost in the plate
F =
in hr
[l-0.24p-0.52p2 -0.16P3)/i
27.6788ww 0
= 1.840
? MCFH by,
l-0.24p-0.52p2 -0.16p3)

The basis for calculating volume flow rate through a square edged orifice plate
is the relationship between the pressure drop across an orifice plate and rate of flow
through the plate This simple relationship is complicated by non-ideal behavior of
most commercial gases. The volume flow rate can be computed by:


Volumetric flow rate.
cD Coefficient of discharge CD C + 0.000511 p \ReJ for flange-tapped 0 17 / + 0.0210+0.0049 V rifice meter. rl 9000(3 V8L < Re. J J ( 106 \ < Re. > 0.35
P Diameter Ratio. () =
D Meter tube inside diameter adjusted to flowing temperature.
d Orifice plate throat diameter adjusted to flowing temperature.
c, Coefficient of discharge at an infinite pipe Reynolds Number for flange-tapped orifice meter. C, =0.5961 + 0.0291 (32 -0.2290(3 + 0.003(l-(3)A/, +tap term
M, Small pipe correction. If pipe inside diameter is greater than 2.8 inches, then Ml is zero, otherwise it is 2.8-D.
tap term = [0.0433 + 0.0712e~8VD 17 2 o ni 0.1145e \ -0.52 / r ^o/d] 1-0.2 < / \1.3l 2 1 J19000P V8 A Re. J J Tiufi nu ' p > <1-P\ >000(3 Y
LId(i-P) lD(l-P)J J ~ Re. ) /
R eD Reynolds Number for meter tub { QbPfir 1 ReD = 0.0114541 4 4 Tb2b{m, J e inside diameter.
& Volume flow rate at base conditions (in cubic feet per hour).

Ph Base pressure (14.73 psia).
Dynamic viscosity in pounds mass per foot-second (average value of 0.0000069 Ibm/ft-sec for natural gas).
Th Base temperature in Rankine.
7 Compressibility of air at 14.73 psia and 60F.
Cr Real gas specific gravity.
Ev Velocity approach factor. E 1 a/i-34
Y/ Expansion factor (upstream tap). Yx = l-(0.41 + 0.35p4)^j
Ratio of differential pressure to absolute static pressure at the upstream tap. K X| 27.01 Pfl
k Isentropic exponent. This factor is approximately 1.3.
K Differential pressure in inches of water at 60F.
pa Flowing pressure at the upstream tap in psia.
T( Flowing temperature in Rankine.
Zh Fluid compressibility at base conditions.
Fluid compressibility at upstream flowing conditions.
Because of practical considerations, the equation above is too unwieldy for use
field operations, and a c' (pronounced "c prime") factor is defined as:
c = (7709.61)(C)(£,)(^)(d!)

The standard error of the estimate (s) of the sample can be computed by:
s =

Where "yc" is the value predicted by a regression analysis for a given x-value,
is the sample value at that V, and N" is the number of sample points. An
acceptable result would be a standard error in the range of 10.0% of the data range.
The sample variance (s^) is a comparison of each of the _y-values in the data to
the average^ (.y) of all the data, as in:
A value for r of greater than 0.8 defines the relationship as a reasonable
approximation to the function proposed.
The coefficient of determination (r) can be calculated by:

[1] Schuster, R.A, "The Effect of Liquids Upon the Measurement of Gas by the
Orifice Meter as Determined by Full Scale Testing", Master's Thesis, Texas
College of Arts and Industries, June, 1958
[2] Wright, JR., "The Comparison of the Effects of Entrained Liquids on Orifice and
Rotary Meters in Gas Measurement", Master's Thesis, Texas College of Arts and
Industries, August, 1962
[3] Manual of Petroleum Measurement Standards, Chapter 14--Natural Gas Fluids
Measurement, Section 3--Concentric, Square-Edged Orifice Meters, Part 1
General Equations and Uncertainty Guidelines, Third Edition, September, 1992,
Published concurrently by American Gas Association as "AGA Report No. 3 Part
1", and Gas Processors Association as "GPA 8185 Part 1"
[4] Compressibility Factors of Natural Gas and Other Related Hydrocarbon Gases,
November, 1992, Published concurrently by American Gas Association as "AGA
Transmission Measurement Committee Report Number 8", and by the American
Petroleum Institute as "MPMS Chapter 14.2"
[5] Nangea, A.G., Reid, L.S., Huntington, R.L., Joyce, M.P., "The Effect of
Entrained Liquid on the Measurement of Gas by an Orifice Meter", Journal of
Petroleum Technology, June, 1965, pp 657-660
[6] Manual of Petroleum Measurement Standards, Chapter 14Natural Gas Fluids
Measurement, Section 3Concentric, Square-Edged Orifice Meters, Part 3
Natural Gas Applications, Third Edition, August, 1992, Published concurrently
by American Gas Association as "AGA Report No 3 Part 3", Gas Processors
Association as "GPA 8185 Part 3", and American National Standards Institute as
"ANSI/API 2530-1991 Part 3"
[7] Wichert, E., "Multi-Phase Flow Measurement by Orifice Meter", Society of
Petroleum Engineers paper number SPE 4688, 1973
[8] Mooney, C.V., "Effects of Entrained Liquid on Orifice Measurement",
Proceedings of the American School of Gas Measurement Technology, 1992, pp

[9] Washington, G., "Measuring the Flow of Wet Gas", Presented at the North Sea
Flowmetering Workshop, Stavanger, Norway, October, 1989
[10] Nangea, A.G., "The Effect of Entrained Liquid on the Measurement of Gas by
an Orifice Meter", Master's Thesis, University of Oklahoma, June, 1963
[11] Amyx, J.W., Bass, D M., Jr., Whiting, R.L, Petroleum Reservoir Engineering
Physical Properties, McGraw-Hill Book Company, 1960
[12] "ACCUPOINT MOISTURE TRANSMITTER, Instruction Manual for FI 10
and FI 120 Models" Revision 2, November, 1992
[13] Burmeister, L.C., Convective Heat Transfer, John Wiley & Sons, 1983
[14] Miller, R.W., Flow Measurement Engineering Handbook, Second Edition,
McGraw-Hill Publishing Company, 1989.
[14] Murdock, J.W., "Two-Phase Flow Measurement with Orifices", Journal of
Basic Engineering, December, 1962, pp 419-433
[15] Chisholm, D "Flow of Incompressible Two-Phase Mixtures Through Sharp-
Edged Orifices", Journal of Mechanical Engineering Science, The Institution of
Mechanical Engineers, 1977, pp 72-78
[16] Chisholm, D., "Research Note: Two-Phase Flow Through Sharp-Edged
Orifices", Journal of Mechanical Engineering Science, The Institution of
Mechanical Engineers, 1977, pp 128-130