Abstrict The present invention is a method and apparatus for monitoring
in real time the mass and energy flow rate of a gas through a pipeline.
The invention determines the mass flow ratio of a pipeline gas flowing
through a pipeline compared to sample gas tapped from the pipeline
line when the volumetric flow of pipeline gas through the pipeline
is measured by a linear flow meter. Sample gas tapped from the pipeline
is flowed to a chamber having a section with a fixed volume until
the pressure in the chamber section is substantially equal to the
pipeline gas pressure. The sample gas is maintained at substantially
the same temperature as the gas in the pipeline while the sample
gas is in the chamber section. A timer measures the time interval
for the sample gas to flow from the chamber section at a selected
rate for a calculated pressure drop the selected rate being controlled
by a flow controller. The mass flow ratio is computed using the
measured time interval and a signal from the linear flow meter.
The energy flow rate of the pipeline gas is determined by measuring
the energy flow rate of the sample gas and relating that value to
the mass flow ratio of the pipeline gas compared to the sample gas.
Claims We claim:
1. An apparatus to be used with a linear flow meter to measure
a ratio of a mass flow rate of a pipeline gas through a pipeline
compared to a mass flow rate of a sample gas tapped from the pipeline,
the apparatus comprising:
a chamber having a section with a fixed volume for containing the
sample gas, the sample gas being maintained at substantially the
same temperature as the pipeline gas in the pipeline when contained
in the chamber section;
means for routing the sample gas to the chamber section;
a valve for controlling the flow of sample gas to the chamber section;
a flow controller for flowing the sample gas from the chamber section
at a selected rate;
a pressure sensor for measuring the sample gas pressure in the
chamber section;
means for closing the valve when the sample gas pressure in the
chamber section reaches the pressure of the pipeline gas in the
pipeline; and
a timer for measuring a time interval for the sample gas to flow
from the chamber section at the selected rate beginning when the
sample gas pressure in the chamber section drops below a first pressure,
and ending when the sample gas pressure in the chamber section drops
below a second pressure, the first pressure being greater than about
one-half of the pipeline gas pressure in the pipeline and the second
pressure being less than about one-half of the pipeline gas pressure
in the pipeline; and
a controller which receives a signal from the timer and a signal
from the linear flow meter representing the volumetric flow of the
pipeline gas through the pipeline and derives the ratio of the mass
flow rate of the pipeline gas through the pipeline compared to the
mass flow rate of the sample gas.
2. An apparatus as recited in claim 1 further comprising means
for quickly reducing the sample gas pressure in the chamber section
from the pipeline gas pressure to the first pressure.
3. An apparatus as recited in claim 2 wherein the means for quickly
reducing the sample gas pressure in the chamber section from the
pipeline gas pressure to the first pressure comprises a second section
in the chamber.
4. An apparatus as recited in claim 1 further comprising a pressure
regulator for reducing the pressure of the sample gas before the
sample gas flows to the flow controller.
5. An apparatus as recited in claim 1 wherein the controller calculates
the mass flow ratio in accordance with the following function: ##EQU40##
where K.sub.x is a constant, f.sub.t is a signal from the linear
flow meter, t.sub.m is the time interval and C.sub.f is a correction
factor dependent on the pipeline gas pressure, temperature and composition.
6. An apparatus as recited in claim 5 further comprising a second
chamber located such that the sample gas flows through the second
chamber before it flows to the flow controller.
7. An apparatus to be used with a linear flow meter for measuring
the energy flow rate of a pipeline gas through a pipeline, the apparatus
comprising:
a chamber having a section with a fixed volume for containing the
sample gas, the sample gas being maintained at substantially the
same temperature as the pipeline gas in the pipeline when contained
in the chamber section;
means for routing the sample gas to the chamber section;
a valve for controlling the flow of sample gas to the chamber section;
a flow controller for flowing the sample gas from the chamber section
at a selected rate;
a pressure sensor for measuring the sample gas pressure in the
chamber section;
means for closing the valve when the sample gas pressure in the
chamber section reaches the pressure of the pipeline gas in the
pipeline;
a timer for measuring a time interval for the sample gas to flow
from the chamber section at the selected rate beginning when the
sample gas pressure in the chamber section drops below a first pressure,
and ending when the sample gas pressure in the chamber section drops
below a second pressure, the first pressure being greater than about
one-half of the pipeline gas pressure in the pipeline and the second
pressure being less than about one-half of the pipeline gas pressure
in the pipeline;
a sample gas energy flow rate meter for measuring the energy flow
rate of the sample gas; and
a controller which receives a signal from the timer, the linear
flow meter which represents the volumetric flow of the pipeline
gas through the pipeline the sample gas energy flow rate meter and
derives the energy flow rate of the pipeline gas through this pipeline.
8. An apparatus as recited in claim 7 wherein the sample gas energy
flow rate meter comprises:
a burner for burning the sample gas with air to form a flame; and
means for maximizing the flame temperature.
9. An apparatus as recited in claim 8 further comprising an air
mass flow meter for measuring the air mass flow rate of the air
burning the sample gas.
10. An apparatus as recited in claim 9 wherein the controller calculates
the energy flow rate in accordance with the following function:
##EQU41## where K.sub.x is a constant, f.sub.t is a signal from
the linear flow meter, t.sub.m is the time interval, .omega..sub.air
is the air mass flow rate and C.sub.f is a correction factor dependent
on the pipeline gas pressure, temperature, and composition.
11. A method for measuring a mass flow ratio ##EQU42## of a pipeline
gas through a pipeline compared to a sample gas tapped from the
pipeline, the method comprising the steps of:
measuring the volumetric flow rate of the pipeline gas through
the pipeline with a linear flow meter;
flowing the sample gas to a chamber having a section with a fixed
volume;
maintaining the temperature of the sample gas at substantially
the same temperature as the pipeline gas in the pipeline when the
sample gas is in the chamber section;
stopping the flow of sample gas to the chamber section when the
pressure in the chamber section reaches the pressure of the pipeline
gas in the pipeline;
flowing the sample gas from the chamber section after the flow
of the sample gas to the chamber section is stopped, thereby reducing
the sample gas pressure in the chamber section;
timing the interval of time t.sub.m for the sample gas to flow
from the chamber section at a selected rate beginning when the sample
gas pressure in the chamber section drops below a first pressure
and ending when the sample gas pressure in the chamber section drops
below a second pressure wherein the first pressure is greater than
about one-half of the pipeline gas pressure in the pipeline and
the second pressure is less than about one-half of the pipeline
gas pressure in the pipeline; and
deriving the mass flow ratio ##EQU43## of the pipeline gas through
the pipeline compared to the sample gas tapped from the pipeline
from a signal f.sub.t from the linear flow meter that is related
to the volumetric flow rate of the pipeline gas, and the time interval
t.sub.m.
12. A method as recited in claim 11 wherein the mass flow ratio
is derived in a control system.
13. A method as recited in claim 12 wherein the control system
calculates the mass flow ratio in accordance with the following
function: ##EQU44## where K.sub.x is a constant, f.sub.t is a signal
from the linear flow meter, t.sub.m is the time interval and C.sub.f
is a correction factor dependent on the pipeline gas pressure, temperature
and composition.
14. A method as in claim 13 further comprising the steps of:
flowing the sample gas to a second chamber of fixed volume;
stopping the flow of sample gas to the second chamber when the
pressure of the sample gas in the second chamber is greater than
or equal to a third pressure;
flowing the sample gas from the second chamber after the flow of
the sample gas to the second chamber is stopped, thereby reducing
the sample gas pressure in the second chamber;
timing the interval of time for the sample gas to flow from the
second chamber at the selected rate beginning when the sample gas
pressure in the second chamber drops below a third pressure and
ending when the sample gas pressure in the second chamber section
drops below a fourth pressure; and
determining a value for the correction factor C.sub.f in accordance
with the following function: ##EQU45## where P.sub.L is the pipeline
gas pressure, c is estimated using data stored in the control system
and b is estimated in accordance with the following function: ##EQU46##
where V.sub.1 is the volume of the chamber section, V.sub.2 is the
volume of the second chamber, P.sub.1 is the first pressure, P.sub.2
is the second pressure, P.sub.3 is the third pressure, P.sub.4 is
the fourth pressure, t.sub.m is the time interval for the pressure
in the chamber section to drop from P.sub.1 to P.sub.2 and t.sub.Y
is the time interval for the pressure in the second chamber to drop
from P.sub.3 to P.sub.4.
15. A method for measuring the energy flow rate of a pipeline gas
through a pipeline, the method comprising:
measuring the volumetric flow rate of the pipeline gas through
the pipeline with a linear flow meter;
flowing the sample gas to a chamber having a section with a fixed
volume;
maintaining the temperature of the sample gas at substantially
the same temperature as the pipeline gas in the pipeline when the
sample gas is in the chamber section;
stopping the flow of sample gas to the chamber section when the
pressure in the chamber section reaches the pressure of the pipeline
gas in the pipeline;
flowing sample gas from the chamber section at a selected rate
after the flow of sample gas to the chamber section is stopped,
thereby reducing the sample gas pressure in the chamber section;
timing the interval of time t.sub.m for the sample gas to flow
from the chamber section at a selected rate beginning when the sample
gas pressure in the chamber section drops below a first pressure
and ending when the sample gas pressure in the chamber section drops
below a second pressure wherein the first pressure is greater than
about one-half of the pipeline gas pressure in the pipeline and
the second pressure is less than about one-half of the pipeline
gas pressure in the pipeline;
measuring the energy flow rate of the sample gas; and
determining the energy flow rate of the pipeline gas through the
pipeline from a signal f.sub.t from the linear flow meter that is
related to the volumetric flow rate of the pipeline gas, the time
interval t.sub.m, and the energy flow rate of the sample gas.
16. A method as recited in claim 15 wherein the energy flow rate
of the sample gas is measured by:
burning the sample gas flowing from the chamber with air; and
adjusting the air flow so that the sample gas burns at maximum
flame temperature.
17. A method as recited in claim 15 wherein the energy flow rate
of the pipeline gas is determined in a control system.
18. A method as recited in claim 17 further comprising the step
of measuring the air mass flow rate of air burning the sample gas.
19. A method as recited in claim 18 wherein the control system
calculates the energy flow rate in accordance with the following
function: ##EQU47## where K.sub.x is a constant, f.sub.t is a signal
from the linear flow meter, t.sub.m is the time interval, .omega..sub.air
is the air mass flow rate and C.sub.f is a correction factor dependent
on the pipeline gas pressure, temperature and composition.
20. A method as recited in claim 19 further comprising the steps
of:
flowing the sample gas to a second chamber of fixed volume;
stopping the flow of sample gas to the second chamber when the
pressure of the sample gas in the second chamber is greater than
or equal to a third pressure;
flowing the sample gas from the second chamber after the flow of
the sample gas to the second chamber is stopped, thereby reducing
the sample gas pressure in the second chamber;
timing the interval of time for the sample gas to flow from the
second chamber at the selected rate beginning when the sample gas
pressure in the second chamber drops below a third pressure and
ending when the sample gas pressure in the second chamber section
drops below a forth pressure; and
determining a value for the correction factor C.sub.f in accordance
with the following function: ##EQU48## where P.sub.L is the pipeline
gas pressure, c is estimated using data stored in the control system
and b is estimated in accordance with the following function: ##EQU49##
where V.sub.1 is the volume of the chamber section, V.sub.2 is the
volume of the second chamber, P.sub.1 is the first pressure, P.sub.2
is the second pressure, P.sub.3 is the third pressure, P.sub.4 is
the fourth pressure, t.sub.m is the time interval for the pressure
in the chamber section to drop from P.sub.1 to P.sub.2 and t.sub.Y
is the time interval for the pressure in the second chamber to drop
from P.sub.3 to P.sub.4.
21. An apparatus that measures a ratio of a mass flow rate of a
pipeline gas through a pipeline compared to a mass flow rate of
a sample gas tapped from the pipeline for use with a linear flow
meter measuring the volumetric flow of the pipeline gas through
the pipeline, the apparatus comprising:
a chamber having a section with a fixed volume for containing the
sample gas, the sample gas being maintained at substantially the
same temperature as the pipeline gas in the pipeline when contained
in the chamber section;
a pressure sensor for measuring the pressure of the sample gas
in the chamber section;
a first line connected to the pipeline for routing the sample gas
to the chamber section;
a valve mounted in the first line for controlling the flow of the
sample gas to the chamber section;
a flow controller for flowing the sample gas from the chamber at
a selected rate;
a second line for routing the sample gas away from the chamber
to the flow controller;
a control for closing the valve when the sample gas pressure in
the chamber section reaches the pressure of the pipeline gas in
the pipeline;
a timer for measuring a time interval for the sample gas to flow
from the chamber section at the selected rate beginning when the
sample gas pressure in the chamber section drops below a first pressure,
and ending when the sample gas pressure in the chamber section drops
below a second pressure, the first pressure being greater than about
one-half of the pipeline gas pressure in the pipeline and the second
pressure being less than about one-half of the pipeline gas pressure
in the pipeline;
a third line for routing the sample gas away from the flow controller;
and
a control system for receiving signals from the pressure sensor,
the timer and the linear flow meter and for computing the ratio
of the mass flow rate of the pipeline gas through the pipeline compared
to the mass flow rate of the sample gas.
22. An apparatus as recited in claim 21 further comprising a second
chamber of fixed volume located in the second line so that the sample
gas flows through the second chamber before it flows to the flow
controller.
23. An apparatus as recited in claim 22 further comprising a pressure
regulator located in the second line for reducing the sample gas
pressure before the sample gas flows to the second chamber.
24. An apparatus as recited in claim 21 wherein the chamber has
a second section located downstream of the chamber section with
the fixed-volume and further comprising a second valve for controlling
the flow of the sample gas from the fixed-volume chamber section
to the second chamber section.
25. An apparatus for measuring the energy flow rate of a pipeline
gas through a pipeline, the apparatus to be used with a linear flow
meter measuring the volumetric flow of the pipeline gas through
the pipeline, the apparatus comprising:
a chamber having a section with a fixed volume for containing the
sample gas, the sample gas being maintained at substantially the
same temperature as the pipeline gas in the pipeline when contained
in the chamber section;
a pressure sensor for measuring the pressure of the sample gas
in the chamber section;
a first line connected to the pipeline for routing the sample gas
to the chamber section;
a valve mounted in the first line for controlling the flow of the
sample gas to the chamber section;
a flow controller for flowing the sample gas from the chamber at
a selected rate;
a second line for routing the sample gas away from the chamber
to the flow controller;
a control for closing the valve when the sample gas pressure in
the chamber section reaches the pressure of the pipeline gas in
the pipeline;
a timer for measuring a time interval for the sample gas to flow
from the chamber section at the selected rate beginning when the
sample gas pressure in the chamber section drops below a first pressure,
and ending when the sample gas pressure in the chamber section drops
below a second pressure, the first pressure being greater than about
one-half of the pipeline gas pressure in the pipeline and the second
pressure being less than about one-half of the pipeline gas pressure
in the pipeline;
a burner for burning the sample gas with an air flow to form a
flame;
a third line for routing the sample gas away from the flow controller
to the burner;
a temperature sensor for measuring the flame temperature;
an air conduit for routing the air flow to the burner;
an air valve located in the air conduit for adjusting the air flow
through the air conduit;
an air mass flow meter for measuring an air mass flow rate through
the air conduit; and
a control system for receiving signals from the pressure sensor,
the timer, the linear flow meter, the air mass flow meter and the
temperature sensor, for communicating with the air valve to adjust
the air flow so that the flame burns at the maximum temperature,
and for computing the energy flow rate of the pipeline gas flowing
through the pipeline.
26. An apparatus as recited in claim 25 further comprising a second
chamber of fixed volume located in the second line so that the sample
gas flows through the second chamber before it flows to the flow
controller.
27. An apparatus as recited in claim 26 further comprising a pressure
regulator located in the second line for reducing the sample gas
pressure before the sample gas flows to the second chamber.
28. An apparatus as recited in claim 25 wherein the chamber has
a second section located downstream of the chamber section with
the fixed-volume and further comprising a second valve for controlling
the flow of the sample gas from the fixed-volume chamber section
to the second chamber section.
29. An apparatus to be used with a linear flow meter to measure
a ratio of a mass flow rate of a pipeline gas through a pipeline
compared to a mass flow rate of a sample gas tapped from the pipeline,
the apparatus comprising:
a chamber having a section with a fixed volume V for containing
the sample gas, the sample gas being maintained at substantially
the same temperature as the pipeline gas in the pipeline when contained
in the chamber section;
means for routing the sample gas to the chamber section;
a valve for controlling the flow of sample gas to the chamber section;
a flow controller for flowing the sample gas from the chamber section
at a selected rate;
a pressure sensor for measuring the sample gas pressure in the
chamber section;
means for closing the valve when the sample gas pressure in the
chamber section reaches the pressure P.sub.L of the pipeline gas
in the pipeline; and
means for determining a time rate of change of pressure in the
chamber section for a condition where the pressure in the chamber
section is about one-half of pressure P.sub.L of the pipeline gas
in the pipeline ##EQU50## a control system which receives a signal
f.sub.t representing volumetric flow through the pipeline from the
linear flow meter, and signals from the pressure sensor, and computes
the ratio ##EQU51## of the mass flow rate of the pipeline gas through
the pipeline compared to the mass flow rate of the sample gas by
the following relationship: ##EQU52## where K.sub.t is a calibration
constant for the linear flow meter, b is a second pressure virial
coefficient of the gas and c is a third pressure virial coefficient
of the gas.
30. A method for measuring a mass flow ratio ##EQU53## of a pipeline
gas through a pipeline compared to a sample gas tapped from the
pipeline, the method comprising the steps of:
measuring the volumetric flow rate of the pipeline gas through
the pipeline with a linear flow meter;
flowing the sample gas to a chamber having a section with a fixed
volume V;
maintaining the temperature of the sample gas at substantially
the same temperature as the pipeline gas in the pipeline when the
sample gas is in the chamber section;
stopping the flow of sample gas to the chamber section when the
pressure in the chamber section reaches the pressure P.sub.L of
the pipeline gas in the pipeline;
flowing the sample gas from the chamber section after the flow
of the sample gas to the chamber section is stopped, thereby reducing
the sample gas pressure in the chamber section;
determining the time rate of change of pressure in the chamber
section for a condition where the pressure in the chamber section
in about one-half of pressure P.sub.L of the pipeline gas in the
pipeline ##EQU54## and deriving the mass flow ratio ##EQU55## of
the pipeline gas through the pipeline compared to the sample gas
tapped from the pipeline by solving the following relationship:
##EQU56## where f.sub.t is a signal from the linear flow meter representing
the volumetric flow rate of the gas through the pipeline, K.sub.t
is a calibration constant for the linear flow meter, b is a second
virial coefficient of the gas, and c is a third virial coefficient
of the gas.
31. A method for monitoring the energy flow rate of a pipeline
gas through a pipeline and representing the flow of the pipeline
gas in terms of an adjusted volumetric flow rate which corresponds
to a volumetric flow rate at a defined pressure and temperature,
the method comprising:
measuring the volumetric flow rate of the pipeline gas through
the pipeline with a linear flow meter;
flowing sample gas to a chamber having a section with a fixed volume;
maintaining the temperature of the sample gas at substantially
the same temperature as the pipeline gas in the pipeline when the
sample gas is in the chamber section;
stopping the flow of sample gas to the chamber section when the
pressure in the chamber section reaches the pressure of the pipeline
gas in the pipeline;
flowing sample gas from the chamber section at a selected rate
after the flow of sample gas to the chamber section is stopped,
thereby reducing the sample gas pressure in the chamber section;
timing the interval of time t.sub.m for the sample gas to flow
from the chamber section at a selected rate beginning when the sample
gas pressure in the chamber section drops below the first pressure
and ending when the sample gas pressure in the chamber section drops
below a second pressure;
measuring the energy flow rate of the sample gas;
measuring the energy content per unit volume of the sample gas;
and
determining the adjusted volumetric flow rate of the pipeline gas
through the pipeline from the volumetric flow rate of the pipeline
gas measured by the linear meter, the time interval t.sub.m, the
energy flow rate of the sample gas, and the energy content per unit
volume of the sample gas.
32. An apparatus to be used with a control system and a linear
flow meter measuring a volumetric flow rate of a pipeline gas flowing
through a pipeline, for monitoring the energy flow rate of the pipeline
gas through the pipeline and representing the flow of the pipeline
gas in terms of an adjusted volumetric flow rate that corresponds
to a volumetric flow rate at a defined pressure and temperature,
the apparatus comprising:
a chamber having a section with a fixed volume for containing the
sample gas, the sample gas being maintained at substantially the
same temperature as the pipeline gas in the pipeline when contained
in the chamber section;
means for routing the sample gas to the chamber section;
a valve for controlling the flow of sample gas to the chamber section;
a flow controller for flowing the sample gas from the chamber section
at a selected rate;
a pressure sensor for measuring the sample gas pressure in the
chamber section;
means for closing the valve when the sample gas pressure in the
chamber section reaches the pressure of the pipeline gas in the
pipeline;
a timer for measuring a time interval for the sample gas to flow
from the chamber section at the selected rate beginning when the
sample gas pressure in the chamber section drops below a first pressure
and ending when the sample gas pressure in the chamber section drops
below a second pressure;
a sample gas energy flow rate meter for measuring the energy flow
rate of the sample gas; and
means for determining the energy content per unit volume of the
sample gas;
wherein the control system calculates the adjusted volumetric flow
rate of the pipeline gas through the pipeline from the volumetric
flow rate measured by the linear flow meter, the time interval,
the energy flow rate of the sample gas, and the energy content per
unit volume of the sample gas.
33. An apparatus to be used with a linear flow meter to measure
a ratio of a mass flow rate of a pipeline gas through a pipeline
compared to a mass flow rate of a sample gas tapped from the pipeline,
the apparatus comprising:
a chamber having a section with a fixed volume for containing the
sample gas, the sample gas being maintained at substantially the
same temperature as the pipeline gas in the pipeline when contained
in the chamber section;
means for routing the sample gas to the chamber section;
a valve for controlling the flow of sample gas to the chamber section;
a flow controller for flowing the sample gas from the chamber section
at a selected rate;
a pressure sensor for measuring the sample gas pressure in the
chamber section;
means for closing the valve when the sample gas pressure in the
chamber section reaches the pressure of the pipeline gas in the
pipeline; and
a timer for measuring a time interval for the sample gas to flow
from the chamber section at the selected rate beginning when the
sample gas pressure in the chamber section drops below a first pressure,
and ending when the sample gas pressure in the chamber section drops
below a second pressure, the first pressure being equal to one-half
of the pipeline gas pressure in the pipeline and the second pressure
being less than the first pressure; and
a controller which receives a signal from the timer and a signal
from the linear flow meter representing the volumetric flow of the
pipeline gas through the pipeline and derives the ratio of the mass
flow rate of the pipeline gas through the pipeline compared to the
mass flow rate of the sample gas.
Description The present invention relates to instrumentation for measuring
in real time the mass and the energy flow rate of gas through a
pipe. In particular, it relates to apparatus for measuring the ratio
of the mass flow rate of pipeline gas flowing through a pipeline
compared to sample gas flowing through the apparatus. The invention
also relates to apparatus for measuring the energy flow rate of
gas through a pipeline.
Mass and energy flow rates of gas through pipelines are normally
calculated in flow computers from contemporaneous measurements of
several gas parameters. Generally, for measuring mass flow rate,
the volumetric flow rate of the gas is measured and gas temperature,
pressure, and composition are measured to enable the gas density
and, thus, the mass flow rate to be calculated from the volumetric
flow rate. The composition of the gas is normally measured by gas
chromatography. When the operating conditions are such that the
supercompressibility of the gas in the calculation of density cannot
be ignored, supercompressibility properties are normally estimated
from either the virial equations of state for the gas or from precalculated
correlations such as NX-19.
Knowledge of the values of the virial coefficients of particular
gas compositions is quite limited in the art, so the calculation
of gas density from the virial equations of state is not always
possible. Furthermore, correlations such as NX-19 for natural gas,
are approximate and the accuracy of extrapolations from such correlations
is questionable. It is therefore difficult to obtain accurate real
time density values for calculating the mass flow rates of gas flowing
through a pipeline with present day equipment.
When energy flow rate, in addition to mass flow rate, is desired,
the energy content of the gas must also be determined. The energy
content of the gas (energy per unit mass or volume) can be determined
either indirectly by measuring the composition of the gas or by
direct measurements such as the stoichiometric ratio method. Once
the energy content of the gas is determined, the energy flow rate
of the gas through the pipeline can be calculated by multiplying
the energy content of the gas (e.g. BTU/lb) by the mass flow rate
of the gas (e.g. lbs./hr.).
Each of these measurements discussed above (volumetric flow, temperature,
pressure, and composition) are measured separately and introduce
an opportunity for measurement error. The aggregation of these measurement
errors can be quite substantial and distort mass or energy flow
calculations. To minimize measurement errors, each piece of instrumentation
must be maintained and calibrated periodically. Moreover, additional
errors can be introduced within the flow computer from calculations
or inaccurate formulas or correlations.
In U.S. Pat. No. 4396299 Clingman disclosed a method and apparatus
for measuring the rate of energy flow of gas through a pipeline
that did not require gas density to be measured either directly
or indirectly. That invention, which flows sample gas through a
calibrated capillary tube, is able to measure the energy flow of
pipeline gas through a pipeline by sampling a constant fraction
of the pipeline gas and measuring the mass flow of air which is
burned with the sample gas at maximum flame temperature. The mass
flow rate of the sample gas varies in direct proportion with the
mass flow rate of the gas through the pipeline.
In a copending patent application entitled "Method and Apparatus
for Measuring Mass Flow and Energy Content Using A Differential
Pressure Meter" filed on Nov. 4 1991 Ser. No. 07/787188
William Vander Heyden explains a method and apparatus wherein the
mass flow rate of the sample gas does not vary with the mass flow
rate of the gas through the pipeline.
The invention disclosed in U.S. Pat. No. 4396299 and the invention
disclosed by Vander Heyden in copending patent application entitled
"Method and Apparatus For Measuring Mass Flow and Energy Content
Using A Differential Pressure Meter" can only be used in connection
with an in-line differential pressure volumetric meter. That is,
a device installed in the pipeline that causes a pressure differential
to occur in the pipeline gas as the pipeline gas flows across the
device. Such in-line devices produce signals proportional to the
velocity squared. As such, these inventions do not operate in conjunction
with flow meters that produce signals which are linearly proportional
to flow velocity. There are many types of linear flow meters including
but not limited to turbine, vortex, rotary, diaphragm or ultrasonic
meters.
SUMMARY OF THE INVENTION
The present invention is a method and apparatus for determining
the ratio of the mass flow rate of pipeline gas flowing through
a pipeline compared to the mass flow rate of sample gas tapped from
the pipeline. The invention allows this determination to be made
in real time.
Sample gas is tapped from the pipeline and flows to a chamber having
a section with a fixed volume. While the sample gas is in the fixed-volume
chamber section, the sample gas must be maintained at substantially
the same temperature as the gas in the pipeline.
A valve controls the flow of sample gas to the chamber section.
When the valve is opened, sample gas flows into the chamber section
until the gas pressure in the chamber section becomes equal to the
gas pressure in the pipeline. The valve is then closed and stops
the flow of sample gas into the chamber section. Sample gas flows
from the chamber section after the valve is closed (but sample gas
may also flow from the chamber section at a slow rate before the
valve is closed). When the sample gas pressure in the chamber section
drops below a starting pressure, a timer begins. The starting pressure
is mathematically related to the pipeline gas pressure. The timer
measures a time interval t.sub.m for the sample gas pressure in
the chamber section to fall from the starting pressure to a stopping
pressure. During the time interval t.sub.m, the sample gas flows
from the chamber section at a selected rate as controlled by a flow
controller that is located downstream of the chamber.
Based on the time interval t.sub.m, proportionality constants,
and information from a flow meter that transmits a signal which
is linear to the velocity of the flow of the pipeline gas through
the pipeline (e.g. a turbine or a vortex meter), the ratio of the
mass flow rate of pipeline gas through the pipeline compared to
the mass flow rate of the sample gas can be determined in a control
system (e.g. a computer).
The present invention requires only two measurements for determining
the mass flow ratio: the time interval t.sub.m and a signal from
a linear flow meter. The present invention alleviates the need to
consider the effects of supercompressibility, temperature, pressure,
density or composition because the critical measurement (i.e. the
time interval t.sub.m) is made when the sample gas is at a condition
related to pipeline conditions.
An object of the present invention is to measure the mass flow
ratio without fluctuating the sample gas flow rate exiting the system.
The present invention accomplishes this object by using a flow controller
to maintain the sample gas exit flow rate at a rate set by the control
system.
The present invention also contemplates using the apparatus described
above with apparatus for measuring the energy content of the sample
gas to determine the energy flow rate of combustible gas through
a pipeline.
When the present invention is used to measure the energy flow rate,
it is preferred that the sample gas be fed to a burner after the
sample gas exits the flow controller, and be burned with an amount
of air at a maximum flame temperature. When the sample gas is burned
at the maximum flame temperature, the energy flow rate of the sample
gas is proportional to the amount of air burning the sample gas.
The energy flow rate of the pipeline gas through the pipeline is
determined from calculations involving the air mass flow rate, the
time interval (t.sub.m), and signals from the linear flow meter
monitoring the flow of pipeline gas.
The present invention allows the energy flow rate of pipeline gas
to be determined with precision from three measurements: the air
mass flow rate to the burner, the time interval for the above identified
chamber section pressure decay, t.sub.m, and the pipeline gas flow
data from the linear flow meter.
The present invention therefore allows accurate real time determination
of the energy flow rate of a pipeline gas flowing through a pipeline
without the need to compensate for the effects of gas temperature,
pressure, density, composition or supercompressibility. It also
allows for the energy flow rate of pipeline gas to be monitored
accurately without substantially interfering with the pipeline gas
flow.
The present invention further provides measurement stability for
the flame temperature and thus assures that the flame temperature
can be maximized. This is important because flame temperature must
be maximized so that, for saturated hydrocarbon gases, the flow
of air burning the sample gas is proportional to the energy content
of the sample gas. The flame is promoted to burn at the constant
height because the sample gas flows from the flow controller to
the burner at a selected flow rate. A thermocouple measuring the
flame temperature can therefore be located in a consistent position
within the flame and measure relative flame temperature more accurately.
Another object of the present invention is to measure the energy
flow rate through each of the multiple pipeline runs at a pipeline
metering station with a single energy measuring apparatus. The present
invention can accomplish this object by systematically sampling
each run sequentially in time. It is required, however, that a separate
linear flow meter be installed in each run to operate in this mode.
The invention also includes a method for measuring the mass flow
ratio of the pipeline gas through the pipeline compared to the sample
gas tapped from the pipeline and a method for measuring the energy
flow rate of the pipeline gas through the pipeline. Both methods
involve measuring the volumetric flow rate of the pipeline gas through
the pipeline with a linear flow meter. They also involve flowing
a sample of gas to a chamber having a section with a fixed volume
and maintaining the temperature of the sample gas at substantially
the same temperature as the pipeline gas in the pipeline when the
sample gas is in the chamber section. The flow of sample gas to
the chamber section is stopped when the pressure in the chamber
section reaches the pressure of the pipeline gas. After the flow
of sample gas to the chamber section is stopped, the sample gas
is flowed from the chamber section thereby reducing the sample gas
pressure in the chamber section. A starting pressure is determined
as a function of the pipeline gas pressure. An interval of time
for the sample gas to flow from the chamber section at a selected
rate, beginning when the sample gas pressure in the chamber section
drops below the starting pressure and ending when the sample gas
in the chamber section drops below a stopping pressure, is timed.
Based on the interval of time and a signal from the linear flow
meter, the mass flow ratio can be calculated in a control system.
The method for measuring the energy flow rate of a pipeline gas
through a pipeline is generally the same as described above but
also includes measuring the energy content of the sample gas.
The foregoing advantages of the present invention will appear from
the following description. In the description, references are made
to the accompanying drawings which form a part hereof and in which
a preferred embodiment of the present invention is shown by way
of illustration. Such embodiment does not necessarily represent
the full scope of the invention however.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic drawing showing the fundamental apparatus
of the present invention;
FIG. 2 is a plot of a sample gas pressure within a chamber section
with a fixed-volume as a function of time when the present invention
as shown in FIG. 1 is operating;
FIG. 3 is a schematic drawing showing an embodiment of the present
invention in which i) the sample gas pressure in the fixed-volume
chamber section can be reduced to a starting pressure more rapidly,
and ii) the temperature of the sample gas in the fixed-volume chamber
section is maintained substantially equal to the temperature of
the pipeline gas flowing through the pipeline;
FIG. 4 is a schematic drawing showing the circuitry for controlling
the starting and the stopping of a timer;
FIG. 5 is a schematic drawing showing an embodiment of the present
invention in which a second chamber is located in-line between a
pressure regulator and a flow controller; and
FIG. 6 is a schematic drawing showing additional apparatus of the
present invention for measuring the energy flow rate of a pipeline
gas through a pipeline.
DESCRIPTION OF THE PREFERRED EMBODIMENT
One class of meters for measuring the volumetric flow of gas through
a pipeline is linear flow meters, that is meters, such as turbine
or vortex meters, which produce a signal directly proportional to
flow velocity. Linear flow meters are different than another class
of volumetric flow meters referred to as differential pressure flow
meters because differential pressure meters produce a signal proportional
to pressure differentials which are proportional to the velocity
squared and not linear to flow velocity. The present invention is
used in conjunction with one or more linear flow meters.
In FIG. 1 the present invention is used in conjunction with a
turbine meter 10. The turbine meter 10 measures the volumetric flow
rate of a pipeline gas 12 flowing through a pipeline 14 in the direction
of arrow 15. The turbine meter 10 communicates the volumetric flow
rate of the pipeline gas 12 as the ratio of turbine frequency f.sub.t
compared to a turbine meter factor K.sub.t. The turbine meter factor
K.sub.t is normally stored in a control system 16; whereas, the
turbine frequency f.sub.t is relayed to the control system 16 periodically.
In the preferred embodiment, the control system 16 is an electrical
system utilizing conventional switching techniques to operate the
instrumentation in accordance with the procedures of the invention.
If desired, the control system 16 may employ conventional solid
state microprocessor techniques, such as: an electronic timing device
or clock, an analog-to-digital converter, output signal amplifiers,
storage memory for the control program, an arithmetic unit for dividing,
and the like.
A sample of gas 18 is tapped upstream of the flow meter 10 at point
19. The sample gas 18 flows into a first fixed-volume chamber 20.
The volume of the chamber is small, about 20 cubic centimeters.
The sample gas 18 must be maintained at substantially the same temperature
as the pipeline gas 12 when it is in the first chamber 20. If the
temperature of the sample gas 18 is maintained at substantially
the same temperature as the pipeline gas 12 the need to compensate
for the effects of supercompressibility can be avoided as will be
discussed below.
The flow of sample gas 18 into the first chamber 20 is controlled
by a first solenoid valve 22. Referring to FIG. 2 the first solenoid
valve 22 is open at the beginning of a sampling cycle 24 and sample
gas 18 flows into the first chamber 20. When the pressure in the
first chamber 20 reaches a pressure P.sub.L of the pipeline gas
12 in the pipeline 14 the first solenoid valve 22 closes and terminates
the flow of sample gas 18 into the first chamber 20. The sample
gas 18 may be held within the first chamber 20 at the pipeline pressure
P.sub.L to assure that the sample gas 18 is substantially the same
temperature and density as the pipeline gas 12.
Referring again to FIG. 1 a flow controller 26 for maintaining
a selected flow of sample gas 18 from the first chamber 20 is located
downstream of the first chamber 20. Flow controllers are known in
the art and an electronically adjustable pressure regulator, or
I/P converter 28 followed by a capillary tube 30 is suitable for
this application. The I/P converter 28 precisely determines the
sample gas 18 pressure in response to an electrical signal 32 from
the control system 16 (typically ranging from 4 to 20 ma direct
current), and thus determines the flow rate of sample gas 18 through
the capillary tube 30.
Referring again to FIG. 2 the flow controller 26 allows sample
gas 18 to flow from the first chamber 20 at a selected rate. As
the sample gas 18 flows from the first chamber 20 after the first
solenoid valve 22 closes, the pressure within the first chamber
20 drops. When the chamber pressure reaches a starting pressure
P.sub.1 a timer 34 (see FIG. 1) starts. When the pressure in the
first chamber 20 drops to a stopping pressure P.sub.2 the timer
34 is stopped and the time interval t.sub.m is recorded. The chamber
20 pressure continues to drop until it reaches an opening pressure
P.sub.o at which time the first solenoid valve 22 opens and a new
sampling cycle 24 begins. This type of apparatus is similar to the
invention disclosed in U.S. Pat. No. 4285245 issued to Kennedy
on Aug. 25 1981.
Referring again to FIG. 1 a pressure sensor 36 senses the pressure
within the first chamber 20. Preferably, the pressure sensor 36
is a strain gauge type sensor with an electrical output, i.e. a
pressure transducer, but other types of pressure sensors or transducers
may be used if desired.
The pressure sensor 36 communicates with the first solenoid valve
22 and with the timer 34 preferably through the control system
16. When the pressure sensor 36 senses that the pressure in the
first chamber has reached the pipeline pressure P.sub.L, it communicates
to close the first solenoid valve 22. When the sensor 36 senses
that the pressure in the first chamber 20 has dropped below the
starting pressure P.sub.1 it communicates to the timer 34 to begin
timing. Likewise, the sensor communicates with the timer 34 to stop
timing when the pressure in the first chamber 20 drops below the
stopping pressure P.sub.2. The sensor 36 also communicates with
the first solenoid valve 22 to open the valve 22 when the pressure
in the first chamber 20 reaches the opening pressure P.sub.o.
Although it is not necessary in all applications, a pressure regulator
38 may be installed in line between the first chamber 20 and the
flow controller 26. A pressure regulator 38 may be necessary, for
example, when the pipeline gas 12 pressure P.sub.L is high.
In order for the accuracy of the present invention to be substantially
independent of the supercompressibility of the pipeline gas 12 two
conditions must exist within the first chamber 20:
1) The temperature and pressure of the sample gas 18 within the
first chamber 20 at the time the first solenoid valve 22 is closed,
must be substantially equal to the temperature and pressure of the
pipeline gas 12 in the pipeline 14; and
2) The starting pressure P.sub.1 must be about one-half of the
pressure P.sub.L of the pipeline gas 12 in the pipeline 14.
The embodiment of the present invention that is depicted in FIG.
3 uses a serpentined hollow coil 20' as the first fixed-volume chamber
20 to facilitate the occurrence of the two conditions stated above.
Referring to FIG. 3 the serpentined hollow coil 20' is located
immediately downstream of the first solenoid valve 22. A second
solenoid valve 42 is located downstream in the serpentined hollow
coil 20'. The volume within the hollow coil 20' that is enclosed
by the solenoid valves 22 and 42 is a first section 43 of the first
chamber 20. The volume within the hollow coil 20' after the second
solenoid 42 and before the flow controller 26 is a second section
44 of the first chamber 20'. The sample gas 18 flows from the second
section 44 continuously at a rate selected by the flow controller
26.
The hollow coil 20' is mounted in intimate contact with the pipeline
14 and serpentines back and forth across the outer surface of a
portion of the pipeline 14. Insulation 45 should be placed around
the hollow coil 20', the solenoid valves 22 and 42 and the pipeline
14. A heat transfer compound may also be used to facilitate temperature
equalization. With this configuration, the temperature of the sample
gas 18 within the first section 43 of the first chamber 20 is maintained
at substantially the same temperature as the temperature of the
pipeline gas 12 flowing through the pipeline 14.
The second solenoid valve 42 is closed when sample gas 18 is filling
the first section 43 of the hollow coil 20' to pipeline pressure
P.sub.L. When the sample gas 18 pressure in the first section 43
reaches P.sub.L, the first solenoid valve 22 closes and the second
solenoid valve 42 opens. The sample gas 18 pressure in the first
section 43' reduces quickly because the sample gas 18 pressure in
the second volume 44 is less than the sample gas 18 pressure in
the first section 43 at that instant. The volume of the second section
44 is such that the pressure in both chambers will stabilize at
a pressure slightly higher than the starting pressure P.sub.1. The
pressure in both sections 43 and 44 combined then decays to P.sub.1
at which time the timer 34 begins and measures the time interval
t.sub.m for the pressure in both sections 43 and 44 to decay from
the starting pressure P.sub.1 to the stopping pressure P.sub.2.
In this embodiment where the first chamber has a first 43 and a
second 44 section, it is necessary for the sample gas pressure in
the first section 43 to reach P.sub.L while being maintained at
substantially the same temperature as the pipeline gas 12 but it
is not necessary for the sample gas pressure in the second section
44 to reach P.sub.L.
This configuration allows rapid containment of the sample gas 18
within the fixed volume of the first section 43 of the hollow coil
20' at pipeline pressure P.sub.L and alleviates the need to wait
for the sample gas 18 pressure to slowly decay to the starting pressure
P.sub.1. Moreover, the second section 44 of the hollow coil 20'
has a much larger volume than the first section 43 (i.e. about 12
fold) and thus the sample gas 18 pressure within the second section
44 does not fluctuate substantially. The flow rate through the flow
controller 26 is thus easier to maintain at the selected rate.
Still referring to FIG. 3 an arching sample gas feed 46 along
with a valve 48 and a valve 50 are used to remove debris from the
sample gas 18 before the sample gas 18 flows to the hollow coil
40. The low velocity in the rising section containing the valve
48 precludes particles from reaching the arch in the arching sample
gas feed 46. Instead, the particles fall into a lower section of
the pipe containing the valve 50. Periodically, the valve 50 can
be opened to blow the collected debris from the lower section of
the pipe through a blow hole 52. A filter 54 is also installed on
the arching sample gas feed 46 to remove debris from the sample
gas 18.
The following analysis is recited to emphasize the significance
that ##EQU1## and to also explain additional features of the preferred
embodiment of the invention that further improve the accuracy of
the invention.
The total derivative of pressure with respect to time must account
for density changes as well as molar flow and is given by: ##EQU2##
where ##EQU3## is the total derivative of pressure with respect
to time at constant temperature T, R is the real gas constant, V
is the volume of the first fixed-volume chamber 20 (or the volume
of the first section 43 of the hollow coil 20' if the embodiment
in FIG. 3 is used), M.sub.W is the molecular weight of the sample
gas 18 .omega..sub.m is the mass flow rate of the sample gas 18
Z is the supercompressibility constant for the gas, and ##EQU4##
is the partial derivative of Z at constant temperature T with respect
to the density of the gas .rho..
The supercompressibility constant Z, which describes the dynamics
of supercompressible gas, can be closely approximated by expanding
the virial equation of state through the first three terms:
where .rho. is gas density, P is the absolute gas pressure, B and
C are the second and third density virial coefficients of the gas,
and b and c are the second and third pressure virial coefficients
of the gas. The virial coefficients depend on gas temperature and
composition. The density virial coefficients are related to the
pressure virial coefficients according to generally accepted mixing
rules: ##EQU5## where R is the real gas constant and T is the absolute
temperature of the gas.
It follows from Eqs. (1), (2) and (3) that the total derivative
##EQU6## for the sample gas is: ##EQU7## In the present invention,
the derivative ##EQU8## is represented by: ##EQU9## where t.sub.m
is the time interval for the sample gas pressure in the first chamber
to drop from P.sub.1 to P.sub.2. There is no requirement that P2
be a specific pressure other than P2 be less than P1 and selected
to appropriately measure ##EQU10##
As shown in FIG. 2 P1 is greater than about one-half of the pipeline
gas pressure in the pipeline while P2 is less than about one-half
of the pipeline gas pressure in the pipeline. Substituting Eq. (5)
into Eq. (4) and solving for the mass flow rate of the sample gas
18 .omega..sub.m, results in: ##EQU11##
Now, the mass flow rate of the pipeline gas 12 is given by: ##EQU12##
where f.sub.t is the frequency signal that the turbine meter 10
communicates to control system 16 and K.sub.t is the turbine meter
calibration constant relating turbine frequency f.sub.t to volumetric
flow rate (i.e. cycles/unit volume).
Using the real gas law and the virial equations of state, Eq. (7)
becomes: ##EQU13## where P.sub.L is the absolute pressure of pipeline
gas 12. Dividing Eq. (8) by Eq. (5) results in: ##EQU14##
From Eq. (9), it is apparent that the effects of supercompressibility,
first represented by the second pressure virial coefficient b, are
minimized if P.sub.1 is approximately equal to P.sub.L /2. The accuracy
of the invention is not compromised significantly provided that
the starting pressure P.sub.1 is within a few percent of half the
pipeline pressure P.sub.L because the second virial coefficient
b is of the order 10.sup.-3.
Referring to FIG. 4 the starting P.sub.1 and the stopping P.sub.2
pressures are determined by a resistor string 56. The pressure sensor
36 senses the pressure in the first chamber 20 (or in the first
section 43 of the hollow coil 20' if the embodiment shown in FIG.
3 is used) and communicates the data to an associated sample and
hold circuit 58 and to the control system 16. The control system
16 determines when the sample gas 18 pressure in the first chamber
20 stabilizes at a maximum pressure, i.e. at the pipeline gas 12
pressure P.sub.L, and sends a signal 45 indicating that maximum
pressure to the sample and hold circuit 58. The sample and hold
circuit 58 memorizes the value of the maximum pressure in the first
chamber 20' for each sampling cycle 24. The circuit 58 is cleared
at the end of each sampling cycle 24 after it receives a signal
that the first solenoid valve 22 has opened.
An output voltage 60 from the sample and hold circuit 58 represents
the maximum chamber pressure (i.e. P.sub.L) and leads to the grounded
resistor string 56. The output voltage 60 is split by the resistors
62 64 and 66. The output voltage 60 drops across resistor 62 to
the P.sub.1 reference voltage 68 and further drops across resistor
64 to the P.sub.2 reference voltage 70. The resistance of the resistor
62 R1 is equivalent to the sum of the resistances of resistors
64 and 66 R2+R3 so that the starting pressure P.sub.1 is P.sub.L
/2. A ratio ##EQU15## is then represented by ##EQU16##
The P.sub.1 and P.sub.2 reference voltages (68 and 70) are stored
in a comparator 72 which compares these values to a signal from
the pressure sensor 36. When the pressure sensor 36 signals that
the pressure in the first chamber 20 has dropped to P.sub.1 the
comparator 72 activates the timer 34. When the pressure drops to
P.sub.2 the comparator 72 signals the timer 34 to stop.
Equation (9) can then be rewritten as: ##EQU17## and since higher
order terms are very small, Eq. (10) can be reduced to: ##EQU18##
where S is a splitting ratio. ##EQU19## by reinserting ##EQU20##
for K.sub.p and, as in Eq. (5), ##EQU21## Equation (11) can be simplified
to: ##EQU22## where K.sub.x is a constant equal to ##EQU23## and
C.sub.f is a correction factor dependent on pipeline gas pressure,
temperature, and composition. The second term ##EQU24## in Eq. (11)
is an error correction term and is significant at high pressures.
For methane gas, b is about 0.0024 and c is about 3.1.times.10.sup.-6
when pressure is measured in bars. If P.sub.L is 30 bar (i.e. 440
psia), the error associated with the second term is about 0.25%.
The error associated by the second term ##EQU25## in Eq. (11) can
be reduced by determining values for b and c. It is convenient to
rewrite the second term ##EQU26## in terms of the third density
virial coefficient C: ##EQU27##
The value of b can be determined by a second measurement at low
absolute pressure. For low absolute pressure, the total derivative
of pressure with respect to time ##EQU28## can be written in the
form of Eq. (4) but neglecting the third virial coefficient c: ##EQU29##
where P.sub.Y1 is a low pressure. The sample gas 18 mass flow rates
.omega..sub.m in Eqs. (4) and (13) are the same as selected by the
flow controller 26. The second virial coefficient b can be estimated
by combining and simplifying Eqs. (4) and (13): ##EQU30## where
P.sub.1 is the total pressure derivative at P.sub.1 and P.sub.Y1
is the total pressure derivative at low pressure. Equation (14)
can be expressed in terms of pressures and time interval measurements:
##EQU31## where t.sub.Y is the time interval for a pressure decay
at low pressure (i.e. P.sub.Y1 -P.sub.Y2) and is determined in a
manner similar to the interval t.sub.m. There is no requirement
that P.sub.Y1 or P.sub.Y2 be a specific pressure other than P.sub.Y2
be less than P.sub.Y1.
Equations (14) and (15) assume that the volume in which the pressure
drops P.sub.1 -P.sub.2 and P.sub.Y1 -P.sub.Y2 occur is constant.
This assumption is true if the pressure drops are both measured
in the first chamber 20 (or in the first section 43 of the hollow
coil 20' if the embodiment shown in FIG. 3 is used), but at different
times.
Referring to FIG. 5 it may be preferable in some circumstances
to use a second fixed-volume chamber 73 downstream of the first
chamber 20 and measure the low pressure drop (P.sub.Y1 -P.sub.Y2)
in the second chamber 73. In FIG. 5 the sample gas 18 pressure
is reduced significantly as the sample gas 18 flows from the first
chamber 20 to the second chamber 73 by an in-line pressure regulator
38. A third solenoid valve 71 is located in line between the pressure
regulator 38 and the second chamber 73. A pressure sensor 69 measures
the sample gas pressure in the second chamber 73. The timer 34 measures
the time interval t.sub.Y for the pressure to decay from P.sub.Y1
to P.sub.Y2 in the second chamber 73. An advantage of the of configuration
shown in FIG. 5 is a reduction in waiting time for the sample gas
pressure to decay to the low pressure P.sub.Y1. If the configuration
shown in FIG. 5 is used and the volume of the second chamber 73
is different than the volume of the first chamber 20 (or the volume
of the first section 43 of the hollow coil 20' if the embodiment
shown in FIG. 3 is used), Eqs. (14) and (15) should be replaced
with: ##EQU32## where V is the volume of the first chamber 20 (or
the volume of the first section 43 of the hollow coil 20' if the
embodiment shown in FIG. 3 is used) and V.sub.Y is the volume of
the second chamber 73.
For natural gas, which usually consists of 80% or more natural
gas, the value of ##EQU33## in Eq. (12) can be approximated by a
relationship in the form of KP.sup.2 where K is a constant and P
is pressure. In Table 1 are listed values of c and of ##EQU34##
for pure methane and also for mixtures containing 80% methane each
at 45.degree. F. and 81.degree. F. The values in Table 1 were obtained
from published data, such as the Brugge Data from Texas A&M,
and from interpolating the published data using thermodynamic mixing
rules for virial coefficients.
TABLE 1 ______________________________________ c c C/4(RT).sup.2
C/4(RT).sup.2 @280.degree. K. @300.degree. K. @280.degree. K. @300.degree.
K. Mixture cm.sup.6 /mol.sup.2 cm.sup.6 /mol.sup.2 10.sup.6 atm.sup.-2
10.sup.6 atm.sup.-2 ______________________________________ Methane
(CH.sub.4) 2649 2438 1.256 1.007 Ethane (C.sub.2 H.sub.6) 10774
10392 80% CH.sub.4 ; 3714 3463 1.761 1.431 20% C.sub.2 H.sub.6 Carbon
Dioxide 5636 4927 (CO.sub.2) 80% CH.sub.4 ; 3130 2844 1.484 1.175
20% (CO.sub.2) Nitrogen (N.sub.2) 1451 1443 80% CH.sub.4 ; 2371
2211 1.124 0.913 20% N.sub.2 ______________________________________
The splitting ratio ##EQU35## is computed in real time by the control
system 16 in accordance with Eq. (11). In the calculation, K.sub.P,
K.sub.t, and V are constants stored within the control system 16
and the turbine frequency f.sub.t, and the time interval t.sub.m
are communicated to the control system 16 for each sampling cycle
24. The second virial coefficient b is estimated by measuring the
time interval t.sub.Y for a pressure decay at low pressure and using
Eq. (15) or (17), whichever is appropriate. The third virial coefficient
c is estimated using data from Table 1. Finally, P.sub.L is measured
by the pressure sensor 36 and relayed to the control system 16.
Referring generally to FIG. 6 the method and apparatus described
above can be used with the method and apparatus described hereafter,
which is much like the method and apparatus for determining the
energy content of the flow of pipeline gas that is described in
U.S. Pat. No. 4125123 issued to Clingman on Nov. 14 1978.
For saturated hydrocarbon gas, the amount of air required to completely
combust gas at maximum flame temperature, i.e. stoichiometric combustion,
is precisely proportional to the energy released during combustion.
If the gas being combusted is a saturated hydrocarbon, the energy
flow rate of the sample gas 18 is represented by: ##EQU36## where
K.sub.sto is the stoichiometric proportionality constant, and .omega..sub.air
is the air flow rate. Likewise, the energy flow rate of the gas
12 through the pipeline 14 is represented by: ##EQU37## where S
is the splitting ratio as defined in Eq. (11).
Equation (19) can be simplified to: ##EQU38## where K.sub.x is
a constant equal to ##EQU39## and C.sub.f is a correction factor
dependent on pipeline gas pressure, temperature, and composition.
In accordance with Eq. 19 the apparatus shown in FIG. 6 determines
the energy flow rate of the pipeline gas 12 through the pipeline
14.
Referring in particular to FIG. 6 the sample gas 18 flows to a
burner 74 at a flow rate maintained by the flow controller 26. Air
is supplied to the burner 74 by an air hose 76 and the sample gas
18 is burned above the burner 74. A temperature sensor 78 which
communicates to the control system 16 monitors flame temperature.
The air flowing through the air hose 76 is monitored by an air mass
flow meter 80. Air mass flow meters are old in the art and are accurate
at ambient conditions. The air flow is adjusted by an air valve
82 which also communicates with the control system 16 until the
sample gas 18 burns at maximum flame temperature. When the flame
burns at the maximum flame temperature, the energy flow rate of
the pipeline gas 12 can be determined.
The energy flow rate of the pipeline gas 12 is calculated in the
control system 16 in accordance with Eq. (19). The value K.sub.sto
in Eq. (19) is a constant and stored in the control system 16. The
splitting ratio S is computed for each sampling cycle 24 as described
above. And, the air mass flow rate .omega..sub.air is measured by
the air flow meter 80 and communicated to the control system 16
for each sampling cycle 24.
U.S. Pat. No. 4125123 issued to Clingman discloses a method for
determining the energy content (energy/volume) of a pipeline gas
at standard operating conditions. It is well known in the art that
the volumetric flow rate adjusted for standard operating conditions
can be determined by dividing energy flow rate (energy/time) by
energy content (energy/volume).
Many modifications and variations of the preferred embodiment that
are within the spirit and scope of the invention will be apparent
to those with ordinary skill in the art. |