Note: Descriptions are shown in the official language in which they were submitted.
i CA 02692179 2009-12-17
0.
MEASURING SYSTEM FOR A EviED;LI!". FLOWING IN A PROCESS LINE
The invention relates to a measuring system for measuring a density of a
medium
variable with respect to a thermodynamic state, especially at least partly
compressible,
flowing in a process line, such as a process pipeline or tube, along a flow
axis of the
measuring system. The measuring system measures by means of a temperature
sensor, a pressure sensor and a measuring electronics communicating, in each
case, at
least at times, with the temperature sensor and the pressure sensor, and
producing, at
least at times, at least one density measured-value representing, as
accurately as
possible, a local density of the flowing medium.
For registering process-describing, measured variables of flowing media, such
asthe
thermodynamic state variable, density, or measured variables derived
therefrom, and
for producing measured-values correspondingly representing such measured
variables,
industrial process measurements technology applies measuring systems installed
near
to the process. This is done especially also in connection with the automation
of
chemical processes or processes involving adding value to materials. These
measuring
systems are often composed of two or more, discrete, measuring, field devices,
which
communicate with one another and are each arranged directly at, on or in a
process
line, through which the medium flows. The measured variables to be registered
can
include, besides density, for example also other thermodynamic state
variables,
especially such variables as are registerable by sensor and, as a result,
directly
measurable, such as e.g. pressure or temperature, directly or indirectly
measurable flow
parameters, such as e.g. a flow velocity, a volume flow, e.g. a volume flow
rate, or a
mass flow, e.g. a mass flow rate, or other complex transport variables, such
as e.g. a
heat flux, as well as also other measured variables specific to the medium,
such as e.g.
a viscosity, of an at least partly liquid, powdered or gaseous medium conveyed
in a
process line embodied, for example, in the form of a pipeline.
Especially for the indirect (in the following, thus, also referred to as
virtual)
measurement of density, based on pressure and temperature measurement signals
generated by means of corresponding sensors, as well as also measured
variables
possibly derived therefrom, for example mass flow or volume flow, a large
number of
industrial standards have become established, which recommend a largely
standardized, and, thus, comparable, calculation, especially also with
application of
directly registered and, thus, actually measured temperatures and/or
pressures, and
which find application as a function of application area and medium. Examples
of such
standards include, by way of example, the industrial standard "IAWPS
Industrial
Formulation 1997 for the Thermodynamic Properties of Water and Steam",
International
Association for the Properties of Water and Steam (lAWPS-IF97), "A.G.A. Manual
for
the Determination of Supercompressibility Factors for Natural Gas - PAR
Research
Project NX-19", American Gas Association (AGA-NX19, Library of Congress No. 63-
23358), the international standard ISO 12213:2006, Part 1 -3 "Natural gas -
Calculation
of compression factor", as well as also the therein cited A.G.A.
Compressibility Factors
for Natural Gas and Other Related Hydrocarbon Gases", American Gas Association
Transmission Measurement Committee Report No. 8 (AGA-8) and "High Accuracy
CA 02692179 2009-12-17
f
Compressibility Factor Calculation for Natural Gases and Similar Mixtures by
Use of a
Truncated Viral Equation", GERG Technical Monograph TM2 1998 & Fortschritt-
Berichte VDI (Progress Reports of the Association of German Engineers), Series
6, No.
231 1989 (SGERG-88).
Often, the ascertaining of density can also serve for converting a directly
measured,
mass flow into an, as a result, indirectly or virtually measured, volume flow,
or vice
versa. For direct measurement of flow parameters serving as primary measured
variables therefor - thus, for example, a local flow velocity, a local volume
flow, or a
local mass flow - measuring systems of the type being discussed include at
least one
corresponding flow sensor, which, by reacting at least predominantly to a flow
parameter primarily to be registered for the flowing medium, or also to
changes of the
same, delivers, during operation, at least one measurement signal, especially
an
electrical measurement signal, correspondingly influenced by the measured
variable
primarily to be registered and representing such as accurately as possible.
The at least
one flow sensor can, in such case, be embodied to contact the medium, at least
partially, for example by being immersed therein, or to measure externally
through the
wall of the process line or a membrane, or diaphragm. Usually, the flow sensor
is
provided, in such case, by means of a, most often, very complex flow
transducer, which
is inserted appropriately directly into the process line, or into a bypass,
conveying the
medium.
Marketed flow transducers are usually implemented as prefabricated, pre-
calibrated
units equipped with a carrier tube insertable into the course of the pertinent
process line
and also with at least one physical-to-electrical converting element
appropriately pre-
assembled therewith. This converting element, possibly in conjunction with the
carrier
tube itself and/or other components of the flow transducer, especially passive-
invasive
components, such as e.g. flow obstacles protruding into the flow and/or active
components of the flow transducer, such as e.g. a coil arrangement placed
externally on
the support tube for generating a magnetic field, or sound producing units,
forms the at
least one flow sensor delivering the measurement signal. Widely distributed in
industrial
measurements technology are, especially, magneto-inductive flow transducers,
flow
transducers evaluating the travel time of ultrasonic waves coupled into
flowing media,
eddy flow transducers, especially vortex flow transducers, flow transducers
with
oscillating measuring tubes, flow transducers making use of pressure
differences, or
thermal flow-measuring transducers. Principles of construction and functioning
of
magneto-inductive flow transducers are described e.g. in EP-A 1 039 269, US-A
6,031,740, US-A 5,540,103, US-A 5,351,554, US-A 4,563,904, while such for
ultrasonic
flow transducers appear e.g. in US-B 6,397,683, US-B 6,330,831, US-B
6,293,156, US-
B 6,189,389, US-A 5,531,124, US-A 5,463,905, US-A 5,131,279, US-A 4,787,252.
Since also the others of the aforementioned principles of measurement usually
put into
practice in industrial flow measuring transducers are likewise sufficiently
known to those
skilled in the art, a further explanation of these and other principles of
measurement
established in industrial measurements technology and implemented by means of
flow
measuring transducers can be omitted here.
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CA 02692179 2009-12-17
7
Industrial measuring systems registcmnc., flow parameters involve, often,
those, in the
case of which, at least one of the measuring points delivering the actual
measurement
signals and thus, in the following, referred to as real, is formed by means of
a compact
inline measuring device having a flow transducer of the aforementioned kind.
Further
examples for such measuring systems, especially measuring systems formed by
means
of compact, inline measuring devices with flow transducers known per se to
those
skilled in the art, are presented, additionally, in detail in, among others,
EP¨A 605 944,
EP-A 984 248, EP-A 1 767 908, GB-A 21 42 725, US-A 4,308,754, US-A 4,420,983,
US-A 4,468,971, US-A 4,524,610, US-A 4,716,770, US-A 4,768,384, US-A
5,052,229,
US-A 5,052,230, US-A 5,131,279, US-A 5,231,884, US-A 5,359,881, US-A
5,458,005,
US-A 5,469,748, US-A 5,687,100, US-A 5,796,011, US-A 5,808,209, US-A
6,003,384,
US-A 6,053,054, US-A 6,006,609, US-B 6,352,000, US-B 6,397,683, US-B
6,513,393,
US-B 6,644,132, US-B 6,651,513, US-B 6,651,512, US-B 6,880,410, US-B
6,910,387,
US-B 6,938,496, US-B 6,988,418, US-B 7,007,556, US-B 7,010,366, US-A
2002/0096208, US-A 2004/0255695, US-A 2005/0092101, US-A 2006/0266127, WO-A
88/02 476, WO-A 88/02 853, WO-A 95/08758, WO-A 95/16 897, WO-A 97/25595, WO-
A 97/46851, WO-A 98/43051, WO-A 00/36 379, WO-A 00/14 485, WO-A 01/02816,
WO-A 02/086 426, WO-A 04/023081 or WO-A 04/081500, WO-A 05/095902, as well as
also in the not pre-published applications DE 102006034296.8 and
102006047815.0 of
the assignee.
For the further processing or evaluation of measurement signals produced in
the
measuring systems, such additionally include at least one corresponding
measuring
electronics. The measuring electronics, communicating in suitable manner with
the
pertinent measuring transducer, especially also with the at least one
converting
element, produces during operation, with application of the at least one
measurement
signal, repeatedly, at least one measured-value instantaneously representing
the
measured variable, thus, for example, a mass flow measured-value, volume flow
measured-value, a density measured-value, a viscosity measured-value, a
pressure
measured-value, a temperature measured-value, or the like. The measured-
values,
especially the indirectly, or also virtually, measured, density measured-
value, are, in
such case, often ascertained by means of highly complex calculations according
to one
of the mentioned industry standards, for example "AGA 4", "AGA 8", "AGA-NX19,
"IAWPS-IF97", "SGERG-88", or the like.
For accommodating the measuring electronics, such measuring systems include,
most
often, a corresponding electronics housing, which, as proposed e.g. in US-A
6,397,683
or WO-A 00/36 379, can be arranged remotely from the measuring transducer and
connected with such via a flexible cable. Alternatively thereto or in
supplementation
thereof, the electronics housing can, however, also, as shown, for example, in
EP-A 903
651 or EP-A 1 008 836, be arranged directly on the measuring transducer or on
a
measuring transducer housing separately housing the measuring transducer, in
order to
form a compact, inline measuring device, for example a Coriolis mass
flow/density
measuring device, an ultrasonic flow-measuring device, a vortex flow-measuring
device,
a thermal flow-measuring device, a magneto-inductive flow-measuring device, or
the
like. In the case in which the electronics housing is arranged on a measuring
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CA 02692179 2009-12-17
transducer housing, the electronics hous:ng selves, as shown, for example, in
EP-A984
248, US-A 4,716,770 or US-A 6,352,000, often also for accommodating some
mechanical components of the measuring transducer, such as e.g. elements
deforming
during operation on the basis of mechanical effects, elements such as
membrane, rod,
sleeve or tubular deformation- or vibration-elements; compare, in this
connection, also
the US-B 6,352,000 mentioned above.
In the case of measuring systems of the described kind, the measuring
electronics is
usually electrically connected via electrical lines, and/or wirelessly by
radio, with a
superordinated, electronic, data processing system arranged, most often,
spatially
remotely, and also spatially distributed, from the measuring electronics. To
this data
processing system are forwarded, in near-time, the measured-values produced by
the
measuring system. The measured-values are forwarded by means of measured-value
signals carrying the measured-values. Measuring systems of the described kind
are,
additionally, usually, by means of a data transmission network (wired- and/or
radio-
based) provided within the superordinated data processing system, connected
together
and/or with corresponding electronic process controls, for example
programmable logic
controllers (PLCs) installed on-site or process control computers installed in
a remote
control room, where the measured-values produced by means of the measuring
system
and digitized in suitable manner and correspondingly encoded are sent. By
means of
process control computers, with application of correspondingly installed
software
components, the transmitted measured-values can be further processed and
visualized
as corresponding measurement results e.g. on monitors and/or converted into
control
signals for other field devices, such as e.g. magnetically operated valves,
electric
motors, etc., embodied as actuators for process control. Accordingly, the data
processing system serves usually also for conditioning the measured-value
signal
delivered from the measuring electronics corresponding to the requirements of
downstream data transmission networks, for example suitably digitizing such
and, on
occasion, converting it into a corresponding telegram, and/or evaluating it on-
site. For
such purposes, provided in these data processing systems, electrically coupled
with the
pertinent connection lines, are evaluating circuits, which pre- or further-
process, and, if
required, suitably convert, measured-values received from the measuring
electronics.
Serving for data transmission in such industrial data processing systems, as
least
sectionally, are, especially serial, fieldbuses, such as e.g. FOUNDATION
FIELDBUS,
CAN, CAN-OPEN, RACKBUS-RS 485, PROFIBUS, etc. or, for example, also networks
based on the ETHERNET standard, as well as the corresponding standardized
transmission protocols, which are, most often, independent of application.
Usually, it is possible to implement by means of control computers, besides
such
process visualization, monitoring and control, also remote servicing,
parametering
and/or monitoring of the connected measuring system. Accordingly, measuring
electronics of modern, measuring, field devices permit, besides actual
measured-value
transmission, also transmission of various setting- and/or operating-
parameters used in
the measuring system, such as e.g. calibration data, measured-value ranges
and/or
also diagnostic values ascertained internally in the field devices. In support
of this,
operating data intended for the measuring system can, most often, likewise be
sent via
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CA 02692179 2009-12-17
the aforementioned data transmission network, which are, most often, hybrid as
regards transmission physics and/or transmission logic.
Besides the evaluating circuits required for processing and converting
measured-values
delivered from connected measuring electronics, superordinated data processing
systems of the described kind include, most often, also electrical supply
circuits serving
for supplying the connected measuring electronics and, as a result, also the
pertinent
measuring system with electrical energy, or power. The supply circuits provide
for the
pertinent measuring device electronics an appropriate supply voltage, which
is, on
occasion, fed directly by the connected fieldbus, and drive the electrical
lines connected
to the measuring device electronics, as well as the electrical currents
flowing
therethrough. A supply circuit can, in such case, for example, be assigned to
exactly
one measuring electronics and accommodated together with the evaluating
circuit
associated with the particular measuring device, for example joined to form a
corresponding fieldbus adapter, in a housing common to both, embodied e.g. as
a top-
hat rail module. It is, however, also quite usual to accommodate such
superordinated
evaluating circuits and supply circuits, in each case, in separate housings,
on occasion
spatially removed from one another and to wire them appropriately together via
external
cables.
In the case of industrial measuring systems of the type being discussed here,
often
involved, as a result, are spatially distributed measuring systems, wherein,
in each
case, a plurality of measured variables of equal and/or different type are
locally
registered by sensors at real, mutually separated measuring points along a
flow axis of
the measuring system defined by the process line. These measured variables are
fed
to the common measuring electronics in the form of corresponding, electrical,
measurement signals by wire, for example also in the so-called HARTO-MULTIDROP-
method or also in the so-called burst-mode method, and/or wirelessly,
especially by
radio and/or optically, on occasion also encoded into a digital signal or in a
digitally
transmitted telegram. For the case described above, in which such a measuring
system
is formed by means of a flow transducer, it is thus possible, for example in
addition to
the at least one, practically directly registered, flow parameter serving as
primary
measured variable, for example the volume flow, to ascertain, at least
indirectly and, as
a result, to measure, by means of the same measuring electronics, at least
virtually,
with application also of other, remotely registered, measured variables, for
example, a
remote, local temperature or a remote, local pressure in the medium, also
derived,
secondary measured variables, such as e.g. a mass flow and/or a density.
Experimental investigations on distributed measuring systems of the type being
discussed, which, as shown e.g. also in US-B 6,651,512, ascertain, by means of
a
directly measured, volume flow and a virtually measured density, a mass flow
as an
indirectly measured variable, have shown that, especially also despite
application of
internally, as well as externally, ascertained, measured variables proved to
be very
precise in the measuring ranges usual for the pertinent caliber of the process
line,
significant errors can arise in the result of a measurement virtual in the
above sense. It
is quite possible for these errors to lie in the range of about 5% of the
actual measured
CA 02692179 2009-12-17
variable or even beyond. This is ihe case, especiaily also when ascertaining
measured
variables, such as e.g. volume flow, temperature or pressure, as intermediate,
really
measured variables, and/or density as an intermediate variable measured
virtually
according to measuring and calculating methods recommended in the
aforementioned
industrial standards.
Further, comparative investigations have, in such case, additionally shown
that the
aforementioned measurement errors can show, among other things, a certain
dependence on the instantaneous Reynolds number of the flow, as well as also
on the
instantaneous thermodynamic state of the medium. However, it has also been
found, in
this connection, that, in numerous industrial applications, especially those
involving
compressible and/or at least 2-phase media, the Reynolds number, or the
thermodynamic state of the medium, can be not only chronologically but also
spatially
variable to a high degree, especially in the direction of the flow axis of the
measuring
system. Besides applications having at least partially compressible media,
additionally
especially also applications show a significant transverse sensitivity to
spatial variances
of the Reynolds number, or the thermodynamic state, when the measurement of at
least
one of the measured variables occurs at a measuring point (real or virtual),
at which the
process line has a caliber deviating at least from one of the measuring points
(real or
virtual) to the other. This is e.g. the case in the application of flow
conditioners
reducing the cross section of the line (such as in the case of e.g. nozzles
serving as so-
called reducers), which can find application in the inlet region of flow
measuring
transducers, or also in the application of flow conditioners increasing the
cross section
of the line (so-called diffusers) in the outlet region of flow measuring
transducers.
Measuring systems with such reducers and/or diffusers are described, for
example, in
GB-A21 42725, US-A 5,808,209, US-A2005/0092101, US-B 6,880,410, US-B
6,644,132, US-A 6,053,054, US-B 6,644,132, US-A 5,052,229 or US-B 6,513,393
and
are used, for example, for improving accuracy of measurement of flow measuring
transducers. It has, in such case, been further ascertained that such
transverse
sensitivities based on application of reducers and/or diffusers are
significant for caliber
ratios between about 0.6 and 0.7, while their influence for caliber ratios
with extreme
diameter jumps of smaller than 0.2 are quite negligible.
Another application area having a significant sensitivity to the
aforementioned variances
as affecting the desired accuracy of measurement concerns, furthermore, those
measuring systems, which are provided for the flow measurement of heavy gases,
such
as, perhaps, carbon dioxide or also phosgene, or long-chain carbon compounds
having
a molecular wa of over 30 g/mol,
The above-described spatial variance of the Reynolds number can, in turn, lead
to the
fact that practically each of the aforementioned, mutually spaced, real
measuring points
of the distributed measuring system has, during operation, a local Reynolds
number
deviating, to a considerable degree, from the local Reynolds number of each of
the
other, also-used, measuring points. Equally, also the mentioned variance of
the
thermodynamic state would lead to the fact that mutually spaced, measuring
points of
the distributed measuring system can have thermodynamic states differing from
one
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CA 02692179 2013-10-09
78639-44
another. In view of this, thus, each of the measured variables, as measured on
a
distributed basis, would have to be adjusted according to the particularly
associated,
local Reynolds number and/or the particularly associated, local thermodynamic
state,
a task which, in the absence of the information required therefore, namely
the, in
each case, other, but remotely measured, state variables, is not directly
possible. If,
for example, the density and/or the mass flow, calculated on the basis of the
measured state variables pressure and temperature, would be calculated without
taking into consideration the variance of the Reynolds number, or
thermodynamic
state, an additional measurement error would result, having essentially a
quadratic
dependence on the flow velocity. Accordingly, for the aforementioned
configuration,
at flow velocities of clearly less than 10m/s, the measuring accuracy of about
0.1`)/0 to
0.5%, currently strived for, is practically no longer significant.
Starting from the above-described disadvantages of measuring systems of the
described kind, especially those ascertaining a mass flow or a volume flow, an
embodiment of the invention may increase the accuracy of measurement for such
secondary measured variables ascertained with application of spatially,
distributedly
registered, thermodynamic state variables such as pressure and/or temperature.
According to one aspect, there is provided a measuring system for measuring a
density of a medium, which flows in a process line along a flow axis of the
measuring
system and which is variable as regards a thermodynamic state, said measuring
system comprising: at least one temperature sensor placed at a temperature
measuring point, reacting primarily to a local temperature of medium flowing
past,
and delivering at least one temperature measurement signal influenced by the
local
temperature of the medium to be measured; at least one pressure sensor placed
at a
pressure measuring point, reacting primarily to a local pressure of medium
flowing
past, and delivering at least one pressure measurement signal influenced by
the
local pressure in the medium to be measured; and a measuring electronics
including
a data memory, which stores at least one measuring system parameter specifying
solely the medium currently to be measured, and communicating, in each case,
with
7
CA 02692179 2013-10-09
=
78639-44
the temperature sensor and the pressure sensor; wherein: the measuring
electronics
produces, with application both of the temperature measurement signal and also
at
least the pressure measurement signal and with application of the at least one
measuring system parameter specifying solely the medium currently to be
measured,
at least one density measured-value representing, instantaneously, a local
density of
the flowing medium at a virtual density measuring point predeterminably
spaced,
along the flow axis, from at least one of: the pressure measuring point and
the
temperature measuring point.
There is also provided a use of such a measuring system for registering and
outputting a density of the medium flowing in the process line as well as at
least one
further measured variable selected from: a mass flow, a volume flow, a flow
velocity,
a viscosity, a pressure, a temperature of the medium flowing in the process
line.
One embodiment of the invention resides in a measuring system for measuring a
density of a medium, which is variable as regards a thermodynamic state,
especially
at least partially compressible, flowing in a process line along a flow axis
of the
measuring system. The measuring system includes therefore: At least one
temperature sensor placed at a temperature measuring point, reacting primarily
to a
local temperature, of medium flowing past and delivering at least one
temperature
measurement signal influenced by the local temperature of the medium to be
measured; at least one pressure sensor placed at a pressure measuring point,
reacting primarily to a local pressure, p, especially a static pressure, of
medium
flowing past, and delivering at least one pressure measurement signal
influenced by
the local pressure, p, in the medium to be measured; and a measuring
electronics
communicating, in each case, at least at times, with at least the temperature
sensor
and the pressure sensor, and producing, at least at times, with application
both of the
temperature measurement signal and also at least the pressure measurement
signal,
at least one density measured-value, especially a digital density measured-
value
representing, instantaneously, a local density, p, of the flowing medium at a
virtual,
density measuring point, especially a locationally fixed, virtual, density
measuring
7a
CA 02692179 2013-10-09
78639-44
point, predeterminably spaced from the pressure measuring point and/or the
temperature measuring point along the flow axis.
In a first embodiment of the invention, it is provided that the measuring
electronics
includes a data memory, especially a non-volatile data memory, which stores,
at least
at times, at least one measuring system parameter specifying solely the medium
currently to be measured, especially a system parameter such as a specific
heat
capacity, cp, of the medium currently to be measured, a molar mass, n, of the
medium and/or the number, f, of degrees of oscillatory freedom of the atoms,
or
molecules, of the medium, as determined by the molecular structure of the
medium.
7b
CA 02692179 2009-12-17
In a second embodiment of the invention, it is provided that the ineasuring
electronics.
ascertains
ascertains the density measured-value with application of the at least one
measuring
system parameter specifying solely the medium currently to be measured.
In a third embodiment of the invention, it is provided that the measuring
electronics
includes a data memory, especially a non-volatile data memory, which stores,
at least at
times, at least one measuring system parameter specifying both the medium to
be
measured by means of the measuring system as well as also instantaneous
circumstances of installation of the measuring system, wherein the
circumstances of
installation are determined by the arrangement of pressure-, temperature- and
density
measuring points relative to one another, as well as, in each case, by the
form and size
of the process line in the areas of the pressure-, temperature- and density
measuring
points. In a further development of this embodiment of the invention, the
measuring
electronics ascertains the density measured-value with application of the at
least one
measuring system parameter specifying both the medium currently to be measured
by
means of the measuring system as well as also instantaneous circumstances of
installation of the measuring system.
In a fourth embodiment of the invention, it is provided that the measuring
electronics
includes a data memory, especially a non-volatile data memory, which stores,
at least at
times, at least one measuring system parameter of a first kind specifying the
medium
currently to be measured, especially a specific heat capacity of the medium
currently to
be measured, a molar mass of the medium and/or the number of degrees of
freedom of
the medium, and which stores, at least at times, at least one measuring system
parameter of a second kind specifying both the medium currently to be measured
as
well as also instantaneous circumstances of installation of the measuring
system,
wherein the instantaneous circumstances of installation are determined by the
arrangement of pressure-, temperature- and density-measuring points relative
to one
another, as well as, in each case, by the form and size of the process line in
the regions
of the pressure-, density- and/or temperature-measuring points, and wherein
the
measuring electronics ascertains the density measured-value with application
at least of
the measuring system parameter of the first kind and the measuring system
parameter
of the second kind.
In a fifth embodiment of the invention, it is provided that the measuring
electronics
receives, at least at times, numerical parameter values, especially numerical
parameter
values ascertained, externally of the measuring system and/or near in time,
for at least
one measuring system parameter specifying a medium to be measured and/or
instantaneous circumstances of installation of the measuring system,
especially a heat
capacity, cp, for medium to be measured, which represents a specific heat
capacity, cp,
earlier ascertained and/or measured remotely from the density measuring point
for the
medium to be measured.
In a sixth embodiment of the invention, it is provided that the measuring
electronics
communicates, especially via fieldbus, at least at times, especially by wire
and/or by
radio, with a superordinated, electronic, data processing system. In a further
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CA 02692179 2009-12-17
development of this embodiment of the invention, it is additionally provided
that the
measuring electronics transmits the density measured-value to the data
processing
system and/or wherein the measuring electronics receives from the data
processing
system, at least at times, measuring system parameters specifying numerical
parameter
values for the medium to be measured currently, especially its thermodynamic
properties and/or its chemical composition, especially a specific heat
capacity, cp, of the
medium currently to be measured, a molar mass, n, of the currently to be
measured
medium and/or the number, f, of degrees of oscillatory freedom of the atoms,
or
molecules, of the currently to be measured medium, and/or that the measuring
electronics is connected with the superordinated, electronic, data processing
system by
means of a fieldbus, especially a serial fieldbus.
In a seventh embodiment of the invention, it is provided that the measuring
electronics
ascertains, during operation, at least at times, a specific heat capacity, cp,
of the
currently to be measured medium, especially on the basis of the formula:
(, R
c = 1+¨ =¨,
2 n
wherein n is a molar mass, R, the absolute gas constant, with R = 8.3143 J/(K
mol) and
f, a number, determined by the molecular structure of the medium, of degrees
of
oscillatory freedom of its atoms, or molecules.
In an eighth embodiment of the invention, it is provided that the measuring
electronics
generates, repetitively, a temperature measured-value, especially a digital
temperature
measured-value, based on the temperature measurement signal, and wherein the
temperature measured-value represents, instantaneously, the temperature of the
medium at the temperature measuring point.
In a ninth embodiment of the invention, it is provided that the measuring
electronics
generates, repetitively, a pressure measured-value, especially a digital
pressure
measured-value, based on the pressure measurement signal, and wherein the
pressure
measured-value represents a pressure instantaneously reigning in the medium,
especially at the pressure measuring point.
In a tenth embodiment of the invention, it is provided that the measuring
system further
includes a flow sensor placed at a flow measuring point and reacting,
primarily, to a
local flow parameter, especially a flow parameter averaged over a cross
section of the
process line, especially a flow velocity, a volume flow or a mass flow, of the
medium to
be measured, especially also changes of the same, and wherein the flow sensor
delivers at least one flow measurement signal influenced by the local flow
parameter.
Developing this embodiment of the invention further, it is provided that
the measuring electronics communicates, at least at times, also with the flow
sensor, and wherein the measuring electronics ascertains the density measured-
value
with application also of the flow measurement signal; and/or
9
CA 02692179 2009-12-17
the medium has, at the virtual density measuring point, a thermodynamic state
corresponding to a thermodynamic state of the medium at the velocity measuring
point;
and/or
the virtual density measuring point and the flow measuring point at least
partially
overlap one another, especially they are coincident; and/or
the temperature measuring point and the flow measuring point at least
partially
overlap one another, especially they are coincident; and/or
the pressure measuring point and the flow measuring point at least partially
overlap one another; and/or
the density measured-value represents a local density of the medium in the
region of the flow sensor; and/or
the measuring electronics communicates with the flow sensor by means of a
field
bus, especially a serial field bus, and/or wirelessly by radio; and/or
the measuring electronics communicates, at least at times, with the flow
sensor,
wherein the measuring electronics ascertains, with application at least of the
flow
measurement signal, a velocity measured-value, especially a digital flow
measured-
value, which represents instantaneously the flow velocity of the flowing
medium.
In an eleventh embodiment of the invention, it is provided that the measuring
electronics
produces the density measured-value also with application of at least one
numerical
compensation factor, especially a digitally stored compensation factor, which
corresponds with a locational variability occurring along the flow axis of the
measuring
system, especially a locational variability ascertained in advance or during
operation, of
at least one thermodynamic state variable of the medium, especially a
temperature, a
pressure or a density, and/or with a locational variability occurring along
the flow axis of
the measuring system, especially a locational variability ascertained in
advance or
during operation, of the Reynolds number of the flowing medium.
Developing this embodiment of the invention further, it is additionally
provided that
the at least one compensation factor is ascertained taking into consideration
the
medium actually to be measured, especially its composition and/or its
thermodynamic
properties, especially during a calibration of the measuring system with
known,
reference medium and/or during start-up of the measuring system on-site;
and/or
the measuring electronics ascertains a compensation factor, at least once,
during
start-up of the measuring system; and/or
the measuring electronics repetitively ascertains the compensation factor
during
operation of the measuring system, especially in conjunction with a change of
at least
one chemical property of the medium to be measured or with a replacement of
the
same with another medium; and/or
the measuring electronics ascertains the at least one compensation factor on
the
basis of a predetermined, specific heat capacity, cp, of the current medium,
especially a
heat capacity ascertained in dialog with a user and/or externally of the
measuring
electronics; and/or
the measuring electronics includes a data memory storing the at least one
compensation factor, especially a data memory embodied as a table memory
and/or a
non-volatile memory; and/or
CA 02692179 2009-12-17
the data memory stores a plura:ity of compensation factors ascertained in
advance for different media and/or for different circumstances of
installation; and/or
the measuring electronics selects the at least one compensation factor taking
into consideration the current medium, as well as the current circumstances of
installation, from the plurality of compensation factors stored in the data
memory.
In a twelfth embodiment of the invention, it is provided that the measuring
electronics
produces the density measured-value with application of at least one density
correction
value ascertained at run time, dependent both on a flow velocity of the medium
as well
as also on the local temperature reigning at the temperature measuring point,
wherein
the correction value corresponds with an instantaneous, locational variability
of at least
one thermodynamic state variable of the medium, especially with such an
instantaneous, locational variability related to the medium currently to be
measured as
well as to instantaneous circumstances of installation and/or with such an
instantaneous, locational variability occurring along the flow axis of the
measuring
system, and/or wherein the correction value corresponds with an instantaneous
locational variability of the Reynolds number of the flowing medium,
especially with a
locational variability of the Reynolds number related to the medium and/or the
type of
construction of the measuring system, or with an instantaneous variability of
the
Reynolds number occurring along the flow axis of the measuring system.
Further developing this embodiment of the invention, it is further provided
that
the measuring electronics ascertains, during operation, a velocity measured-
value, especially a digital velocity measured-value, representing,
instantaneously, the
flow velocity of the flowing medium and that the measuring electronics
ascertains, with
application of the velocity measured-value as well as the temperature measured-
value,
the density correction value; and/or
the measuring electronics compares, repetitively, during operation, the
density
correction value with at least one predetermined reference value; and/or
the measuring electronics, based on a comparison of density correction value
and reference value, quantitatively signals an instantaneous deviation of the
density
correction value from the reference value and/or generates an alarm, which
signals an
undesired discrepancy, especially an unallowably high discrepancy, between
density
correction value and associated reference value.
In a thirteenth embodiment of the invention, it is provided that the measuring
electronics, based on the pressure measurement signal, as well as on the
temperature
measurement signal, ascertains a provisional density measured-value,
especially
according to one of the industry standards AGA 8, AGA NX-19, SGERG-88 lAWPS-
1F97, ISO 12213:2006, representing a density which the flowing medium only
apparently has at the virtual density measuring point.
Further developing this embodiment of the invention, it is additionally
provided that
the measuring electronics ascertains, repetitively during operation, a density
error corresponding with a deviation, especially a relative deviation, of the
provisional
density measured-value from the density measured-value, and especially issues
such
also in the form of a numerical, density measured-value; and/or
11
CA 02692179 2009-12-17
the measuring electronics issues an instantanenus density error corresponding
with a deviation, especially a relative deviation, of provisional density
measured-value
and density measured-value, in the form of a numerical, density error value
and/or
compares the instantaneous density error with at least one predetermined
reference
value and, based on this comparison, generates, at times, an alarm signaling
an
undesired, especially impermissibly high, discrepancy between provisional
density
measured-value and density measured-value.
In a fourteenth embodiment of the invention, it is provided that the measuring
system
includes, further, at least one flow sensor placed at a flow measuring point
and reacting
primarily to a local flow parameter, especially a flow parameter averaged over
a cross
section of the process line, especially a flow velocity, a volume flow or a
mass flow of
the medium to be measured, especially also to changes of the same, and
delivering at
least one flow measurement signal influenced by the local flow parameter,
wherein
the measuring electronics communicates, at least at times, with the flow
sensor
and wherein the measuring electronics, with application at least of the flow
measurement signal, ascertains a volume flow measured-value, especially a
digital
volume flow measured-value, representing, instantaneously, a volume flow rate
of the
flowing medium; and/or
the measuring electronics ascertains, with application at least of the density
measured-value and the volume flow measured-value, a mass flow measured-value,
especially a digital mass flow measured-value, representing, instantaneously,
a mass
flow rate of the flowing medium; and/or
wherein the measuring electronics ascertains, with application at least of the
temperature measurement signal, the pressure measurement signal and the flow
measurement signal, a mass flow measured-value, especially a digital mass flow
measured-value, representing, instantaneously, a mass flow rate of the flowing
medium;
and/or
the flow measuring point is arranged upstream of the temperature measuring
point
and/or upstream of the pressure measuring point; and/or
the at least one flow sensor is formed by means of at least one piezoelectric
element and/or by means of at least one piezoresistive element; and/or
the at least one flow sensor is formed by means at least of an electrical
resistance element, especially a resistance element through which a heating
current
flows, at least at times; and/or
the at least one flow sensor is formed by means of at least one measuring
electrode tapping electrical potentials, especially a measuring electrode
contacting
flowing medium; and/or
the at least one flow sensor is formed by means of at least one measuring
capacitor reacting to changes of the flow parameter; and/or
the at least one flow sensor, especially a flow sensor protruding at least
partially
into a lumen of the process line, is located downstream of at least one bluff
body
immersed in the medium and protruding into a lumen of the process line.
12
CA 02692179 2009-12-17
In a fifteenth embodiment of the invention, it is provided that the measuring
electronics
communicates with the temperature sensor by means of a fieldbus, especially a
serial
fieldbus, and/or wirelessly by radio.
In a sixteenth embodiment of the invention, it is provided that the measuring
electronics
communicates with the pressure sensor by means of a field bus, especially a
serial
fieldbus, and/or wirelessly by radio.
In a seventeenth embodiment of the invention, it is provided that the medium
at the
density measuring point is in a thermodynamic state differing, at least at
times,
significantly, especially to a degree significant for a desired accuracy of
the measuring
accuracy of the measuring system, as regards at least one local, thermodynamic
state
variable, especially a temperature and/or a pressure and/or a density, from a
thermodynamic state of the medium at the temperature measuring point and/or a
thermodynamic state of the medium at the pressure measuring point.
In an eighteenth embodiment of the invention, it is provided that the flowing
medium has
a Reynolds number greater than 1000.
In a nineteenth embodiment of the invention, it is provided that the medium is
compressible, having, especially, a compressibility K = - 1/V = dV/dp, which
is greater
than 10-6 bar-1, and/or is at least partially gaseous. The medium can, in such
case, be a
gas loaded with solid particles and/or with droplets.
In a twentieth embodiment of the invention, it is provided that the medium has
two or
more phases. One phase of the medium can, in such case, be liquid and/or the
medium can be a liquid containing gas and/or solid particles.
In a twenty-first embodiment of the invention, it is provided that the
measuring system
further includes a display element communicating, at least at times, with the
measuring
electronics, for visual signalizing at least of the density measured-value.
In a twenty-second embodiment of the invention, it is provided that the
process line is
embodied, at least sectionally, especially in the region at least of the
density measuring
point and/or in the region at least of the pressure measuring point, as a
pipeline
essentially stable in form at least under operating pressure, especially in
the form of a
rigid pipeline and/or a pipeline having a circular cross section.
In a twenty-third embodiment of the invention, it is provided that the process
line is
embodied at least sectionally, especially in the region between density
measuring point
and pressure measuring point and/or between density measuring point and
temperature
measuring point, as an essentially straight pipeline, especially a pipeline
having a
circular cross section.
In a twenty-fourth embodiment of the invention, it is provided that the
process line has at
the virtual density measuring point a caliber differing from a caliber of the
process line at
3'
CA 02692179 2009-12-17
the pressure measuring point. Deveioping this embodiment of the invention
further, it is -
provided that the caliber of the process line is greater at the pressure
measuring point
than the caliber of the process line at the virtual density measuring point,
especially it is
provided that a caliber ratio of the caliber of the process line at the
pressure measuring
point to the caliber of the process line at the virtual density measuring
point is kept
greater than 1.1.
In a twenty-fifth embodiment of the invention, it is provided that a caliber
ratio of a
caliber of the process line at the pressure measuring point to a caliber of
the process
line at the virtual density measuring point is kept smaller than 5.
In a twenty-sixth embodiment of the invention, it is provided that a caliber
ratio of a
caliber of the process line at the pressure measuring point to a caliber of
the process
line at the virtual density measuring point is kept in a range between 1.2 and
3.1.
In a twenty-seventh embodiment of the invention, it is provided that the
process line
has, between the virtual density measuring point and the pressure measuring
point, a
line segment which is embodied as a diffuser, especially a funnel-shaped
diffuser,
having a lumen widening in the flow direction, especially continuously
widening.
In a twenty-eighth embodiment of the invention, it is provided that the
process line has,
between the virtual density measuring point and the pressure measuring point,
a line
segment which is embodied as a nozzle, especially a funnel-shaped nozzle,
having a
lumen narrowing in the flow direction, especially continuously narrowing.
In a twenty-ninth embodiment of the invention, it is provided that the process
line has at
the virtual density measuring point a caliber which is essentially equal to a
caliber of the
process line at the pressure measuring point.
In a thirtieth embodiment of the invention, it is provided that the process
line has, at the
virtual density measuring point, a caliber differing from a caliber of the
process line at
the temperature measuring point. Developing this embodiment of the invention
further,
it is additionally provided that the caliber of the process line is greater at
the
temperature measuring point than the caliber at the virtual density measuring
point,
especially that a caliber ratio of the caliber of the process line at the
temperature
measuring point to the caliber of the process line at the virtual density
measuring point
is kept greater than 1.1.
In a thirty-first embodiment of the invention, it is provided that a caliber
ratio of the
caliber of the process line at the temperature measuring point to the caliber
of the
process line at the virtual density measuring point is kept smaller than 5.
In a thirty-second embodiment of the invention, it is provided that a caliber
ratio of the
caliber of the process line at the temperature measuring point to the caliber
of the
process line at the virtual density measuring point is kept in a range between
1.2 and
3.1.
14
CA 02692179 2009-12-17
In a thirty-third embodiment of the invention, it is provided that the process
line has,
between the virtual density measuring point and the temperature measuring
point, a line
segment embodied as a diffuser, especially a funnel-shaped diffuser, having a
lumen
widening in the flow direction, especially continuously widening.
In a thirty-fourth embodiment of the invention, it is provided that the
process line has,
between the virtual density measuring point and the temperature measuring
point, a line
segment embodied as a nozzle, especially a funnel-shaped nozzle, having a
lumen
becoming narrower in the flow direction, especially continuously narrower.
In a thirty-fifth embodiment of the invention, it is provided that the process
line has, at
the virtual density measuring point, a caliber essentially equal to a caliber
of the process
line at the temperature measuring point.
In a thirty-sixth embodiment of the invention, it is provided that the virtual
density
measuring point is placed upstream of the temperature measuring point and/or
upstream of the pressure measuring point.
In a thirty-seventh embodiment of the invention, it is provided that the
pressure
measuring point is arranged downstream from the temperature measuring point.
In a thirty-eighth embodiment of the invention, it is provided that a
separation of the
pressure measuring point from the virtual density measuring point is different
from a
separation of the temperature measuring point from the virtual density
measuring point.
In a thirty-ninth embodiment of the invention, it is provided that a
separation of the
pressure measuring point from the virtual density measuring point is greater
than a
separation of the temperature measuring point from the virtual density
measuring point.
In a fortieth embodiment of the invention, it is provided that a separation of
the pressure
measuring point from the virtual density measuring point is greater than a
caliber of the
process line at the pressure measuring point and/or wherein a separation of
the
pressure measuring point from the temperature measuring point is greater than
a
caliber of the process line at the pressure measuring point. Developing this
embodiment of the invention further, it is additionally provided that a
separation of the
pressure measuring point from the virtual density measuring point corresponds
at least
to 3-times, especially more than 5-times, a caliber of the process line at the
pressure
measuring point and/or that a separation of the pressure measuring point from
the
temperature measuring point corresponds at least to 3-times, especially more
than 5-
times, a caliber of the process line at the pressure measuring point.
In a forty-first embodiment of the invention, it is provided that the
measuring electronics
includes a microcomputer. Developing this embodiment of the invention further,
it is
additionally provided that the measuring electronics produces at least the
density
measured-value by means of the microcomputer.
CA 02692179 2013-10-09
=
78639-44
,
In a forty-second embodiment of the invention, it is provided that the
measuring
system further includes at least one electronics housing, especially an
explosion-
and/or pressure- and/or impact- and/or weather-resistant housing, in which the
measuring electronics is at least partially accommodated. In a further
development of
this embodiment, it is additionally provided that the at least one, especially
metal,
electronics housing is held to the process line and/or placed in the immediate
vicinity
of the virtual density measuring point.
A basic idea of an embodiment of the invention is to improve accuracy of
measurement of measuring systems of the described kind by ascertaining, with
improved accuracy, the density derived from, indeed, real, but, however, of
necessity,
distributedly measured, state variables. This derived density serves as a
central
measured variable in numerous applications of industrial measurements
technology
in the case of flowing media. The improved accuracy is achieved by taking into
consideration possible spatial variance, especially also the degree thereof,
of
Reynolds number and/or thermodynamic state of the flowing medium. This is done
in
the case of the measuring system of the invention by a reliable calculating of
the
density, by referencing it to a reference point defined earlier for the
particular
measuring system and serving as a locationally fixed, imaginary, measuring
point.
The density is, thus, measured virtually. Developing this basic idea further,
the
measurement accuracy, with which the measuring system ascertains the local
density, can be significantly improved further by having the measuring system
ascertain said density also taking into consideration an equally locally
measured,
extant flow velocity, in order to achieve a further compensation of the error
accompanying the mentioned variances of Reynolds number and/or thermodynamic
state of the flowing medium.
An embodiment of the invention is based, in such case, on the surprising
discovery
that spatial variance in the Reynolds number and/or in the thermodynamic
state, and
the measurement errors associated therewith, can be projected onto a single
dimension lying in the flow direction and/or coinciding with the flow axis of
the
16
CA 02692179 2013-10-09
78639-44
measuring system and, thus, can be mapped into a correspondingly simplified
set of
measuring system parameters, which can be ascertained, at least predominantly
in
advance, experimentally and/or with computer support, for example in the
course of a
calibration of the measuring system, during completion of manufacturing and/or
during start-up of the same. The spatial variances, or their extent and, as a
result,
also the set of device parameters, are, it is true, specific for each concrete
measuring
system and each concrete medium, so that the calibration is individual, but
such can
then, however, be viewed as invariant in the face of possible changes of
Reynolds
number and/or thermodynamic state arising during operation, if the measuring
system remains unchanged, with essentially constant medium as regards its
chemical composition. In other words, for a given, distributed measuring
system, the
size of changes of the thermodynamic state arising along the flow axis can be
determined ahead of time, so that their influence can be calibrated and, as a
result,
also compensated with accuracy sufficient for the measurements, with it having
been
found, surprisingly, that the size of the change is largely constant for a
16a
CA 02692179 2013-10-09
= 78639-44
given measuring system with constant medium, so that such can be mapped into a
set
= of, it is true, specific, but also constant, device parameters.
A possible advantage of embodiments of the invention is additionally to be
seen in
the fact that the fundamental method can be directly retrofitted into
numerous,
already installed, measuring systems, at least insofar as the measuring device
electronics permits a change of the pertinent processing software.
The invention, as well as additional advantageous embodiments, will now be
explained
in the following on the basis of examples of embodiments, on occasion with
reference to
the drawing, the figures of which show as follows:
Fig. 1 perspectively, in side view, a measuring system
for
measuring a local density possessed by a medium flowing in
a process line at a density measuring point, by means of a
pressure sensor arranged at a pressure measuring point and
a temperature sensor arranged at a temperature measuring
point;
Fig. 2 the measuring system of Fig. 1, this time in
the form of a
block diagram;
Figs. 3a, 3b perspectively and partially sectioned, in views
from different
angles, eddy flow transducer suitable for application in a
measuring system of Fig. 1 and working according to the
vortex principle; and
Figs. 4a to 4h schematically in section, different variants
for embodying the
process line and for relative arrangement of the individual
measuring points in the measuring system of Fig. 1.
Fig. 1 shows, schematically, a measuring system 1, which can be modularly
constructed
and which is suitable, and provided, for ascertaining, at least at times, and
very
precisely, and, equally very robustly, a density of a medium flowing in a
process line 20
and for mapping such, occasionally even in real time, into a corresponding,
reliable, for
example even digital, density measured-value X. Besides a single phase medium,
it is
also possible that the medium can have two or more phases. Examples of media
include e.g. gas, liquid (which can contain gas and/or solid particles), a gas
containing
solid particles and/or droplets, vapor or steam (which can be a saturated
vapor or dry
steam), or the like, such as hydrogen, nitrogen, chlorine, oxygen, helium or
compounds
and/or mixtures formed thereof, such as e.g. carbon dioxide, water, phosgene,
air,
natural gas or other hydrocarbon mixtures.
Especially, the measuring system serves for measuring, very accurately, the
density of
the flowing medium also for the case in which the medium is variable as
regards a
thermodynamic state in the direction along the flow axis of the measuring
system, such
17
CA 02692179 2009-12-17
as can be the case, for example, in situations nvcvir. media reacting within
the
process line or for sectionally cooled media or for sectionally heated media,
compressible media and/or in the case of process lines of cross section
varying in the
direction of the flow axis. The measuring system is further provided for
ascertaining
density of flowing media having a Reynolds number, Re, greater than 1000,
and/or
compressible media having a compressibility, K, of more than 10-6 ball.
The measuring system includes therefor: At least one temperature sensor placed
at a
temperature measuring point Ms, primarily reacting to a local temperature, 9,
and
delivering at least one temperature measurement signal xs influenced by such
local
temperature, of the medium to be measured flowing past; as well as at least
one
pressure sensor placed at a pressure measuring point Mp, reacting primarily to
a local,
e.g. static and/or absolute, pressure, p, of, and delivering at least one
pressure
measurement signal xp influenced by such local pressure in, the medium to be
measured flowing past. Although the pressure measuring point in the example of
an
embodiment shown here is located downstream from the temperature measuring
point,
it can, in case required, of course, also be arranged upstream of the
temperature
measuring point.
Besides the temperature sensor and pressure sensor, the measuring system
includes,
additionally, at least one measuring electronics 100 communicating, at least
at times,
both with the temperature sensor and with the pressure sensor and receiving,
by wire
and or wirelessly, measurement signals xs, xp from the temperature sensor and
the
pressure sensor. The measurement signals xs, xp can, if required, be
appropriately
converted before being sent to the measuring electronics 100.
Serving as temperature sensor can be, for example, an industrial temperature
sensor
such as e.g. a thermocouple or a resistance thermometer of type Pt 100 or Pt
1000,
while the pressure sensor can be, for example, an industrial, especially
absolutely,
and/or relatively, measuring, pressure sensor, e.g. one with a capacitive
pressure
measuring cell. Of course, if necessary, also other pressure measuring cells
converting
pressures registered and transferred from the medium into corresponding
measurement
signals can be used, as well as other suitable temperature sensors. The
temperature
sensor can, additionally, be provided, for example, as a component of a self-
sufficient,
industrial grade, temperature measuring device having its own measuring-device
electronics. Such temperature measuring devices, known per se to those skilled
in the
art, are well established in industrial process measurements technology and
are sold,
for example, also by the firm, Endress+Hauser VVetzer GmbH+Co. KG, under the
designations "Easytemp TSM" or "Omnigrad T". Alternatively thereto or in
supplementation thereof, the temperature sensor can, as explained in more
detail
below, also be embodied as an integral part of a complex in-line measuring
device
possibly registering even a plurality of measurement variables of the flowing
medium.
Equally, the pressure sensor also can be an integral part of such a complex,
inline,
measuring device, or a component of a self-sufficient, industrial grade,
pressure
measuring device with its own measuring-device electronics. Such pressure
measuring
devices, likewise known to those skilled in the art, are also well established
in industrial
18
CA 02692179 2009-12-17
process measurements technology and are sold, for ex.dmple, also by the firm,
Endress+Hauser GmbH+Co. KG under the designations "Cerabar S", "Cerabar M" or
"Cerabar I'. Also, the pressure sensor and the temperature sensor can,
however, also
be provided in the form of a single measuring device for pressure and
temperature
measurement, for example, an industrial, combination, measuring device as
proposed
in WO-A 97/48970.
As shown schematically in Fig. 1, the measuring electronics can be
accommodated, at
least partly, in an electronics housing 110, especially an explosion- and/or
pressure-
and/or impact- and/or weather-resistant housing. The electronics housing 110,
for
example of metal, can, as also shown in Fig. 1, on occasion, be mounted on the
process line.
For the measurement-system-internal, further processing of the pressure
measurement
signal and the temperature measurement signal, an embodiment of the invention
additionally provides in the measuring electronics a microcomputer pC, which
serves
especially also for producing the density measured-value Xp, and which can be
formed,
for example, by means of at least one microprocessor and/or by means of at
least one
signal processor. Alternatively thereto or in supplementation thereof, for
implementing
the microcomputer pC, also application-specific, integrated, ASIC circuits
and/or
programmable logic components or systems can be used, such as e.g. so-called
FPGAs (field programmable gate array) and/or, as also proposed in WO-A
03/098154,
so-called SOPCs (system on programmable chip) can be used. Furthermore, the
measuring electronics includes, in another embodiment of the invention, at
least one
display element HMI, for example, placed in the immediate vicinity of the
measuring
electronics and communicating, at least at times, with the measuring
electronics,
especially with the microcomputer possibly provided therein, for the visual
signaling at
least of the density measured-value. Display element HMI can, in such case, be
embodied also in the form of a combined, display and servicing element, which
permits,
besides the visualizing of measured-values, also user input of service
commands
parametering, and/or controlling, the measuring electronics.
In a further embodiment of the invention, it is additionally provided that the
measuring
electronics generates, based on the temperature measurement signal, for
example also
with application of the, on occasion, provided microcomputer, repetitively, a
temperature
measured-value )c), especially a digital one, instantaneously representing a
local
temperature of the medium, especially the temperature of the medium at the
temperature measuring point, and/or that the measuring electronics generates,
based
on the pressure measurement signal xp, for example, in turn, with application
of the, on
occasion, provided microcomputer, repetitively, a pressure measured-value Xp,
especially a digital one, instantaneously representing a pressure reigning in
the
medium, especially at the pressure measuring point.
At least for the above-described case, in which the measuring system is formed
by
means of two, or also more, self-sufficient, measuring devices, in the case of
the
measuring system of the invention, also the measuring electronics itself can
be
19
CA 02692179 2009-12-17
implemented by appropriate interconnecting, by wire and/or wireiessly, of
individual
measuring device electronics thus forming subcomponents of the measuring
electronics
and can, as a result, also be built-up modularly. In such case, the measuring
electronics can communicate with the temperature sensor and/or with the
pressure
sensor, for example, by means of a fieldbus, especially a serial fieldbus.
Alternatively to
a distributed construction, the measuring electronics can, however, also be
embodied,
in case necessary, in the form of a single electronics module, into which the
measurement signals produced by the pressure and/or temperature sensors are
directly
fed.
The, on occasion, at least two measuring device electronics, or electronics
subcomponents, 1001, 1002 are to be so coupled together in manner known to
those
skilled in the art that, during operation of at least one of the two measuring
device
electronics 1001, 1002, correspondingly produced measurement data can be
transmitted
at least unidirectionally to the other, functioning, thus, as master
electronics. This can
be done, in manner known to those skilled in the art, in the form of
measurement
signals coded in their voltage, their current and/or their frequency and/or in
the form of
measured-values encapsulated in the form of digitally coded telegrams, e.g. in
the
HART -MULTIDROP method or in the burst-mode method. Of course, instead of
this,
however, also data connections communicating bidirectionally between the two
measuring device electronics 1001, 1002 can be used for transmission of the
locally
ascertained, measured variables to, in each case, the other measuring device
electronics 1001, 1002, respectively, for example via external fieldbus. For
implementing
the necessary communication connection between the two measuring device
electronics 1001, 1002, it is possible to apply, in advantageous manner,
standard
interfaces correspondingly established in industrial measurements and
automation
technology, such as e.g. line-conveyed, 4-20 mA, current loops, on occasion
also in
connection with HART or other applicable fieldbus protocols and/or suitable
radio
connections.
In a further advantageous embodiment of the invention, the at least one
measuring
electronics 1001, 1002 is additionally so designed, that it communicates, at
least at
times, as indicated schematically in Fig. 1, with a data processing system
superordinated thereto, and, indeed, in a manner such that, at least in normal
measuring operation, measured-values repetitively ascertained on the part of
the
measuring system are transferred, on occasion even in the form of a digitally
coded
telegram, as near-time as possible and/or in real time, to the data processing
system.
For registering measured-values transmitted from the measuring electronics,
data
processing system 2 is additionally provided with at least one evaluating
circuit 80
suitably communicating, at least at times, therewith. The superordinated data
processing system 2 can be, for example, part of a process-near, automatic
control unit
or also a long-distance process control system having a plurality of process
control
computers and/or digital programmable logic controllers, which are arranged
spatially
distributed within an industrial plant and coupled together via a
corresponding data
transmission network, especially also by means of digital fieldbusses.
Equally, the data
processing system can be connected with further measuring devices and/or with
control
CA 02692179 2009-12-17
Jg
devices, such as e.g. valves or pumps, involved in the process. In a further
development of the invention, the data processing system further includes at
least one
fieldbus FB, especially a serial fieldbus, serving for the transmission of
digital
measurement- and/or operational-data. The at least one fieldbus FB can be, for
example, one operating according to one of the standards established in
industrial
process automation, such as e.g. FOUNDATION FIELDBUS, PROFIBUS, CANBUS,
MODBUS, RACKBUS-RS 485 or the like. In an advantageous further development, it
is, in such case, additionally provided that the aforementioned evaluation
circuit 80 is
coupled to the at least one fieldbus, especially for forwarding of measured-
values
received in the form of digital measurement data from the measuring system.
Depending on how fieldbus and measuring electronics are embodied, the latter
can be
connected to the data processing system 2 either directly or by means of an
adapter,
which suitably converts the signal carrying the measured-value.
The measuring electronics and the data processing system 2 distanced, on
occasion
considerably, spatially therefrom are, in a further development of the
invention,
connected electrically together by means of at least one line-pair 2L, through
which
current I, especially a variable current I, flows, at least at times, during
operation. The
current can be fed, for example, from an external electrical energy, or power,
supply 70
provided in the superordinated data processing system. During operation,
supply 70
provides at least one supply voltage Uv, especially a uni-polar supply
voltage, driving a
current I flowing in the line-pair 2L. The energy source can, in such case, be
e.g. a
battery and/or a direct or alternating voltage source circuit fed via a plant-
internal supply
grid. For connecting, especially releasably connecting, of the at least one
line-pair 2L to
the measuring electronics 100 and, thus, the measuring system 1 itself, such
further
includes at least one, externally accessible, terminal pair.
For the above-described case of the measuring electronics assembled modularly
of
separate subcomponents, each of the subcomponents 1001, 1002 can, for example,
be
connected separately to the external energy supply, for example also by means
of the
aforementioned 4-20 mA current loop. Alternatively thereto or in
supplementation
thereof, however, also one of the subcomponents 1001, 1002 can be so connected
to
the other that it can feed such, at least at times, with electrical energy.
The measuring electronics is, in a further embodiment, additionally so
embodied that
the measured-values generated internally in the measuring system, be it, now,
measured-values of a single, registered, measured variable or measured-values
of
diverse, registered, measured variables, such as e.g. the ascertained density
and an
ascertained mass flow, are transmitted at least in part, via the at least one
line-pair 2L to
the superordinated data processing system 2. The pair of electrical lines 2L
can, in
such case, be part of a so-called two-conductor current loop well proven in
industrial
measurements technology. For this case, then, on the one hand, the measured-
values,
produced at least at times, are transmitted via this single line-pair 2L to
the
superordinated data processing system in the form of a load modulated (for
example, by
means of conventional coupling circuits) loop current, especially a clocked or
continuously variable, loop current, and, on the other hand, the measuring
electronics,
21
CA 02692179 2009-12-17
and, thus, the measuring system, are suppiied, by means of a corresponding,
especially
clocked, DC inverter, at least at times and/or at least in part, with
electrical energy, or
electrical power IN = UN, via the line pair 2L.
The measuring electronics 100 is, in a further embodiment of the invention,
additionally
designed for generating, during operation, a plurality of measured-values,
especially
digital measured-values, representing, at least in part, the at least one
measured
variable and for transmitting such, at least partially, via terminals and the
line pair 2L
appropriately connected thereto, to the connected data processing system 2 in
a form
appropriate for the data processing system 2. In case required, the measuring
system
can, in this connection, be further developed such that the measuring
electronics 100
and data processing system 2 are also connected together by means of at least
one
additional, second line pair (not shown), through which, during operation, at
least at
times, an electrical current correspondingly flows. For this case, the
measuring system
can further transmit the internally generated measured-values, at least
partially also via
the additional line-pair to the data processing system. Alternatively thereto
or in
supplementation thereof, measuring system and data processing system can also
communicate with one another wirelessly, for example by means of radio waves.
Especially for this last case, it can also be of advantage to supply the
measuring system
with electrical energy, especially also exclusively, by means of an internal
and/or
external, especially replaceable and/or re-chargeable, battery and/or fuel
cell.
Moreover, the measuring system can additionally be fed, partially or
exclusively, by
means of power converters using regenerative energy sources and placed
directly on
the field measuring device and/or placed remotely therefrom, examples of such
power
converters being e.g. thermogenerators, solar cells, wind generators, and the
like.
In a further embodiment of the invention, it is provided that the measuring
system can
exchange via the measuring electronics, at least at times, with an external
service- and
control-unit, for example a handheld service unit, or a programming device
provided in
the superordinated data processing system, device-specific data, such as
settings-
parameters, internal to the measuring device, for the measuring electronics
itself and/or
diagnostic parameters internal to the measuring system. For this purpose,
provided in
the measuring electronics 100 is, additionally, at least one communication
circuit COM,
which controls communications on the at least one line pair 2L. Especially,
the
communication circuit serves for converting the measuring-system-specific data
to be
sent, into signals transmittable via the pair 2L of electrical lines and to
then couple such
signals into the lines. Alternatively thereto or in supplementation thereof,
the
communication circuit COM can, however, also be designed for receiving
measuring
system specific data, for example a set of settings-parameters to be changed
for the
measuring electronics, sent from the exterior via the pertinent pair of
electrical lines.
The communication circuit can be e.g. an interface circuit working according
to the
HART@-Field-Communications-Protocol (HART Communication Foundation, Austin,
TX), which applies high frequency, FSK-coded (frequency shift keying),
alternating
voltages as signal carrier, or, however, also one working according to the
PROF1BUS
standard. In case required, also, additionally, externally running (for
example in a
runtime environment of the superordinated data processing system) processes
22
CA 02692179 2009-12-17
-
communicating with the measuring electronics 100 and processing data can
have direct
access to the measuring electronics.
In the case of the measuring system of the invention, it is further provided
that the
measuring electronics produces during operation, with application at least of
the
temperature measurement signal xa as well as the pressure measurement signal
xp, the
density measured-value >Cr, in such a manner that it represents an instant,
local density,
which the flowing medium actually has at an imagined reference point (which
can also
be predeterminably spaced from the real pressure measuring point and/or the
real
temperature measuring point along the flow axis) defined locally within the
process line
20. This imagined reference point, in the absence of a corresponding density
sensor
thereat and for distinguishing from the actually formed and, thus, real
measuring points
provided by means of the temperature sensor and pressure sensor, respectively,
is
referred to as a virtual density measuring point M'I). The virtual density
measuring point
M'p can, in such case, both be referenced to a reference point selected during
operation
from a plurality of predetermined reference points and, thus, be locationally
variable in
defined manner and it can also be kept locationally fixed. At least for the
last case, a
further embodiment of the invention provides that the electronics housing,
with the
measuring electronics located therein, is placed in the immediate vicinity of
the virtual
density measuring point M'p. The definition of the virtual density measuring
point M'p
occurs, in such case, by a corresponding configuration of the measuring
electronics,
especially the calculative method executed therein for purposes of the density
measurement, taking into consideration position and geometric character of the
real
measuring points Mp, Ma. In such case, according to a further embodiment of
the
invention, it is provided that the virtual density measuring point M'p is
situated upstream
of the temperature measuring point Ma and/or upstream of the pressure
measuring point
M. Furthermore, it can be of advantage for ascertaining the density, to permit
the
density measuring point to coincide either with the temperature measuring
point or with
the pressure measuring point.
In the case of the measuring system being discussed, it is presumed, in such
case, that
the flowing medium has at least one state variable, for example a temperature
and/or a
pressure and/or a density, and/or a Reynolds number Re, which, singly or
together,
assume(s), at the virtual density measurement point M'p, at least at times,
especially in
the time period relevant for production of the density measured-value and/or
repetitively,
an, at least in the sense of a measurement accuracy desired for the density
measurement, significantly different magnitude than at least one of the real
measuring
points delivering actual measurement signals, thus, the temperature measuring
point
and/or the pressure measuring point. In other words, one proceeds with the
understanding that the medium at the virtual density measuring point is, at
least at
times, in a thermodynamic state and/or in a flow state, which differ(s)
significantly,
especially to a degree significant for a desired measuring accuracy of the
measuring
system, as regards at least one, local, thermodynamic state variable
(temperature,
pressure, density, etc.) from a thermodynamic state of the medium at the
temperature
measuring point and/or from a thermodynamic state of the medium at the
pressure
measuring point. This spatial variance of thermodynamic state and/or flow
state in the
23
CA 02692179 2009-12-17
flowing medium can arise, as already rnemiioned, e.g in the case of .a
compressible
medium, a medium reacting in the process line, an additionally cooled medium
or an
additionally heated medium. Moreover, such a variance of thermodynamic state
and/or
flow state can also be brought about by allowing the medium to flow through a
process
line which is sectionally narrowing and/or sectionally widening along the flow
axis, such
as is the case, for example, in the application of nozzles or diffusers in the
process line,
so that the medium is accelerated or decelerated, on occasion accompanied by a
compression or an expansion of the same.
In an embodiment of the invention, it is, therefore, additionally provided
that the
measuring electronics, based on the pressure measurement signal as well as the
temperature measurement signal, ascertains first a provisional density
measured-value
X'p, for example according to one of the mentioned industrial standards AGA 8,
AGA
NX-19, SGERG-88 IA\NPS-1F97, ISO 12213:2006, for representing a density which
the
flowing medium solely apparently has at the virtual density measurement point,
this
because of preliminarily neglecting the spatial variances being discussed as
regards the
thermodynamic state and/or the flow state.
The ascertaining of the provisional density measured-value X'p can, in such
case, be
accomplished, at least at times, especially also for at least partially
gaseous media,
such as natural gas, air, methane, phosgene, etc., based on the formula:
II X p
X'p = (1)
z=Rm X,
wherein n is a molar mass, z a real gas factor of the medium ascertained
according to
one of the industry standards AGA 8, AGA NX-19, SGERG-88 IA\NPS-1F97, ISO
12213:2006 and/or with application of the temperature measurement signal
and/or the
pressure measurement signal, and Rm the relative gas constant of the medium,
corresponding to the absolute gas constant R normalized with the molar mass n
of the
medium, thus R / n, with R= 8.3143 J / (K mol).
Alternatively thereto or in supplementation thereof, the measuring electronics
can
ascertain the provisional density measured-value X'p, at least at times,
especially in the
case of media containing, at least in part, steam, based on the formula:
X 0
X'=
p lAWPS-IF97 71AWPS-1F97 1AWPS-1F97 (2)
_______________________________ =
1,-*1AWPS-1I-97 P.M = Xs
wherein TriAwps_1F97=Xp/P*1Awps-1F97 and yiAwps-iF97=91AwPs-iF97/(Rm*X9), with
P* being a
medium-specific, critical pressure according to the industrial standard 1A1NPS-
1F97,
especially 16.53 MPa, for the case in which the medium to be measured is
water, above
which the medium to be measured cannot be liquid, and glAWPS-IF97 a medium-
specific,
free enthalpy (Gibbs free energy) according to the industrial standard lAVVPS-
1F97.
CA 02692179 2009-12-17
Selection of the currently actually suitable, calculative torrilula for the
provisional density
measured-value Xfp and, thus, in the end, also for the actual density measured-
value Xp
can, in such case, be accomplished automatically and/or in dialog with the
user on-site,
or, via a superordinated data processing system, semi-automatically, on
occasion also
taking into consideration the currently measured pressure and the currently
measured
temperature and/or according to the selection method proposed in the initially
mentioned WO-A 2004/023081.
In a further embodiment of the invention, it is additionally provided that the
measuring
electronics produces the density measured-value also with application of at
least one
numerical compensation factor K, for example a digitally stored compensation
factor,
corresponding with a measuring-system-specific and medium-specific, locational
variability arising along the flow axis of the medium for at least one
thermodynamic state
variable of the medium, especially temperature, pressure or density itself,
and/or
corresponding with a measuring-system-specific and medium-specific, locational
variability arising along the flow axis of the medium for the Reynolds number
of the
flowing medium.
The aforementioned locational variabilities and, as a result, the compensation
factor K
can, in such case, be determined in advance, at least for measuring systems
with
conditions remaining constant, and/or, during operation, for example taking
into
consideration the medium actually to be measured, especially its chemical
composition
and/or its thermodynamic properties. The ascertaining of the compensation
factor K
can occur e.g. during a calibration of the measuring system with known
reference
medium and/or during start-up of the measuring system on-site. For certain
applications, especially with media of chemical composition which remains
constant and
thermodynamic properties which remain constant, it can be quite sufficient to
ascertain
the at least one compensation factor K at least once, solely during start-up
of the
measuring system. In the case of media changing significantly during operation
of the
measuring system as regards composition and/or thermodynamic properties, on
occasion also as a result of replacement of the same, it can, however, be
quite
advantageous to have the measuring electronics ascertain the compensation
factor K
repetitively also following the start-up, during operation of the measuring
system. The
- ascertaining of the compensation factor K can, in such case, be carried out
on the basis
of a predetermined (on occasion ascertained in dialogue with the user, on-site
or
remotely, and/or externally of the measuring electronics) specific heat
capacity, cp, of
the current medium. For example, the heat capacity, cp, or also other
parameters for
specifying the medium currently to be measured, can be transmitted from the
superordinated data processing system to the measuring electronics and thus,
as well,
to the measuring system.
In another further development of the invention, the measuring electronics
includes,
especially for simplifying the ascertaining of the compensation factor K, at
least one
data memory 16, especially a non-volatile data memory, for storing measurement
system parameters required for operating the measuring system, especially for
defining
its measuring and transmitting functionalities. Especially, it is, in such
case, further
CA 02692179 2009-12-17
provided that the data memory, for example a data memory in the form of a
table
memory and/or a non-volatile memory, stores, at least at times, the at least
one
compensation factor K, if necessary, also when the measuring electronics is
turned off.
For example, the data memory can store for such purpose also a plurality of
compensation factors ascertained for a different media and/or for different
circumstances of installation, so that the measuring electronics can select
from a
plurality of compensation factors stored in the data memory the at least one
currently
appropriate compensation factor K, taking into consideration the current
medium as well
as the current circumstances of installation.
Especially also for ascertaining the compensation factor K, a further
embodiment of the
invention additionally provides that the data memory stores, at least at
times, at least
one measuring system parameter SPm of a first kind solely specifying the
medium
currently to be measured and that the measuring electronics ascertains the
density
measured-value Xp with application at least of the at least one measuring
system
parameter SPm of the first kind. The measuring system parameter SPm of the
first kind
can be, for example, a specific heat capacity, cp, of the medium currently to
be
measured, a molar mass, n, of the medium and/or the number, f, of oscillatory
degrees
of freedom of the atoms or molecules of the medium, as determined by the
molecular
structure of the medium, and/or parameters derived therefrom, such as e.g. the
real gas
or also (super-) compressibility factor, on occasion also ascertained
according to one of
the industrial standards AGA 8, AGA NX-19, SGERG-88 lAWPS-IF97, ISO
12213:2006.
As a result, it is clear that, accordingly, also two or more of such measuring
system
parameters SPm of the first kind, of different dimensions and/or units of
measurement,
can be stored in the data memory for specifying the medium currently to be
measured.
In a further embodiment of the invention it is additionally provided that the
data memory
stores, at least at times, at least one measuring system parameter SPmE of the
second
kind specifying both the medium currently to be measured as well as also
instantaneous
circumstances of installation of the measuring system, and that the measuring
electronics ascertains the density measured-value Xp with application at least
of the
measuring system parameter SPmE of the second kind and, especially, however,
also
with application of the measuring system parameter SPm of the first kind. The
circumstances of installation are, in such case, determined, at least to a
degree
significant for the ascertaining of the density measured-value, by the
arrangement of
pressure-, temperature- and/or density measuring point(s) relative to one
another, as
well as, in each case, by the form and size of the process line in the region
of the
pressure-, density- and/or temperature measuring point(s). Consequently, the
measuring system parameter SPmE of the second kind can be, for example, a part
of a
parameter set reflecting the measuring points as regards their actual
positions and
actual character of the process line in the region of the measuring points, as
well as
also the thermodynamic properties of the medium currently to be measured, or
also can
be a numerical value of a complex parameter appropriately taking into
consideration
such influences, definitively ascertained, for example experimentally and/or
empirically,
first during operation of the measuring system, on occasion also with
application of the
measuring system parameter SPm of the first kind.
26
CA 02692179 2009-12-17
,
In a further embodiment of the invention, it is additionally provided that the
measuring
electronics receives, at least at times, especially telegraphed from the
superordinated
data processing system and/or ascertained in near-time, numerical parameter
values for
at least one medium to be measured and/or measuring system parameters SPm,
SPmE
specifying instantaneous circumstances of installation of the measuring
system, for
example, thus, the heat capacity, cp, for medium to be measured currently
and/or in the
future. The heat capacity, cp, or also an equally transmitted, other system
parameter Sm
of the first kind can, in such case, be ascertained in advance by a
corresponding
measurement performed, for example, by the density measuring point and/or also
externally of the measuring system and/or by an input from the user-side, on
occasion
also with application of the superordinated data processing system. Further,
it is,
therefore, also provided in the measuring system of the invention that the
measuring
electronics communicating, at least at times, by line or by radio, with the
superordinated, electronic, data processing system transmits the density
measured-
value to the data processing system and/or that the measuring electronics, at
least at
times, receives, from the data processing system, numerical parameter values,
especially in the form of a standardized telegram, for the medium currently to
be
measured, for example, thus, measuring system parameters SPm of the first kind
specifying its thermodynamic properties and/or its chemical composition. If
required, it
is also additionally possible to ascertain, by means of the data processing
system,
measuring system parameters SPmE of the second kind and to transmit such in
the form
of numerical parameter values directly to the measuring electronics.
For the described case, in which the measuring electronics is to automatically
ascertain
during operation, on the basis of system parameters Sm of the first kind, at
least at
times, the specific heat capacity, cp, of the medium currently to be measured,
such can
be done, for example, based on the formula:
r, f R
c 1+ ¨ = ¨ (3)
II
wherein n is the measuring system parameter, molar mass, R, the absolute gas
constant, with R = 8.3143 J / (K = mol), and f, the measuring system
parameter, number
of oscillatory degrees of freedom of the atoms or molecules of the medium
currently to
be measured.
In a further embodiment of the invention, it is provided that the compensation
factor is
determined solely by the medium currently to be measured, especially its
chemical
composition, as well as the physical properties derived directly therefrom, as
well as the
concrete embodiment of the measuring system as regards installation sizes and
installed positions of the individual measuring points, as well as size and
form of the
process line in the region of the measuring points, so that it, in the end, is
largely
independent of the really measured, measurement variables, pressure and
temperature.
27
CA 02692179 2009-12-17
On account of, and considering, the fact that the variance of the
thermodynamic state,
or the flow state, of the flowing medium and, in accompaniment therewith, the
measurement accuracy of such measuring systems can be quite co-determined also
by
the actual flow velocity of the medium, a further embodiment of the invention
additionally provides that the measuring electronics ascertains the density
measured-
value Xi) with application at least of a density correction value XK
ascertained during run-
time and depending both on a flow velocity of the medium and also on the local
temperature reigning at the temperature measuring point. This density
correction value
XK is, in such case, so embodied that it corresponds with an instantaneous
local
variability at least of a thermodynamic state variable of the medium,
especially such as
depends on the medium currently to be measured as well as on instantaneous
circumstances of installation and/or which corresponds with an instantaneous
local
variability of the Reynolds number of the flowing medium, especially such as
results
from the medium and/or the construction of the measuring system and occurs
along the
flow axis of the measuring system.
For this, a further embodiment of the invention provides that available, at
least at times
in the measuring electronics, is a corresponding velocity measured-value Xv
representing instantaneously, as currently as possible, a flow velocity of the
medium
flowing in the measuring system.
With application of the velocity measured-value Xv and the temperature
measured-value
Xs, as well as the already mentioned, compensation factor K, then, the density
correction value XK can be very simply ascertained by means of the measuring
electronics based on the formula
1
X= _______
K (1+ K = Xv2 = (4)
X
9
At least for the above-described case, in which the measuring electronics 100
ascertains the provisional density measured-value X'p by means of a
calculative
algorithm based on the calculative formula (1) and/or on the calculative
formula 2, the
density measured-value Xp for the virtual measured density can be very simply
and
rapidly ascertained with application both of the provisional density measured-
value X'p
and also the density correction value XK additionally with the formula:
= (5)
Accordingly, in a further embodiment of the invention, the measuring
electronics is so
configured that it ascertains the density measured-value Xp with application
of the above
formulas (4), (5), as well as (1) or (2), at least at times, based on the
formula:
28
CA 02692179 2009-12-17
11 = X p n =X
X = __________________________________________________________ (6)
z-Rm .(X,9 +K=X,2) z-Rm =Xp,9
1+K _______________________________________
X
)
and/or, at least at times, based on the formula:
X
_________________________________________________ g I AWPS-1F97
Xp lAWPS-11797 (7) IAWPS-1F97 = r , Ty, 2
A r lAWPS-1F97 r X,
1+ K = ______________________________________________ 1+K __
)
)
For testing the plausibility of the instantaneously ascertained, density
measured-value,
for example in the course of a self-validation of the measuring system, the
measuring
electronics, in a further, advantageous embodiment of the invention, compares
the
density correction value XK during operation repetitively with at least one
reference
value specific to the predetermined measuring system. Developing this further,
in such
case, it is provided that the measuring electronics, based on the comparison
of density
correction value XK and reference value, quantitatively signals an
instantaneous
deviation of the density correction value XK from the reference value and/or,
at times,
generates an alarm signaling an undesired, especially unallowably high,
discrepancy
between density correction value XK and associated reference value.
Alternatively
thereto or in supplementation thereof, the measuring electronics is
additionally so
embodied that it ascertains, repetitively during operation, a density error,
which
corresponds with a deviation, especially a relative deviation, of provisional
density
measured-value X'p and density measured-value Xp, especially such values
ascertained
according to standards in the above sense, and also issues such in the form of
a
numerical density error value. An impermissibly high discrepancy between
provisional
density measured-value X'p and density measured-value Xp, or between density
correlation value XK and associated reference value, can, for example, be
attributed to
an erroneously parametered measuring electronics, or an unexpected change of
the
medium to be measured and/or a disturbance of a plant containing the process
line. In
view of this, in an embodiment of the invention, it is provided that the
measuring
electronics only applies the density correction value XK in the generating of
the density
measured-value Xp when it amounts to at least one, especially lies in a range
between 1
and 1.2. In an embodiment alternative thereto, the measuring electronics is so
configured that it applies the density correction value XK in the generation
of the density
measured-value Xp only when it amounts to, at most one, especially lying in a
range
between 0.8 and 1. Additionally, it can be of advantage for the user, when the
measuring electronics outputs the instantaneous density error in the form of a
numerical
density error value and/or compares the instantaneous density error with at
least one
predetermined reference value and, based on this comparison, generates, at
times, an
alarm, which signals the undesired, especially impermissibly high, discrepancy
between
provisional density measured-value X'p and density measured-value Xp, for
example,
on-site, by means of the display element HMI.
29
CA 02692179 2009-12-17
In a further development of the invention, the me,-asuring system additionally
delivers at
least one flow measurement signal xv influenced by the local flow velocity.
This is done
especially also for the purpose of automatic and near-time ascertaining of the
density
correction value XK. In order to accomplish the delivery of this at least one
flow
measurement signal xõ, the measuring system is equipped with at least one flow
sensor
placed at a velocity measuring point Mv for reacting primarily to a local flow
velocity of
the medium to be measured, especially to a flow velocity averaged over a cross
section
of the process line, especially also to changes of the flow velocity. During
operation,
measuring electronics 100 and flow sensor therefore communicate, at least at
times,
with one another, at least in a manner such that the measuring electronics has
available
to it, at least at times, the flow measurement signal xv generated by the flow
sensor.
Especially, it is, in such case, additionally provided that the measuring
electronics
ascertains the density measured-value Xp also with application of the flow
measurement
signal. At least therefor, the measuring electronics communicates, at least at
times,
also with the flow sensor, e.g. also via external fieldbus and/or wirelessly
by radio.
Furthermore, it is provided that the density measured-value is generated by
means of
the measuring device electronics in such a manner that it represents a
locational
density of the medium in the region of the flow sensor.
In the example of an embodiment shown here, at least the flow sensor,
especially,
however, also one of the electronics modules of the measuring electronics, is
provided
by means of an industrial grade, in-line, measuring device for flowing media,
for
instance one embodied as a compact device. The in-line measuring device
includes at
least one, essentially rigid and sufficiently pressure resistant, carrier
tube, through which
the medium to be measured flows during operation, especially a carrier tube
inserted
into the course of the process line and, thus, forming a line-segment of the
same. On
and/or in the carrier tube is appropriately placed the actual flow sensor.
Depending on
application, the carrier tube can be made, for example, of metal, plastic
and/or ceramic.
In the case of the example of an embodiment shown here by way of example, the
flow
sensor is provided by a compact in-line measuring device in the form of a
vortex flow
meter inserted into the course of the process line. Such vortex flow meters
serve,
conventionally, for registering, highly accurately, as primary physical,
measured
variable, a flow velocity and/or volume flow of flowing media, especially
media of high
temperature and/or high pressure.
The views selected in Figs. 3a and 3b show the vortex flow meter perspectively
in
section, in one case seen in the flow direction (Fig. 3a) and, in the other
case, seen
counter to the flow direction (Fig. 3b). The vortex flow meter includes a
vortex sensor
30 fixed on a tube wall 21 of a carrier tube 20 serving as a line segment of
the process
line. Vortex sensor 30 extends through a bore 22 formed in tube wall 21 and
serves as
flow sensor in the above sense. Vortex sensor 30 can be, for example, a
dynamically
compensated, vortex sensor having a paddle immersed in the medium and a
capacitive
transducer element registering its deformations, as such is also described in
US-A
6,003,384.
CA 02692179 2009-12-17
In the interior of the carrier tube 20, which itself is inserted into the
pipeline, for example,
by means of appropriate flange connections, additionally arranged along one of
the
diameters of the carrier tube is a bluff body 40, which is securely connected
with the
carrier tube 20 at diametrally oppositely lying, securement locations 41,41*.
The center
of the bore 22 and the center of the securement location 41 lie on a
generatrix of the
carrier tube 20. Bluff body 40 includes an impingement surface 42, against
which
medium to be measured flows during operation. Bluff body 40 has, additionally,
two
side surfaces, of which only a facing side surface 43 is visible in Figs. 3a
and 3b.
Formed by the impingement surface 42 and the side surfaces are two separation
edges,
of which only a facing separation edge 44 is visible completely in both views,
while the
location of the rear separation edge is evident in Fig. 3a. Bluff body 40 of
Figs. 3a and
3b has, here, essentially the form of a right, triangular column, thus a
perpendicular
column of triangular cross section. In case required, of course, also bluff
bodies of
other shape can be applied for implementing the measuring system of the
invention.
By the flowing of the medium against the impingement surface 42, there forms
downstream of the bluff body, in known manner, a Karman vortex street, in that
vortices
separate alternately at each separation edge and then proceed downstream in
the
flowing medium. These vortices entrained by the flow produce, in turn, local
pressure
fluctuations in the flowing medium and their time-referenced separation
frequency, thus
their so-called vortex frequency, is a measure for the flow velocity and/or
the volume
flow of the medium. The pressure fluctuations released from the entrained
vortices are
then converted by means of the vortex sensor 30, formed, here, by means of
paddle
and placed downstream of the bluff body, into a vortex signal corresponding to
the local
flow velocity and serving as electrical, flow measurement signal xv.
The transducer element 36 produces the above-mentioned measurement signal,
whose
frequency is proportional to the volume flow of the flowing medium.
The vortex sensor 30 is inserted downstream of the bluff body 40 into the bore
22 in the
tube wall 21 of the carrier tube 20 and seals the bore 22 against escape of
medium from
the interior of the carrier tube 20 to the outer surface of the carrier tube
20, this being
accomplished by a screwed engagement of the vortex sensor 30 with the wall 21.
Serving for this are e.g. four screws, of which the screws 5, 6, 7 are visible
in Figs. 3a
and 3b. Parts of the vortex sensor visible in Figs. 3a and 3b are the wedge-
shaped
sensor vane 31 extending into the interior of the carrier tube 20 through the
bore 22 of
the tube wall 21 and a housing cap 32. Housing cap 32 runs out to an extension
322,
with interposition of a thin-walled intermediate piece 323; compare, in this
connection,
also the already mentioned US-A 6,003,384. Sensor vane 31 has principal
surfaces, of
which only the principal surface 311 is visible in Figs. 3a and 3b. The
principal surfaces
are aligned with the mentioned generatrix of the carrier 20 and form a front
edge 313.
Sensor vane 31 can also have other spatial forms; thus, e.g., it can have two
parallel
principal surfaces, which form two parallel front edges. Sensor vane 31 is
shorter than
the diameter of the carrier tube 20; it is, furthermore, flexurally stiff and
can include, for
example, a blind hole, in which a transducer element can be inserted, in the
form of a
thermocouple or resistance thermometer serving to detect the temperature of
the
31
CA 02692179 2009-12-17
medium, on occasion for generating the temperature measurement signal and,
thus,
also for implementing the temperature measuring point itself; compare, in this
connection, also the already mentioned US-B 6,988,418 or US-B 6,910,387. In
order
that the blind hole 314 has a sufficient diameter, wall portions protrude out
of the
principal surfaces, such a wall portion 315 being indicated in Fig. 3a. The
blind hole
314 extends into the vicinity of the front edge 313 and has there a floor.
To the vortex sensor 30 belongs, additionally, a diaphragm 33 covering over
the bore 22
and having a first surface 331 facing the medium and a second surface 332
facing away
from the medium; see Figs. 3 and 4. Sensor vane 31 is affixed to the surface
331, while
a physical-to-electrical transducer element 36 reacting to bending, or
movements, of
vane 31 is affixed to the surface 332. Sensor vane 31, diaphragm 33, as well
as its
annular edge 333, can be manufactured of a single piece of material, e.g.
metal,
especially stainless steel.
It is to be noted here that, instead of the vortex flow meter shown here by
way of
example, having at least one bluff body protruding into a lumen of the process
line and
immersed in the medium, and at least one flow sensor arranged downstream of
the at
least one bluff body, especially a flow sensor protruding at least partially
into a lumen of
the process line, of course, also other in-line measuring devices equally
established in
process automation technology can be used for providing the at least one flow
sensor
delivering said flow measurement signal and, thus, for forming the flow
measuring point
as such, examples being e.g. magneto-inductive flow meters, thermal flow
meters,
pressure-difference flow meters, ultrasonic flow measuring devices, or the
like. The
flow sensor itself can, in such case, as also usual in the case of such
measuring
devices, and depending on the implemented principle of measurement, be formed
by
means of at least one electrical resistance element, especially one through
which flows,
at least at times, a heating current, by means of at least one measuring
electrode
tapping electrical potentials, especially a measuring electrode contacting
flowing
medium, by means of at least one measuring capacitor reacting to changes of
the flow
parameter, and/or by means of at least one piezoelectric and/or piezoresistive
element.
The flow sensor can be, especially in the case of application of a measuring
capacitor
and/or a piezoelectric or piezoresistive element for forming the flow sensor,
one which is
subjected during operation repeatedly to mechanical deformations under action
of the
medium flowing in the measuring system for generating the measurement signal
and/or
which is moved during operation repeatedly relative to a static, rest position
under
action of the medium flowing in the measuring tube, such as is usually the
case,
besides the aforementioned in-line measuring devices measuring the flow
parameter on
the basis of vortices entrained in the flow with formation of a Karman vortex
street, e.g.
also for such in-line measuring devices which measure flow parameters of the
kind
being discussed on the basis of pressure differences. For the latter case, the
at least
one flow sensor can be formed, for example, by means of at least one flow
obstacle
narrowing a cross section of the process line, especially an orifice plate or
a nozzle, as
well as by means of at least one pressure difference sensor, which registers a
pressure
difference arising across the flow obstacle and delivers a representative
pressure
difference measurement signal. The at least one pressure difference sensor
can, in
32
CA 02692179 2009-12-17
such case, be formed e.g. partly by means of a pressure sensor placed at the
pressure
measuring point. Alternatively to the aforementioned sensor- or measuring-
device-
types, the at least one flow sensor can, moreover, also be formed in
conjunction with a
line segment of the process line, wherein vibrations of such line segment,
excited
actively from the outside by means of an oscillation exciter and/or passively
by the
medium itself, are detected by means of at least one transducer element
registering, for
example electrodynamically or opto-electronically, mechanical oscillations and
delivering a corresponding oscillation signal, such as is known to be the
case, for
example, also with Coriolis mass flow meters. Commercial Coriolis mass flow
meters
are usually in-line measuring devices, offered as compact measuring devices,
in which
at least one measuring tube equipped externally with oscillation exciters and
sensors
are inserted by means of flanges into the course of the process line to form
the line
segment vibrating, at least at times, during operation.
The application of measuring systems with an in-line measuring device of the
aforementioned kind enables, thus, in addition to the virtually measured
density, other
measured variables, especially a mass flow, a volume flow, a flow velocity, a
viscosity, a
pressure, a temperature and/or the like, of the medium flowing in the process
line
equally to be ascertained highly accurately, occasionally also in real time.
At least in the case of application also of a flow sensor internal to the
measuring
system, it is possible, moreover, also to ascertain the above-mentioned
compensation
factor K directly, in advance, especially also in the course of a wet
calibration. For
example, compensation factor K can be very simply so selected, that the
formula
K = AXp =X __ 9 ,) (8)
X,-
is fulfilled, wherein AXp corresponds to a deviation ascertained in advance,
especially in
the course of a calibration of the same and/or in an essentially equal
measuring system
with known reference medium and/or in the course of start-up of the measuring
system
on-site, e.g. a calculated and/or measured, measuring-system-specific
deviation, which
the provisional density measured-value X'p, ascertained for a reference medium
defined
at least with respect to its actual density, pRef, has from such density pRef
of the
reference medium. As a result, AXp can be viewed practically also as the
measurement
error inherent to the measuring system, i.e. the measurement error with which
the
provisional density measured-value X'p ascertained by means of the measuring
system
itself is burdened at the virtual measuring point in comparison with the
actual density.
With knowledge of the provisional density measured-value X'p, as well as also
the actual
density, PRef, of the reference medium, this measurement error can be
quantified as
follows:
X',
AXp ______ ¨1 , (9)
PRef
33
CA 02692179 2009-12-17
so that the compensation factor K, as a result, is to be so selected that it
obeys, as
exactly as possible, the following formula:
X, ( X,9
K = AXp = -,, = __ 1 (10)
2
X, \\PRef Xv
Alternatively thereto or in supplementation thereof, at least in the case of
application of
a flow sensor internal to the measuring system, it is, however, also quite
possible to
ascertain the compensation factor K experimentally by means of a reference
measuring
system and corresponding reference media and/or by computer simulation and,
based
thereon, to extrapolate further numerical values for the compensation factors
K for other
measuring systems similar to the reference measuring system and/or to other
media.
In a further embodiment of the invention, it is additionally provided that the
measuring
electronics, with application at least of the flow measurement signal, also
ascertains a
velocity measured-value Xv, especially a digital, velocity measured-value Xv,
which
instantaneously represents the flow velocity of the flowing medium, and/or
that the
measuring electronics, with application at least of the flow measurement
signal, also
ascertains a volume flow measured-value Xv, for example a digital, volume flow
measured-value, which instantaneously represents a volume flow rate of the
flowing
medium. Alternatively thereto or in supplementation thereof, the measuring
electronics,
with application at least of the temperature measurement signal and the
pressure
measurement signal, or the density measured-value, as well as the flow
measurement
signal, or the volume flow measured-value derived therefrom, can, during
operation,
ascertain, further, a mass flow measured-value Xm, for example a digital, mass
flow
measured-value, which represents, instantaneously, a mass flow rate, or an
integrated,
i.e. totalized, mass flow.
For simplifying construction of the measuring system and, along therewith, for
further
improving accuracy of the density measured-value, the flow sensor can, in
advantageous manner, be so placed that, as proposed, for example, also in US-B
6,988,418 or US-B 6,910,387, at least the flow measuring point and the
temperature
measuring point, or, as proposed, for example, also in US-B 7,007,556, at
least the flow
measuring point and the pressure measuring point, at least partially overlap
one
another, especially are coincident. Alternatively thereto or in
supplementation thereof,
the flow measuring point can, however, also, as shown schematically in Figs. 1
and 2,
be arranged remotely from the temperature measuring point and/or the pressure
measuring point, for example upstream of the temperature measuring point
and/or
upstream of the pressure measuring point.
In a further embodiment of the invention, it is additionally provided that the
temperature
sensor of the measuring system and/or the pressure sensor are, as proposed,
for
example, also in US-B 6,988,418, US-B 6,910,387 or US-B 6,651,512, likewise
provided by means of the in-line measuring device containing the flow sensor,
for
example an in-line measuring device in the form of a compact measuring device.
34
CA 02692179 2009-12-17
in a further embodiment of the invention, the virtual density measuring point
and the
flow measuring point are so selected that the medium has at the virtual
density
measuring point a thermodynamic state corresponding to a thermodynamic state
of the
medium at the velocity measuring point and/or that the medium has at the
virtual density
measuring point and velocity measuring point essentially equal Reynolds
numbers.
This can, for example, be achieved by so defining the virtual density
measuring point
that it and the flow measuring point at least partially overlap one another,
especially are
coincident. In other words, thus the density measured-value should be
ascertained in
such a manner that it exactly represents a local density of the medium in the
region of
the flow sensor and consequently also exactly represents the local density of
the
medium at the velocity measuring point.
For further simplifying the measuring, another embodiment of the measuring
system
provides that the process line is an essentially straight pipeline, thus no
elbows or
bends, at least sectionally, especially in the region between density
measuring point
and pressure measuring point and/or between density measuring point and
temperature
measuring point. Moreover, the process line should be embodied, at least
sectionally,
especially in the region of the temperature measuring point and/or in the
region of the
pressure measuring point, as an essentially form-stable pipeline, at least
under
operating pressure, especially a rigid pipeline and/or a pipeline circular in
cross section.
In a further embodiment of the invention, the aforementioned variance is
produced
during operation in largely defined manner by providing the process line, at
least at the
virtual density measuring point, additionally with a caliber D1 differing from
a caliber D2
of the process line at the pressure measuring point. Alternatively thereto or
in
supplementation thereof, another embodiment of the invention additionally
provides that
the process line has at the virtual density measuring location a caliber D1
differing from
caliber D3 of the process line at the temperature measuring point, and/or that
the caliber
D2 of the process line at the pressure measuring point is different from the
caliber D3 of
the process line at the temperature measuring point. In detail, thus, a large
number of
possibilities of combination results as regards the arrangement of the
individual
measuring points relative to one another, as well as also the choice of
caliber of the
process line at the particular measuring points. A selection of especially
suited variants
of embodiment herefor is, moreover, also shown schematically in Figs. 4a, 4b,
4c, 4d,
4e, 4f and 4h.
As shown therein, it can be of advantage to embody the measuring system such
that
the caliber D2 of the process line is greater at the pressure measuring point
than the
caliber D3 of the process line at the temperature measuring point, or,
however, also
such that the caliber D3 of the process line at the temperature measuring
point is
greater than the caliber D2 of the process line at the pressure measuring
point.
Alternatively thereto or in supplementation thereof, the caliber D2 of the
process line at
the pressure measuring point can also be so selected that it is greater than
the caliber
D1 of the process line at the virtual density measuring point and/or the
caliber D3 of the
process line at the temperature measuring point can be so selected that it is
greater
than the caliber D1 at the virtual density measuring point. Especially, it is
further
CA 02692179 2014-10-14
78639-44
provided that a caliber ratio D3/D1 of the caliber D3 of the process line at
the
temperature measuring point to the caliber D1 of the process line at the
virtual density
measuring point is greater than 1.1 and/or smaller than 5, for example thus
lying in a
range between 1.2 and 3.1. Further, it is at least for this case, of advantage
when the
process line at the virtual density measuring point has a caliber D1, which is
essentially
equal to a caliber D2 of the process line at the temperature measuring point.
In another
embodiment of the invention, it is provided that a caliber ratio D2/D1 of the
caliber D2 of
the process line at the pressure measuring point to the caliber D1 of the
process line at
the virtual density measuring point is kept greater than 1.1 and/or smaller
than 5, for
example thus lying in a range between 1.2 and 3.1. For this case it is, in
turn, of
advantage when the process line at the virtual density measuring point has a
caliber D1, =
which is essentially equal to a caliber D3 of the process line at the
temperature
measuring point.
The differences between the calibers D1, D2, D3, respectively, can, depending
on
desired configuration, be implemented by providing the process line between at
least
two of the aforementioned measuring points, for example thus between the
virtual
density measuring point and the temperature measuring point and/or the
pressure
measuring point, or also between the temperature measuring point and the
pressure
measuring point, with a line segment embodied as a diffuser, especially a
funnel-
shaped diffuser, having a lumen widening in the flow direction, especially
continuously
widening in the flow direction, or a line segment which is formed as a nozzle,
especially
a funnel-shaped nozzle having a lumen narrowing in the flow direction,
especially
continuously narrowing in the flow direction.
Experimental investigations have shown further that the measuring points
should, in
advantageous manner, be so placed, or defined, that a distance L21 of the
pressure
measuring point from the virtual density measuring point differs from a
distance L31 of
the temperature measuring point from the virtual density measuring point. For
example, -
it can be quite advantageous for the measurement, when the distance L21 of the
pressure measuring point from the virtual density measuring point is greater
than the
distance L31 of the temperature measuring point from the virtual density
measuring
point and/or when the distance L21 of the pressure measuring point from the
virtual
density measuring point and/or a distance L23 of the pressure measuring point
from the
temperature measuring point are/is greater than the caliber D2 of the process
line at the
pressure measuring point. Found to be quite suitable are, in such case, a
distance L21
and/or a distance L23 of at least three times, especially more than five
times, the caliber
D2.
Further information for layout and dimensioning of the process line of the
measuring
system as regards aforementioned installed lengths and/or caliber ratios in
the case of
application of a reducer are and/or a diffuser, as well as also other
embodiments of the
process line upstream of the flow sensor and or downstream of the flow of
sensor are
also shown in the assignee's not-prepublished applications DE 102006034296.8
and 102006047815.0, and in subsequent applications corresponding
36
CA 02692179 2014-10-14
.
78639-44
therewith, respectively.
Further investigations with measuring systems of the invention have shown
additionally
for the arrangements of temperature, pressure and density measuring points
shown in
the Figs. 4a, 4b, 4c, 4d relative to one another as well as with reference to
the
aforementioned caliber ratios, that that the density correction value
ascertained therefor
at least according to formula (4) and used for the ascertaining of the density
measured-
value according to the formula (1), or (2), should always be greater than one;
otherwise,
as already mentioned, a malfunctioning measuring system or a disturbance of
the plant
would be assumed. Equally, for the constellations shown in Figs. 4e, 4f, 4g,
and 4h, the
density correction value, assuming application of the same calculative
formulas, should
always be smaller than one.
Beyond this, the following Table 1 provides constellations as regards calibers
D1, D2,
D3, in each case in the units mm, and selected gases as medium, as well as in
each
case a correspondingly suitable compensation factor K in the units K = s2 =m-
2, especially
suitable for a measuring system with a flow sensor according to the example of
an
embodiment shown in Figs. 2 and 3.
Table 1:
GAS D1, D3 D2
CH4
(n = 16 g = mol-1,
f = 6)
13.9 24.3 27851.08558
_
13.9 _________ 26.7 26084.12357 -
_____________________________________ 13.9 _________ 27.2 25671.22129
13.9 28.5 24567.65186
_____________________________________ 13.9 38.1 17069.51792
13.9 40.9 15350.28348
13.9 41.2 15178.90947
=
13.9 43.1 __ 14147.85441
24.3 38.1 3086.763684
_____________________________________ 24.3 _________ 40.9 __ 3035.482335
24.3 41.2 3026.384008
24.3 43.1 2957.410639
_____________________________________ 24.3
49.2 __ 2662.97974
24.3
52.6 2484.170531
24.3 _______ 52.7 2478.934254
_____________________________________ 24.3 _______ 54.5 2385-X6-2-684
38.1_
49.2 448.2000215
38.1 52.6 487.9209744
37
CA 02692179 2009-12-17
38.1 54.5 500.3838513
38.1 73.7 459.369374
38.1 78 435.8925863
38.1 78.lf 435.337907
38.1 82.5 410.9043438
49.21 73.7 183.0929623
49.21 78 183.4977725
49.21 78.11 183.4687956
49.21 82.51 180.8940523
49.2 971 162.4571647
49.2 102.31 154.3167919
49.2 102.41 154.1619225
49 2j 107.1 146.8997624
73.7 97 32.98911974
73.7 102.4 35.0370316
73.7 107.1 36.01526944
73.7 146 32.12475476
73.7 151 31.10798557
73.7 154.2 30.45138942
73.7 159.3 29.40598339
97 146 12.12975471
97 151 12.16106709
97 154.2 12.14098846
97 159.31 12.05687371
97 1999!.10.30674712
97 202.7 10.16121596
97 206.5 9.963705636
97 2073!.9.922187549
146 1999. 2.245529752
146 202.7 2.273600656
146 206.5 2.304852917
146j 2073. 2.310502276
146 248.8 2.317268815
146 254.5 2.291734778
146 258.8 2.2702775
146 260.4 2.261877863
Natural gas
(n = 16....40 g = morl ,
depending on composition,
f = 6)
13.9 24.3 31170.01324
1 13.9 26.7
29190.34938
1 13.91 27.21
28727.93943
38
CA 02692179 2009-12-17
13.91 28.5 27492.24479
13.9 38.11 19099.80535
13.91 40.91 17175.91318
13.9 41.21 16984.14311
13.9 43.1 15830.39114
24.31 38.11 3455.020015
24.31 40.9 3397.337203
24.3 41.2 3387.128821
24.3 43.1 3309.793458
24.31 49.2 2980.007098
24.3 52.61 2779.822049
24.3 52.71 2773.96038
24.3 54.51 2669.329455
38.11 49.21 501.8495813
38.1 52.61 546.2444885
38.11 54.51 560.159696
38.11 73.71 ........... 514.0710105
38.11 781 487.7826811
38.11 78.1 487.1616486
38.11 82.5 459.8077209
49.21 73.7 204.9496071
49.21 78 205.3864268
49.2 78.1 205.3536589
49.2 82.5 202.458931
49.2 97 181.8004079
49.2 102.3 172.6858252
49.2 102.4 172.5124389
49.2 107.lj 164.3825333
73.7 97 36.93625048
737j 102.4 39.22468158
737j 107.1 40.31654938
73.7 146 35.94964274
73.7 151 34.81116896
73.7j 154.2 34.07605503
73.7 159.3 32.90573249
97 146 13.57764009
97 151 13.61203427
97 154.2 13.58918743
97 159.3 13.49451405
97 199.9 11.53365739
97 202.71 11.37072445
97f 206.51 11.14960825
97 207.31 11.10312955
146j 2.5139906
39
CA 02692179 2009-12-17
4
146 202.7 2.545346756
146 206.5 2.580243371
146 207.3 2.586549405
146 248.8 2.593473866
146 254.5 2.564840534
146 258.8 2.540788021
146 260.4 2.531374101
H20
(n = 18g=marl,
f = 6)
13.9 24.3 31256.24144
13.9 26.7 29271.0454
13.9 27.2 28807.34836
13.9 28.5 27568.21927
13.9 38.1 19152.54293
13.9 40.9 17223.33422
13.9 41.2 17031.03432
13.9 43.11 ........... 15874.09507
24.3 38.11 3464.588763
24.3 40.91 3406.738816
24.3 41.21 3396.501521
24.3 43.11 3318.948505
24.3 49.2 2988.242826
24.31 52.61 2787.502227
24.31 52.71 2781.624305
24.31 54.5 2676.703394
38.11 49.2 503.2441144
38.1 52.61 547.7602846
38.1 54.51 561.7131315
38.1 73.71 515.492087
38.1 78 489.1306726
38.1 78.11 488.5079154
38.1 82.5 461.07809
49.2 73.7 205.5175663
49.2 78 205.9551717
49.2 78.1 205.9223044
49.2 82.5 203.0192259
49.2 97 182.3029139
49.2 102.3 173.1630088
49.2 102.41 172.9891412
49.2 107.1 164.8366844
73.7 97 37.03884498
73.7 102.41 39.33351491
73.7 107.1 40.42832654
CA 02692179 2009-12-17
73.71 1461 36.04900682
73.71 1511 34.90736955
73.7 154.21 34.1702149
73.7 159.3 32.99664598
97 146 13.61526406
97 151 13.64973647
97 154.2 13.62681665
97 159.3 13.53186744
97 199.9 11.56552973
97 2027].11.40214452
97 2065].11.18041482
97 207.3 11.1338072
146 1999. 2.52096787
1461 2027].2.552409208
1461 206.5 2.587400279
1461 207.3 2.593723327
146 248.8 2.600650057
146 254.5 2.571936044
146 258.8 2.547815996
146 260.4 2.538375687
Air
(n = 29 g = mol-1,
f= 5)
13.9 24.3 50338.90921
13.9 26.7 47124.38089
13.91 27.2 46375.14885
13.91 28.5 44374.58191
13.91 38.1 30815.23069
13.91 40.9 27710.05332
13.9 41.2 27400.56851
13.9 4311 25538.71377
24.3 38.1 5583.208016
24.3 41.2 5470.96068
24.3 43.1 5344.897321
24.3 49.2 4810.117614
24.3 52.6 4486.285526
24.3 52.7 4476.808075
24.3 54.5 4307.671069
38.1 49.2 812.4565419
38.1 52.6 883.65719
38.1 54.5 905.8569033
38.1 73.7 829.8882553
38.1 78 787.3215533
38.11 78.1 786.316573
41
CA 02692179 2009-12-17
38.11 82.5 742.0716954
49.2 73.7 331.3026455
49.21 78 331.8738927
49.2 78.1 331.8181848
49.2 82.5 327.0348906
49.2 97 293.4714706
49.2 102.3 278.7184046
49.2 102.4 278.437899
49.2 107.1 265.289832
73.7 97 59.78309893
73.7 102.4 63.449488
73.7 107.1 65.18836646
73.7 146 58.03092489
73.7 151 .......... 56.18799037
73.7j 154.2j 54.9986214
73.7 159.3j 53.10590103
97 146 21.94754221
97 151 21.99771435
O71 154.2!
97j
97 159.3 21.80041304
97 1999. 18.61596382
97 202.71 18.35235887
97 206.51 17.99471318
97 2073!. 17.91954828
146 1999!. 4.067220274
146 202.71 4.117361285
146 206.5 4.173054129
146 207.3 4.183100739
146 248.8 4.188923875
146 254.5 4.142218763
146 258.8 4.103061713
146 260.4 4.087749585
42
