Data processing: measuring – calibrating – or testing – Calibration or correction system – Fluid or fluid flow measurement
Reexamination Certificate
2000-03-22
2003-01-28
Bui, Bryan (Department: 2863)
Data processing: measuring, calibrating, or testing
Calibration or correction system
Fluid or fluid flow measurement
C702S099000, C073S861355, C073S861356
Reexamination Certificate
active
06512987
ABSTRACT:
FIELD OF THE INVENTION
This invention relates to apparatus for and a method of operating Coriolis flowmeters over an extended temperature range that includes cryogenic temperatures. More particularly, the invention provides apparatus for and a method of generating accurate output temperature compensated flow information by a Coriolis flowmeter operated at cryogenic temperatures.
Problem
It is known to use Coriolis effect mass flowmeters to measure mass flow and other information pertaining to a material flow as disclosed in U.S. Pat. No. 4,491,025 issued to J. E. Smith, et al. of Jan. 1, 1985 and Re. 31,450 to J. E. Smith of Feb. 11, 1982. These flowmeters have one or more flow tubes of a straight or curved configuration. Each flow tube configuration has a set of natural vibration modes, which may be of a simple bending, torsional, radial, or coupled type. Each flow tube is driven to oscillate at resonance in one of these natural modes. The natural vibration modes of the vibrating, material filled Coriolis flowmeter system are defined in part by the combined mass of the flow tubes and the material within the flow tubes. Material flows into the flowmeter from a connected material source on the inlet side of the flowmeter. The material is then directed through the flow tube or flow tubes and exits the flowmeter to a material destination connected on the outlet side of the flowmeter.
A driver applies a vibrational force to the flow tube to cause the flow tube to oscillate. When there is no material flowing through the flowmeter, all points along a flow tube oscillate with an identical phase. As a material begins to flow, Coriolis accelerations cause each point along the flow tube to have a different phase with respect to other points along the flow tube. The phase on the inlet side of the flow tube lags the driver, while the phase on the outlet side leads the driver. Sensors are placed at two different points on the flow tube to produce sinusoidal signals representative of the motion of the flow tube at the two points. A phase difference of the signals received from the two sensors is calculated in units of time. The phase difference between the two signals is proportional to the mass flow rate of the material flowing through the flow tube or flow tubes.
Coriolis flowmeters are in wide spread use that generated accurate information regarding material flow. This information includes material mass flow rate as well as material density. Coriolis flowmeters range in size from those having a flow tube diameter of 0.16 centimeters to those having a diameter of 15 centimeters. These flowmeters serve a wide range of material flow rates ranging from approximately several drops per minute, such as for use in anesthesiology systems, to several tons a minute, such as those used in oil pipelines or for the loading and unloading of oil tankers. Regardless of size, most of the applications in which Coriolis flowmeters are used require a high degree of accuracy such as, a maximum error of 0.10%. This accuracy can be achieved by many of the currently available Coriolis flowmeters provided they are operated at the conditions for which each flowmeter is designed.
Operating temperature is a condition of paramount concern to a Coriolis flowmeter. A typical range of operating temperatures for a Coriolis flowmeter is approximately 33 k to 473 k (−240° C. to +200° C.). In designing a Coriolis flowmeter to generate accurate output information under this temperature range, the thermal stresses generated within the Coriolis flowmeter as well as temperature differentials between the internal parts of the Coriolis flowmeter must be considered. The design must include a consideration of the thermal expansion/contraction of the various parts of the Coriolis flowmeter to prevent damage to these parts as well as to compensate for the affect this thermal expansion/contraction may have on the output accuracy of the flowmeter.
The output data of a Coriolis flowmeter that is of great importance is the mass flow rate since the accuracy of most data generated by the Coriolis flowmeter is dependent upon the accuracy of the mass flow rate. The accuracy of the mass flow rate is dependent upon the accuracy of the Young's Modulus E term used in the mass flow rate determination. An accurate determination of mass flow rate requires that Young's Modulus E be determined with precision over the temperature range in which the Coriolis flowmeter operates. It is often assumed that the Young's Modulus E variation with temperature is linear over the temperature range with which the Coriolis flowmeter operates. Therefore, Young's Modulus E is typically calculated using a linear expression containing a temperature term T representing the measured temperature of the Coriolis flowmeter. This linear expression for E is then used to determine the mass flow rate.
The above assumptions are satisfactory for temperature ranges for which Young's Modulus E varies linearly with temperature. However, the above assumptions are not useful in determining Young's Modulus E at cryogenic temperatures (those below 273 k). It is known from an article by HM Ledbetter from the
Journal of Applied Physics
of March 1981 that the Young's Modulus E for stainless steel varies linearly over a range of approximately 100 k to 300 k and higher; but has a non-linear variation at cryogenic temperatures, such as those below 100 k.
The use of an assumed linear variation of E at cryogenic temperatures results in a calculation of Young's Modulus E that has an unacceptable accuracy. The use of a linear expression for Young's Modulus E at cryogenic temperatures requires that the calculated Young's Modulus E be altered by an arbitrary amount for each different cryogenic temperature to determine Young's Modulus E and, in turn, the mass flow rate of the Coriolis flowmeter with a satisfactory accuracy. This procedure however, is cumbersome and is limited to a small number of predetermined temperatures.
Solution
The above and other problems are solved and an advance in the art is achieved by the apparatus and method of the present invention which calculates Young's Modulus E with accuracy over the conventional range of the conventional temperature range of −100° C. to +200° C. as well as at cryogenic temperatures below −100° C. and down to −269° C.
The apparatus and method of the present invention involves the steps of calculating Young's Modulus E for a wide range of temperatures ranging from 4 k to 473 k. It does this by applying non-linear curve fitting to priorly measured data representing Young's Modulus E for the temperature range of interest. This provides a non-linear expression characterizing Young's Modulus E over this temperature range. This non-linear expression is then used in the mass flow rate calculation to generate an accurate mass flow rate.
The step of subjecting a range of measured values of Young's Modulus E to non-linear curve fitting may involve deriving a plurality of expressions for Young's Modulus E including a linear expression as well as expressions of the second, third, and fourth order, or higher orders. The expression for each order is unique. The first order linear expression contains a term of T. The second order expression contains the terms T
2
and T. The third expression contains terms T
3
, T
2
, and T. The fourth order expression contains the terms T
4
, T
3
, T
2
, and T. These expressions are evaluated compared to determine the accuracy of the output data each generates. The expression of the lowest order that yields the desired accuracy is used. It was found that Young's Modulus E expression becomes increasingly accurate for the higher order expressions for cryogenic temperatures. All expressions generate a Young's Modulus E having an accuracy of at least 0.15% down to an approximately −100° C. Below that temperature, the error for the first order linear curve fit increases exponentially to an unaccept
Bui Bryan
Faegre & Benson LLP
Micro Motion Inc.
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