|Publication number||US3334513 A|
|Publication date||Aug 8, 1967|
|Filing date||May 15, 1964|
|Priority date||May 15, 1964|
|Publication number||US 3334513 A, US 3334513A, US-A-3334513, US3334513 A, US3334513A|
|Inventors||Thomas Jess W|
|Original Assignee||Whirlpool Co|
|Export Citation||BiBTeX, EndNote, RefMan|
|Patent Citations (6), Referenced by (13), Classifications (7)|
|External Links: USPTO, USPTO Assignment, Espacenet|
Aug. 8, 1 967 J. w. THOMAS 3,334,513
GAS ANALYZER Filed May 15, 1964 3: 2 30) 10 J6 n 1 1,: VACUUM l PUMP nurse nuwomm PUMP 7 I SAM/1L1 j] 29) 38 \/.'M. I @ael STANDARD v.,M. I (e.9.AlR) l VACUUM PUMP FILTER HUMtmF'lER PUMP -I-= I .9 I J co manna: TEMPERATURE ucnosFnTZf Eh-5 Patented Aug. 8, 1967 3,334,513 GAS ANALYZER Jess W. Thomas, Chatham, N.J., assignor to Whirlpool Corporation, a corporation of Delaware Filed May 15, 1964, Ser. No. 367,645 8 Claims. (Cl. 73-23) This invention relates to a continuous gas analyzer in which the amount of a third gas in a mixture with a pair of other gases is indicated substantially regardless of the amount of either of the pair of other gases.
A continuous analyzer for the amount of one gas of a mixture of the one gas with another gas by indicating flow characteristics is old in the art. However, with this invention it is now possible to indicate the amount, and particularly the varying amount, of a third gas mixed with a pair of other gases substantially without regard to the amount of either of the pair of other gases.
One of the features of this invention therefore is to provide an improved apparatus for indicating the amount, and particularly the varying amount, of a third gas in a mixture with two other gases.
Another feature of the invention is the provision of such an apparatus which is extremely inexpensive and simple in structure yet which provides accurate indication of the amount of the gas being analyzed.
Other features of the invention will be apparent from the following description of certain embodiments thereof as shown in the accompanying drawing.
The single figure of the drawing is a diagrammatic View of one system for indicating the amount of a third gas' in a mixture with a pair of gases without regard to the varying amounts of either of the pair of gases so long as the first gas of the pair has a lower molecular weight and a higher viscosity than the molecular weight and viscosity of the second gas of the pair.
The gas analyzer of this invention operates by indicating the varying resistance to flow of a mixture of at least three gases as the direct result of varying amounts of one of these gases and substantially regardless of varying amounts of the other two, with this varying resistance being utilized to indicate precisely the varying amounts of the one gas.
In the embodiment of the drawing there is provided a system 30 having a first line 10 for a mixture of gases. This mixture comprises a pair of gases mixed with a third gas in which a first gas of the pair has a lower molecular weight and higher viscosity than the molecular weight and viscosity of the second gas of the pair. In this embodiment the line 10 includes a vacuum pump 11 for drawing in a sample of mixed gases to be analyzed through an inlet line 12 and a filter 13 for filtering out from the gases foreign materials such as solids. In the line 10 there is also located a humidifier 29 for saturating the mixed gases with moisture vapor. The gases are saturated in order to eliminate the effect that varying moisture content of the incoming gas mixture would have on the observed results.
From the humidifier the line continues to a capillary 14 having particular dimensions as explained later. Downstream of the capillary 14 is a positive displacement pump 15 which draws a constant flow of gas through the capillary. As shown, the line 10 also includes a bleed-off line 16 of the ordinary type. The combination of the vacuum pump 11 for drawing the sample to be analyzed into the line and the bleed-off line 16 functions to supply the gas to be analyzed to the entrance 17 of the capillary at substantially atmospheric pressure. Thus, the vacuum pump 11 draws in the gas sample to be analyzed at a pressure that is slightly in excess of atmospheric and the bleed-off line 16 eliminates the excess.
In system 30, the test capillary 14 is supplied with the gas mixture at atmospheric pressure and the volume drawn through the capillary is maintained constant by the positive displacement pump 15. Variations in consistency of the gas being tested are therefore indicated by the pressure drop through the capillary 14.
If desired, the vacuum pump 11, filter 13 and humidifier 29 can be eliminated, particularly if the gas sample being tested is substantially free of foreign material and if the highest degree of accuracy is not required. The varying characteristics of the gas mixture being tested are indicated by the pressure drop through the capillary as shown by a pressure gauge 18.
The vacuum pump 11, filter 13 and humidifier 29 are employed as shown and in addition there is an identical counterbalancing second line 19 arranged in parallel with the first line 10 and also containing a vacuum pump 20, filter 21, humidifier 22 and positive displacement pump 23, each as nearly as possible identical with the cone sponding element in the first line 10. The second line 19 is adapted to draw in, through an inlet line 24, a standard gas that is substantially unvarying in consistency, e.g., the standard gas may be air.
In order to indicate the varying characteristics of the gas mixture being tested, the pressure gauge 18 is connected across the lines 10 and 19 downstream from the capillaries 14 and 25. As the standard gas in the second line 19 is unvarying, changes in the gauge 18 will indicate changing characteristics of the gas sample being tested. Any changing exterior environmental factors will affect both the test gas and the counterbalancing gas alike.
In the second line 19 there is also provided zero control valve 26 in order to permit accurate zeroing of the analyzer. This is necessary because the capillaries 14 and 25 cannot be made exactly identical. In order to correct for this, identical gases are drawn through the two lines 10 and 19 and the measuring capillary 14 and counterbalancing capillary 25, and the valve 26 is adjusted until the pressure indicator 18 indicates zero. This adjustment compensates for any variations in the two capillaries 14 and 25.
Because a standard gas, such as air, is passed through the counterbalancing capillary 25, the pressure drop therein in passing through this capillary is constant. However, the pressure drop through the capillary 14 will vary with variations in the constituents of the gas being tested. In order to maintain a uniform and similar temperature of the gases, the capillaries 14 and 25, as well as the pumps 15 and 23, are placed in a constant-temperature enclosure 27, and the capillaries are placed as close together as possible. This temperature is preferably higher than ambient in order to insure against condensation of moisture in the analyzer and particularly in the capillaries.
In the following description of the mathematical basis of this invention, the identification of the symbols is given at the end of this specification.
The formula for determining the length of the capillary 14 (and thus of the identical capillary 25) is as follows:
This formula is effective for a blend of a pair of gases in which a first gas of the pair has a lower molecular weight. and higher viscosity than the second gas of the pair. The formula is effective for measuring the length of the capillary regardless of its diameter so long as the diameter is such as to give a pressure drop between the two ends of the capillary when subjected to fluid flow therein, and so long as the formula gives a positive result. This formula shows that the length of the capillary is directly proportional to the gas pressure of the pair of gases at the inlet of the capillary and the volumetric flow rate of the gases and the difference in the molecular weights of the two gases. The length is inversely proportional to the absolute temperature and difference in viscosity of the two gases.
With a capillary of a length determined according to this formula, the mixture of the two gases flowed through the capillary gives the same pressure drop regardless of the relative proportions of the two gases. Therefore, any changes in pressure drop in the mixture of the pair of gases and the third gas whose amount is to be indicated will only be caused by changes in amounts of the third gas in the mixture. This is so accurate that the gauge 18 may be calibrated to show with a high degree of accuracy the actual percentages of the third gas in the mixture.
Flow through the capillary 14 is of course a pressurevolume relationship. The volume is kept constant by the positive displacement ump 15 and the apparatus indicates variations in pressure drop through the capillary to indicate variations in amount of the third gas. If desired, the relative amounts of the third gas could be indicated by maintaining the pressure in the line downstream from the capillary 14 constant as by the pressure regulator 35 (indicated in phantom) and noting variations in volume at the pump required to maintain this constant pressure as by the volume meter 36 (also indicated in phantom). In the counterbalancing second line 19 there are provided a similar pressure regulator 37 and similar volume meter 38. Therefore, in the system of this invention the amount, and particularly variations in amount, of the third gas in the three gas mixture is indicated by maintaining either the pressure or the volume in the system constant and observing variations in either the pressure or the volume.
Pressure drop through a capillary such as capillary 14 depends primarily upon two effects. One of these is the pressure drop in the body of the capillary between the two ends 17 and 28 which is due to the viscosity of the gases flowing through the capillary. The other pressure drop cause is the effect of the entrance end 17 and exit end 28 of the capillary as these ends operate as orifices. The pressure drop due to these orifice effects is a function of the molecular weight of the fluids. The mathematical expression of this pressure drop through the capillary is 7T7 Mw 1r r Mw (2) where P is pressure at the entrance end 17 to the capillary and P is the pressure at the exit end 28.
The above equation is a preferred form of the Brillouin equation (M. Brillouin, Lecons sur la Viscosit des Liquids et des Gas, vol. 1, p. 133; vol. 2, p. 37). In Equation 2 the first portion to the right of the second equal sign is an expression of the pressure drop in the body of the capillary which is a function of the viscosity of the fluids while the last portion of the equation is an expression of pressure drop due to the orifice effects and is related to the molecular weight as explained above. As indicated, these are additive to give the total pressure drop (AP) through the capillary.
This Equation 2 of Brillouin is based on Poiseuilles law (Partington, I. R., An Advanced Treatise on Physical Chemistry, 1st ed., p. 881, Longmans, London, 1949) which may be expressed as follows:
V 7I'(P1P2)T t 81113 in which V is measured at mean pressure of /2 (PH-P This law expresses the gas flow through a capillary tube and assumes no slip, i.e., that the fluid velocity at the tube wall is Zero.
Equation 2 is the same as Equation 3 except Equation 2 is corrected for end effects. At very low pressures slip becomes important. However, the slip can be ignored when the fluids flowing through the capillaries are at a pressure that is near atmospheric, as any error due to the slip effect is extremely small.
4 As reported by Benton (A. F. Benton, Phys. Rev. 14, pp. 403-408, 1919), Brillouins formula for expressing fluid flow through a capillary including end effect conditions is in which P and d are measured under the same conditions. For the purpose of this invention, however, this Formula 4 is expressed in Formula 2 wherein the term P/d has been replaced by the equivalent RT /M w, since In order for these formulas to work and thus in order to design the apparatus of this invention, it is necessary that the fluids flowing through the capillary be in streamline flow. This, of course, requires that the Reynolds number must not be greater than 2100.
As explained above, Equation 1 gives the length of the capillary for the pair of fluids regardless of the relative amounts of each fluid in the blend of the pair of fluids. With this calculated length, the pressure drop for both fluids of the pair of fluids through the capillary will be substantially identical so that the blend of the pair of fluids operates as a single fluid. This is proven as follows.
The Brillouin Equation 2 Written to equate the pressure drops of fluids 1 and 2 of the pair of fluids is as follows:
The subscripts l and 2 are used to identify the first fluid (having the lower molecular weight and greater viscosity of the pair) and the second fluid, respectively, of the pair of fluids.
The mass flow rates M and M are related as follows when the preferred positive displacement pump is used:
M1 PioP- R PZQP- (7) where Q is measured at the pressure P.
As the pressure drops are equal, P equals P so that the mass flow rates are related as follows:
This Equation 9 expresses the conditions that must exist for the pair of fluids to have the same pressure drop through the capillary. As can be seen, Equation 9 is the same as Equation 1.
Because the first and second fluids constituting the pair of fluids has the pressure drop effect of a single fluid regardless of the relative amounts of each of the pair of fluids the introduction of a third fluid will mean that this resulting mixture will have pressure drop variations due to the varying amounts of the third fluid only.
In order for the pair of fluids to act as a single component in the pressure drop through the capillary, it is necessary, as mentioned above, that Equation 1 give a positive value which means that the first fluid of the pair of fluids must have a lower molecular weight and a higher viscosity than the molecular weight and viscosity of the second fluid.
Typical pairs of gases which act as a single gas in passing through the capillary are the following two-component mixtures of gases:
The continuous gas analyzer of this invention is parpreservation of plant and animal materials as disclosed in Bedrosian and Brody US. Patent No. 3,102,777, issued Sept. 3, 1963, and assigned to the same assignee as the present application.
Here the system as described above and as illustrated in the drawing is very useful for continuously indicating the amount of oxygen in the mixture of oxygen, carbon dioxide and nitrogen of the inert gases. The other inert gases in air are present in such minor amounts that they may be ignored.
Nitrogen has a lower molecular weight and a higher viscosity than has carbon dioxide. Thus, When passed through a capillary of a length determined by the above Formula 1 and any diameter (preferably at least 0.2 mm.) so long as streamline flow exists, the carbon dioxide and nitrogen will give the same pressure drop as if only a single gas were present and without regard to any variations in the amounts of carbon dioxide and nitrogen.
Thus, any variations in the pressure-volume relationship will be due solely to the varying amounts of oxygen. Where the volume is kept constant these variations will be indicated by variations in pressure and these can be calibrated easily to show the percentage of oxygen in the mixture. Similarly, when the pressure is kept constant variations in the amount of oxygen will result in varia tions in the volume passing through the capillary and here again this can be calibrated to show percentages of oxygen.
To prove that any mixture of fluids 1 and2 will have the same pressure drop as all fluid l or all fluid 2, with fluids 1 and 2 defined as above, let x be the mol fraction of fluid 2, and (1-x) be the mol fraction of fluid 1, and Mw and 1 be the molecular Weights and viscosities of the resulting mixture. Then Mw =Mw x+Mw (l-x) (10) and to a good approximation The conditions for the same pressure drop for the mixture as for fluid l or 2 is that L be the same with Mw, and 1 substituted for Mw and 1 in Equation 9, or, does and Equation 12 is proven. This means: that the mixture requires the same length L to give the same pressure drop as fluid 1 or fluid 2.
In one embodiment of the invention, the suction at each of pumps 15 and 23 with nitrogen flowing through each capillary 14 and 25, each having a diameter of 0.061 cm., Was 11.0 inches of Water giving P =0.7 l0 dynes/cm. Pump displacement Q was 436 cm. /min. or 7.3 cmfi/sec. The temperature was about 25 C. and RT=2.475 10 Theoretical length for no AP response regardless of proportion of nitrogen and carbon dioxide was, for Equation 9,
L P QP L: 0.90 10 5.77+10 =52 cm.
In the above embodiment of the invention where the amounts of oxygen in a saturated atmosphere of oxygen, carbon dioxide and nitrogen in line 10 were measured,
7 and air was used in line 19, the amounts of oxygen varied directly with the pressure drop through the capillary as shown in the following table:
Oxygen Nitrogen Carbon P Gauge Dioxide (inches water) As can be seen, the reading on the gauge changes substantially uniformly with changes in oxygen content and is not affected materially b variations in either the nitrogen or carbon dioxide content.
Symbols Having described my invention as related to the embodiments set out herein, it is my intention that the invention be not limited by any of the details of description, unless otherwise specified, but rather be construed broadly within its spirit and scope as set out in the accompanying claims.
The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:
1. Apparatus for indicating varying pressure-volume changes in a mixture of a third gas with a pair of gases with said changes being due to variations in amounts of said third gas only in which a first gas of said pair has a lower molecular weight and higher viscosity than the molecular weight and viscosity of the second gas of said pair, comprising: means providing a gas line for said mixture; pump means for forcefully flowing said mixture through said line; a capillary tube flow restrictor forming a part of said line and providing streamline flow of said mixture in said tube, said tube having an entrance and an exit and a length such that said pair of first and second gases has substantially constant pressure-volume flow characteristics in said tube at uniform volumetric flow rates regardless of the relative proportions of said pair of gases, the length being determined by the following equation:
L=capillary length, centimeters P=gas pressure of said pair at said capillary outlet,
dynes Q =volumetric displacement of pump, cm. per sec. Mw =molecular weight of said first gas Mw =molecular weight of said second gas 1 =viscosity of said first gas, poises 1 =viscosity of said second gas, poises R=gas constant, 8314x10 for c.g.s. units T K.;
means for flowing said mixture through said line including said capillary; means for maintaining one of said pressure and volume of said mixture flowing through said capillary constant; and means for simultaneously measuring variations in the other of said pressure and volume to indicate said variations in amount of said third gas.
2. The apparatus of claim 1 wherein said means for flowing produces gas flow at substantially constant volume but varying pressure due to said third gas, and said indicating means responds to said varying pressure.
3. The apparatus of claim 1 wherein said means for flowing produces gas flow at substantially constant pressure but varying volume due to said third gas, and said indicating means responds to said varying volume.
4. The apparatus of claim 1 wherein means are provided for subjecting said capillary to substantially constant temperature.
5. Apparatus for indicating varying pressure-volume changes in a mixture of a third gas with a pair of gases with said changes being due to variations in amounts of said third gas only in which a first gas of said pair has a lower molecular weight and higher viscosity than the molecular weight and viscosity of the second gas of said pair, comprising: means providing a pair of gas lines; a capillary tube restrictor forming a part of each said line and providing streamline flow of said mixture in said tube, said tube having an entrance and an exit and a length such that said pair of first and second gases has substantially constant pressure-volume flow characteristics in said tube at uniform volumetric flow rates regardless of the relative proportions of said pair of gases, the length being determined by the following equation:
L P Qp M LUZ-M 10; 8112 1 71 -712 wherein:
L=capillary length, centimeters P=gas pressure of said pair at said capillary outlet,
dynes Q =volumetric displacement of pump, cm. per sec.
Mw =molecular weight of said first gas Mw =molecular weight of said second gas v =viscosity of said first gas, poises vg viscosity of said second gas, poises Rzgas constant, 8.3l4 10 for c.g.s. units T= K.; pump means for flowing said mixture through one of said lines including said capillary; pump means for flowing a constant component gas through said other line; means for maintaining in each line one of the volume and pressure therein constant; and means for indicating differences between the two lines in the other of volume and pressure to indicate variations in amounts of said third gas.
6. The apparatus of claim 5 wherein said means for maintaining maintains the volume constant.
7. The apparatus of claim 5 wherein said means for maintaining maintains the pressure constant.
8. The apparatus of claim 5 wherein means are provided for subjecting said capillaries to substantially constant temperature.
References Cited UNITED STATES PATENTS 1,633,352 6/1927 Tate 73-23 1,884,896 10/1932 Smith 7323 2,674,118 4/1954 Westmoreland 7355 X 3,005,552 10/1961 Muller 73-55 X 3,086,386 4/1963 Kapff 7323 3,234,781 2/1966 Bragg 7355 JAMES J. GILL, Acting Primary Examiner.
RICHARD C. QUEISSER, Examiner.
J. F. FISHER, Assistant Examiner.
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|U.S. Classification||73/31.4, 73/54.9, 73/54.6|
|International Classification||G01N11/00, G01N11/08|