Anal. Chem. 1981, 53, 2313-2318 F
I
7
2313
further much better resolution has been obtained by the secondary development in another direction with acetone. MgTPP and CdTPP have still shown a blended zone on the chromatogram.
LITERATURE CITED Uden, Peter C.; Blgley, Imogene E.; Walters, Frederick H. Anal. Chlm. Acta 1978. 100. 555-561. Huber. J. F. K.: Kraak. J. C.: Veenlna, Hans Anal. Chem. 1972, 44, 1554-1 559. Henderson, D. E.; Chaffee, R.; Novak, F. P. J . Chromatogr. Sci. 1981, 19, 79-83. Uden, Peter C.; Bigley, Imogene E. Anal. Chim. Acta 1977, 9 4 , 29-34 _
Saitoh, Koichi; Nobuo Suzuki J . Chromatogr. 1974, 92, 371-379. Suzuki, Nobuo; Saitoh, Koichi; Shibukawa, Masami J . Chromatogr. 1977, 138,79-87. Saltoh, Kolchl; Suzuki, Nobuo Bull. Chem. SOC. Jpn. 1978, 51, 116-120. Suzuki, Nobuo; Suzuki, Junichi; Saitoh, Koichi J . Chromatogr. 1079, 177, 166-169. Saitoh, Koichi; Suzuki, Nobuo Anal. Chem. 1980, 5 2 , 30-32. Hanson, Louise K.; Gouterman, Martin; Hanson, Jonathan C. J . Am. Chem. SOC. 1973, 95, 4822-4829. Adler, Alan D.; Longo, Frederick R.; Varadi, V. Inorg. Synth. 1978, 16, 213-220. Felton, Ronald H.; Linschitz, Henry J . Am. Chem. SOC. 1988, 88, 1113-11 16. Wei, Peter E.; Corwln, AlsoDh H.; Arellano, Robert J . Org. Chem. 1962, 27, 3344-3346. Chu, Tseng C.;Chu, Edith J-H. J . Blol. Chem. 1955, 212, 1-7. Chu, Tseng C.; Chu, Edith J.-H. J . Chromatogr. 1976, 2 8 , 475-478. Lamson, Davis W.; Coulson, Andrew F. W.; Yonetani Takeshi Anal. Chem. 1979, 45, 2273-2276. Sato, Mltsuo; Kwan, Takao Chem. Pharm. Bull. 1972, 20, 840-641. Hui, K. S.;Davis, 9. A.; Baulton, A. A. J . Chromatogr. 1975, 175, 581-586. Adier, Alan D.; Longo, Frederick R.; Finavelli, John D.; Goldmackier, Joel; Assour, Jacques; Korsakoff, Leonard J . Org. Chem. 1967, 32, 476. Barnett, Graham H.; Hudson, Mervyn F.; Smith, Kevin M. J . Chem. Soc. Perkin Trans. 11975, 1401-1403. Adler, Alan D.; Longo, Frederick R.; Kampas, Frank; Kim, Jean J . Inorg. Nucl. Chem. 1970, 32, 2443-2445. Albers, V. M.; Knorr, H. V. J . Chem. Phys. 1941, 9 , 497-502. Dorough, G. D.; Miller, J. R.; Huennekens, Frank M. J . Am. Chem. SOC. 1951, 73,4315-4320. Snyder, L. R. "Modern Practice of Liquid Chromatography"; Kirkland, J. J., Ed.; Wiley: New York, 1971; Chapter 4.
Flgure 6. Twodimensional HPTLC separation of metal TPP chelates, HPTLC plate RP-18 F254s(Merck no. 13724). Developers: I (primary), acetone-propylene carbonate (20:80(v/v)) (2-fold development);I1 (secondary),acetone (+, origin; F, solvent front).
compounds can be regulated by changing the composition of the above solvent mixture. Choice of Chromatographic System for Mutual Separation of Metal TPP Chelates. The separation efficiency of these chelates is quite dependent on the stationary phase substance as well as mobile phase solvent, but the mutual separation of metal TPP chelates with different central metals is unsuccessful with either cellulose or silica gel. For example, CuTPP amd Ni'I'PP cannot be completely resolved on either of these stationary phases, and MnTPP and FeTPP show the same migration behavior on silica gel unless ethyl ether is mixed with the developing solvent. On the contrary, alkylated silica, such as the (&-bonded one, is quite effective for the mutual separation of metal TPP chelates of interest. The migration,sequence for the metal TPP chelates on C18-bondled silica is analogous to that on C8-bonded silica, but a larger separation factor for a given chelate pais can be expected on C18-bondedsilica rather than on the C8-bonded one, provided the same solvent is used as the developer. A demonstration of two-dimensional HPTLC separation of seven imetal TPP chelates on a C18-bonded silica layer is shown in Figure 6. These chelates have been primarily resolved into four solute zones by %fold development with the 20:80 (v/v) mixture of acetone and propylene carbonate, and
RECEIVED for review May 15,1981. Accepted September 16, 1981.
Comimsri Orifice Flow for Precision Gas Mixing Wm. Dean WaYlace, * Justin S. Clark, and Christopher A. Cutler' Primary Children's Medical Center, 320 72th A venue, Salt Lake City, Utah 84 103
A new approach is described for dynamlc on-site mixing of gases, which utilizes the princlple of sequential flow of gases, under choked conditions, through a common orlflce. Practical application of the princlple is accomplished by mlcroprocessor control of valve open-times determined by calculations based on the desired gas fractions and the gas flow ratios through the commlon orifice of each gas with respect io the other gases In the mlxture. The resultant varlable gas mlxtures can be used In1 lndustrlal, medlcal, production, and research laboratories. Evaluation of the instrument demonstrates the accuracy to be better than f O . i % absolute for a three-gas system of nitrogen (N2), oxygen (02),and carbon dioxide
(cod. Present address: Medicor,
Inc., Salt Lake City, UT 84103.
Numerous applications exist for accurate, known gas mixture compositions. For example, variable known gas mixtures are needed for instrument calibration of the following: infrared analyzers, gas chromatographs, mass spectrometers, and chemical electrode transducers such as medical blood-gas electrodes. Other applications include regulation of environmental chambers, semiconductor manufacture, vehicle emission control, air pollution abatement, laser mixtures, and uses in industrial, medical, production, and research laboratories. The above list plus other demands for variable, absolute gas fraction compositions has stimulated the growth of a large industry for the preparations of such mixtures. The complexity and safety of this preparation have resulted in several solutions, the most common being a central preparation plant with high-pressure metal cylinders serving as transport containers. The two most common gas mixture techniques
0003-2700/81/0353-2313$01.25/00 1981 American Chemical Society
2314
ANALYTICAL CHEMISTRY, VOL. 53, NO. 14, DECEMBER 1981
do not lend themselves to practical general laboratory methods due to their complexity and safety requirements. The most widely utilized method is the preparation by partial pressures. This method is the least accurate and requires analytical measurement by Scholander, gas chromatography, or other means for certified analysis to be f 2 % of component gas. Robert Scacci has reported using this method to optimize high-pressure, multicomponent gas mixing to be done on-site in a laboratory (1). The mass measurement method of gas mixture preparation utilizes a high mass gravimetric (and often electronic) balance and achieves the highest level of accuracy possible. This preparation is named Primary Standard and has a specified accuracy of f0.02% absolute or 1%of the component gas, whichever is smaller. The balance is calibrated by weights traceable to NBS. The approach of having preparation sites physically separated from use sites has several disadvantages. One problem is the large storage areas required where versatility of different compositions is required since a separate container is needed for each mixture. Another disadvantage is expense incurred from handling, etc. which is especially evident when only small amounts of many different gas fractions are needed. Pertaining especially to research laboratories, a third disadvantage is the long time required from the conception of a need for a new gas mixture until its delivery. Another solution to the preparation of variable gas compositions is gas mixing systems which require pure gas input and which mix the gas to the specifications required by the user on-site. Reportedly, the most accurate gas mixers are based on volume proportioning. For instance, the mechanical piston-type devices such as the Digamix type M/300 F (H. Wosthoff OHG. D-4630 Bochum l),which advertises mixtures of the two gases from 1% to 100% in 1% increments, mixtures fl% relative of the selected ratio. It has many fixed gas fractions available that can be set by the choice of various piston gearing combinations. Another on-site gas mixing system is the Digital Static Gas Blender (BI-M Instruments Co. Houston, TX). It operates on the partial pressure method and therefore has the disadvantage of errors caused by nonideal gas behavior. It is unique in that it uses a sensitive electronic pressure transducer, dynamic temperature compensation, and a computer-controlled static blending valve for “direct volume addition” of the blending gases. It can blend 8,12,19, or 23 components. Such mechanical mixers are bulky, expensive, and inconvenient to use for continuous gas fraction control capability. However, such devices have found reasonable acceptance in certain laboratories. Another solution to preparation of variable gas compositions is gas mixing by flow proportioning. Matheson Gas Products, the Linde Division of Union Carbide Corp., and several others have developed a system for mixing gases based on mass flow measurement. The basic units incorporate a mass flowmeter measuring the flow of the carrier gas and one or more mass flow controllers measuring and controlling the flow of the component gas. These systems advertise a range of control from 2% to 100% of full scale with an accuracy of f2-3% of component gas. They have the advantage of continuous gas fractions but they are inherently complex, costly systems which depend on the stability of two or more separate mass flowmeters and control valves. However, they have fulfilled the needs of many users requiring in-house gas mixture capability. Another flow proportioning method of mixing gases, sometimes used in place of certified mixed gases operates on the principle of combining fixed flows of several gases flowing through restrictors. The constency of gas flows depends on regulated pressure sources, constant flow limiters for each gas, and constant temperature and output pressure. Because of
-
. I I ! I I
GAS SUPPLY
VALVE
I
:: !:
I
I I w n
I
I
i t
GiS SUPPLY
VALVE
-
I l !
GAS OUTLET
I
SUPPLY GL
I
COMMON ORIFICE
VALVE
Ill
ISOBARIC REGULATOR SYSTEM
I
U Figure 1. Simplified diagram of gas mixing apparatus.
inherent uncertainty of regulated pressure valves as well as variability of the gas flow limiters, the accuracy of these devices is less certain than the above methods. In addition the gas-flow limited mixers while compact, have fixed predetermined mixing ratios. Described in this paper is an accurate and practical flow proportioning method for mixing gases with variable compositions from 0 to 100%. This system is unique in that it uses a microprocessor to sequentially control valve open-times to meter pure gases through a common orifice under choked flow conditions. The low cost yet sophistication of the microprocessor logic and control has made the gas mixer a practical and compact tool in research laboratories and other areas where versatility in providing on-site mixed gases is desirable.
THEORY Principle of Operation. The principle of operation of the system for mixing three pure gases is illustrated in Figure 1. The same concept can be extended to mixing any number of gases. The three gases are delivered to an isobaric regulator system, which forces each gas to a common pressure at the input of its central valve. By appropriate sequencing of the valve operations, each gas flows independently through the common orifice restrictor in time sequence between the other two gases. A particular time averaged mixture is determined by the relative time each valve is open relative to the other two. The accuracy of the method is determined by the accuracy of valve timing, the precision of relative gas pressure regulation of the isobaric regulator, the establishment of common gas temperature, and the invariance of relative resistance to flow through the common orifice of each gas with respect to each of the others. A more detailed block diagram of the gas mixing pneumatics is shown in Figure 2. The isobaric regulation system is comprised of the filter and orifice units in series with each gas cylinder regulator which feeds into a common point at the back-pressure regulator. Pure gases A, B, and C are introduced into the system through adjustable pressure reducing regulators attached to the cylinders. The jewel orifices, protected by filters, restrict gas flow into the isobaric regulation system. Equal pressures
ANALYTICAL CHEMISTRY, VOL. 53, NO. 14, DECEMBER 1981
2315
w FILTER B
FILTER ---
1 F + 3 =i =d ORIFICE
MIXING CHAMBER NEEDLE VALUE
OUTLET b
7!?+1
GREE,N LED
cy5~ i:g --
MIXTURE
Nr2E
I
11
COMMON ORIFICE
SOLENOID OPERATED VALVES
- . ~
ORIFICE
COMMON PRESSURE HEAD
LYELLQW LED
SYSTEMBACK PRESSURE REC.
SYSTEM PRESSURE ADJUST 25PSI SoLENolD r-7
EXHAUST
Flgure 2. Detailed diagram of a single-channel gas mixing apparatus.
of the three gases a t the input of the solenoid valves are maintained by the connections to the common pressure of the back-pressure regulator This regulator bleeds all flow into the system abovc! 25 psig to exhaust. In initial setup, flow of each gas into the system is adjusted by its cylinder pressure regulator so the flow through its input orifice exceeds (10-20%) flow in the common orifice when its solenoid valve is open. Sufficient flow into the system is monitored by a pressure drop across a restrictor with the use of a pressure switch. This pressure switch turns on a light under sufficient flow conditions. This procedure assures a sufficient bulk flow of each gale toward the reservoir and prevents contamination due to back diffusion of gases at the solenoid valve inputs. A common pressure head in the gas lines at the inputs to the solenoid valves will exist as the gas lines offer negligible resistance to flow. Equal temperatures of the three gases are maintained by housing the solenoid valves in a block which radiates to room temperature. Another feature which adds to the accuracy of the method is the removal of flow dependence on outlet pressure. This is accomplished by maintaining choked flow conditions within the common orifice. This flow condition exists when the upstream absolute pressure is at least twice downstream absolute pressure (2). When this condition is met, supersonic or choked flow through the orifice exists and downstream pressure fluctuations do not affect the flow through the orifice. Mathematical Development. The following mathematical development of the equations used for timing the gas control valves assumes that the ratios of flow through the common orifice for each gas relative to each of the other gases are constant. The accuracy to which the flow ratios are known determines; the ultimate accuracy of method. For ideal gases and a mathematically perfect orifice, the flow ratio for gas (i) relative to gas 6) is given by
Rij =
dg
where Rij = Fi/Pj, F is gas flow, and MW is the molecular
weight of the gas. This equation also assumes identical input pressure and temperature for each gas at the orifice as well as choked flow conditions. However, with real gases and physical orifices, the viscosity of each gas also contributes some degree to the orifice resistance. The viscosity component of the total resistance is influenced by the geometry of the orifice. Small geometrical differences from orifice to orifice which occur in their manufacture produce a difference in the relative amount of the viscosity vs. density resistance components of the common orifice. Therefore, to achieve the maximum gas mixing accuracy by this method, an independent calibration must be made to determine the flow ratios (Rs)of the common orifice. This process is discussed later in the paper. Once a calibration is made, recalibration should be unnecessary because the common orifice geometry is fixed. The gas fraction of any one gas ( X I )in a mixture of n gases is the volume of the gas (Vj)divided by the total volume of gases in the composition Ci=lnVi.This volume of gas can be expressed as the flow of that gas (Fj) multiplied by its time of flow (Tj).
x i s -Vj- - n
FjTj n
(1)
We can reference all subsequent gas flows to gas number one and define this ratio as Rp This makes R1 = 1. In addition, we defiie the period (P)to be the sum of the times of all gases. n
P=CTi i=l
We can now substitute expression 2 into 1 and obtain
(4)
2316
ANALYTICAL CHEMISTRY, VOL. 53, NO. 14, DECEMBER 1981
Chart I
=P
t T3 t .*.T,, t Tl Tl t * . . R,X,T, X , T , t R l ( X l - 1 ) T , t R3XlT3 t R 3 ( X 3- 1 ) T 3 t . * * R,X,T, R2X3T1 X3T1
XnTi t RiXnTi
t R3Xn7'3
Using expression 4 in expansion form and substituting the expansion form of (3) for the case when j = 1 in expression 4, we can write the system of equations shown in Chart I. This is a linear system of n first-order polynomial equations in n unknowns of T . This system is best solved by using numerical analysis techniques such as the Gaussian elimination algorithm with scaled partial pivoting (3). For a three-gas system, these equations are readily solved by determinants or other straightforward algebraic methods to yield
TI = P - (T2 + T3) T2 =
x2pR3 X 2 ( l - R2)R3 + X 3 ( l - R3)R2 + R2R3
(5) (6)
t
.
*
R,(X,
=o =o -
1)T,
=0
During short valve times, the washout time is dependent on the time a gas flows into the dead-volume because the volume is not washed out with this gas. In addition, during short valve times, the initial gas flowing through the orifice is a mixture of the previous gases. In the strictest sense then, the washout time is dependent on the valve on-time, and the washout flows are dependent on combinations of previous gases. This dependency approaches a constant for large valve-time/dead-volume ratios when the dead-volume is effectively washed out by each new pure gas. For this situation then Tjw= constant and R," is the flow ratio of the j gas. For a three-gas system, eq 6 and 7 now become
T2 = (X2PR3 + X2R3E1+ [ ( X 2+ X 3 - l ) R 3- X 3 ] E 2+ X2E3J X z ( 1 - Rz)R3 + X 3 ( l - R3)Rz + R2R3 (11)
where P period of cycle, T1 time of valve 1, T2= time of valve 2 , T3 = time of valve 3, X 2 = fraction of gas 2, X 3 = fraction of gas 3, R2 = ratio 2 f 1gas flow, and R3 = ratio 3 f 1 gas flow. The above derived times are based upon pure gases flowing directly through a common orifice. In reality, pure gas flows are controlled by open-times of solenoid valves. There exists a dead-space volume between the output porta of these valves and the common orifice. A washout time, therefore, exists since each pure gas is sequentially introduced into this small common volume and then flows out the orifice. These washout times mean that during a short period of the next solenoid on-time, the previous gas (or some mixture of gases) will flow through the orifice. The final gas composition becomes stable since all pure gases are continuously cycled through this small common volume. However, the absolute gas fractions as predickd from the above equations will differ slightly because the valve times do not quite represent the pure gas flow through the orifice and hence the exact pure gas added to the final mixture. Of course, the magnitude of this error caused due to the washout of this volume can be minimized by (1) increasing the flow, (2) increasing the period, or (3) decreasing the dead-volume. A refinement of the above model is made which takes into account the dead-volume error. Let Tjwrepresent the small amount of time which is required to effectively wash gas j out of the dead-volume after gas j valve turns off and the valve for gas j 1 turns on. Then the volume of gas j (Vi)coming out the orifice is
+
Vj = FjwTjw+ Fj(Tj - Tj-iw)
(8)
where Fjw is the flow of gas through the orifice during the washout of the dead-volume and Tj..lw is the time in which the previous gas (I' - 1)washes out of the dead-volume. Thus eq 1 can be rewritten after substitution of eq 2 as
xi = (R~T,.+ E ~ )i=l / $ ( R ~ T+, EJ .
(9)
Ej = RiwTiW- RiTWI-l
(10)
where and represents the volume of gas which flows through the orifice during the washout time of the dead-volume.
T3 = (X3PR2 + X,R2Ei+ X3E2 + [ ( X z + X3 - 1)R2 - X21E3) X 2 ( 1 - RJR3 + X 3 ( l - R3)Rz + R2R3 (12) where
El = RlWTiW- R1T3"
(13)
E2 = R2"T2"
(14)
- R2TiW
E3 = R3"T3" - R3T2"
(15)
The dead-space volume in the gas mixing system described in this paper is 0.028 mL. With a flow rate of 60 mL/min for N 2 , this yields a TIwof 28 ms for N 2 , Tzwof 30 ms for 0 2 , and T3wof 34 ms for C 0 2 . By inputing the gas fractions desired of a gas mixture and by knowing gas flow ratios of these gases through the common orifice along with their washout times, one can place the final gas composition under automated control of a microprocessor system. One final theoretical consideration is adequate mixing of the outlet mixture by the mixing chamber since there is temporal pulsatile variation caused by the sequential flow of the system. This is accomplished by designing of the mixing chamber into five separate subchambers through which the output gas must pass. Each subchamber has a volume approximately equal to the volume of gas comprising one period which is equal to one pulse of each gas mixed by the system. These separate volumes allow the gas pulses to equilibrate by diffusion into an integrated mixture. The effect is that of five washin-washout chambers in series, which if considered as independent exponential washout chambers, the output composition will be within 5 time constants of the final value or 99.33%. Exponential washout chambers combined in series improves the mixing.
EXPERIMENTAL SECTION Figure 3 is a drawing of a gas mixing system which is used to mix any three gases. The gas mixer used in the blood-gas laboratory provides a gas mixture of nitrogen (N,), oxygen (Oz), and and CO,. The carbon dioxide (CO,) from inputs of pure N2, 02, pure gases of N,, O,, and COzsupply the porta labeled gas A, gas B, and gas C, respectively. By dialing the desired gas percentages of 0,and CO, on the front panel thumbwheels and then pressing
ANALYTICAL CHEMISTRY, VOL. 53, NO. 14, DECEMBER 1981
[
GAS A r
G
A
3 0 /--GAS
FLOW INICATOR LlOHTS
Table I. CO, and 0, Gas Mixer Accuracy Comparison by Gas Chromatography a CO,
Flgure 3.
Drawing of precision gas mixer for mixing three-component
gases. the NEW GAS ENTER button, gas composition of the percentageri chosen flows from the outlet located on the back panel. N2makes up the balance gas percentage which is not O2 and COz. Three gas flow indicator lights are located on the front panel. These lights indicate that sufficient gas flow exists for each of the three pure gases. The NEW GAS ENTER button, when pressed, sets the output composition to the percentages shown on the thumbwheel switches. New percentages dialed into the thumbwheel switches are not mixed until this button is presaed. On the back panel is located the gas mixture outlet fitting. The input gas fittings for Nz202,and C02are also located on the back panel. In the present system, the gas flow is fixed at approximately 60 mL/min. With the mixing chamber volume of 10 mL, the time constant for changing to a new gas is 10 s. Therefore, the time required to obtain a new gas mixture within 99.9% of the new value is 69 s. One of the advantages of this system is the minimum specification requirements of the input pressure regulators. A small continuous flow of the t h e e gases exists at all times either through the common orifice or through the back-pressure regulator. Therefore, the input regulators are never subjected to sudden pressure fluctuations during operation. As long as the regulator pressure never falls below the initial setup flow tolerance of 10-20%, there will be no error due to the input regulators. Most inexpensive single-stage regulators meet this requirement. System Calibration. The common orifice is a synthetic sapphire, which is shaped liked a short funnel, and therefore, mass flow through these nozzle-shaped holes with large velocity changes should approximate adiabatic, isentropic (Le., no heat, friction loss, or no entropy change of the gas) flow (5). For these theoretical conditions the flows or gas flow ratios through the orifice can be computed. For instance considering only density flow, a theoretical gas flow ratio of oxygen to nitrogen is 0.9354 and a ratio of w b o n dioxide to nitrogen is 0.7953. The actual flow ratios are obtained empirically by comparing the output of the gas mixer with a primary standard gas mixture using a mass spectrometer as a detector. The output of the gas mixer is varied until a null compariEon is achieved with each gas component. Equations 11 and 12 are then riolved in terms of the gas flow ratios (R2,R3) since the gas fractions (X2,XJ and valve times (TI,T2,T3),are known. Evaluation Procedure. Gas flow ratios for 42 separate gas mixers were determined during the initial (and only) calibration process by the nulling method described above against a primary standard mixture (12% co2-30% 02). To evaluate the gas mixer accuracy, we compared the 42 gas mixers against gas chromatography. A Hewlett-Packard HP5880A gas Chromatograph (Hewlett-Packard, Avondale, PA) was used in the study. This instrument has the capability for multilevel primary sitandard calibration and is equipped with an automatic gas sampling valve. The reproducibility of the instrument over a 36-h period was found to be h0.046 and h0.052 for oxygen and carbon dioxide, respectively, measured using a 50% O2-15% C02 gas mixture. The gas chromatograph (GC) was calibrated by five and C 0 2 (Linde primary istandad grade mixtures of Nz, 02, Division, Union Carbide, Denver, CO) which covered the range of the gases (0-50% 02,2-20% C02). Each gas mixer was evaluatedl by use of the same set of mixtures of O2 and C02 (as determined by the gas percentages dial settings on the front panel) and analyzing each mixture on the GC. Six points of different COz and O2combinations were analyzed. The six mixtures were
2317
0 2
gas Pas chrom&ograph chromatograph thumbresults thumbresults wheel ___ wheel % mean std dev % mean std dev 2.00 1.94 0.027 4.00 4.05 0.036 3.00 2.96 0.027 7.00 7.06 0.045 5.00 4.97 0.027 12.00 12.03 0.033 7.00 6.98 0.031 20.00 20.02 0.036 10.00 9.98 0.037 50.00 50.04 0.045 20.00 20.05 0.056 a Number of data points were 42 for each gas percentage.
2% c02-20% 02, 3% co2-7%02, 5% c02-12% 0 2 , 7% 50% 02, 10% C02-0% 02,and 20% co2-4% 02.
-
coz-
Evaluations of time stability were performed on five gas mixers. Gas mixtures produced from each unit with fixed settings of 12% O2 and 5% C02were analyzed by gas chromatography daily for a 2-month period. Another two gas mixers were placed in continuous 24 h/day operation as calibrators for blood-gas analyzers for 2 years. Comparisons were made periodically against certified premixed cylinders (12% O2and 5% COz) using Radiometer BMS 3 Mark 2 blood-gas analyzers. Output load-sensitivity was studied to verify that variations in back-pressure has no measurable effect on the system within limits required for the choked flow conditions. This condition exists when the output pressure (absolute) is less than half the isobaric regulation pressure (absolute). For this study, the gas mixer was set to mix 5.00% C02and 12.00% 0 2 with an isobaric regulation pressure of 25 psig. The output pressure was varied from 0 to 17.5 psig. The output mixture was compared to a 12.00% 02-5.00% C 0 2 gas standard by mass spectrometry. The output flow was also measured by a bubble meter during this pressure load increase. Temperature sensitivity was checked by setting the gas mixer to 21% 02,5% C 0 2 and comparing to a 21% 02-5% C02 gas standard. The mixer temperature was raised to 48 "C with a heat gun. The mixer temperature wm measured at the block containing the output orifice. Only oxygen data were recorded.
RESULTS The mean gas flow ratio of 02/N2for the 42 units was 0.933 with a standard deviation of 0.001 and for C02/N2 was 0.823 with a standard deviation of 0.002. This compares to a theoretical ratio of 0.9354 and a ratio of 0.7953 for CO2/N2, respectively, as explained above. Results for the gas chromatograph comparisons for the forty-two (42) gas mixer evaluation study are given in Table I. Averages and standard deviations are recorded for 42 data points at each of the six gas percentages of COz and 02.Each data point came from a different gas mixer. The gas mixer GC comparisons are seen to be within *0.05% absolute over the total range as indicated for each gas. Stability determinations on the five units over the 2-month period and for the units over the 2-year period also showed reproducibilities within *0.05%. The output load-sensitivity to pressure is shown in Figure 4. With the isobaric pressure regulation a t 25 psig and barometric pressure at this altitude of 12.5 psia, choked flow should be maintained until the back-pressure load reaches approximately 7 psig. This predicted result is shown to occur. An effect on the gas flow ratios is first observable for COz at a back-pressure of 10 psig. A measurable effect for 0 2 does not occur until the back-pressure exceeds 12.5 psig. Temperature sensitivity results showed a change from 22.00% O2 at 25 OC, to 21.93% O2 at 48 "C. This is a change of O.O03%/"C.
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ANALYTICAL CHEMISTRY, VOL. 53, NO. 14, DECEMBER 1981
1
'4 rco, 13.00
I
FLOW
FLOW
hL/MIU
K,W
0
5
10
15
20
BACK PRESSURE (BIG)
Figure 4. Gas mixer pressure sensitivity to increase output load back-pressure. Atmospheric pressure is 12.5 psia and system pressure is 25 psig.
DISCUSSION The theoretical vs. empirical gas flow ratio for Oz/Nz compare within 0.2% while for COZ/Nzthey compare within 3%. The small differences from density flow are both explainable by viscosity effects since C 0 2 is significantly less viscous than Nz while Oz is somewhat more viscous than Nz. Flow through these orifices differs from a mathematically ideal density orifice and should therefore have some dependence on orifice geometry. However, since the geometry is fixed, one calibration is all that should be required for a given orifice. The accuracy and reproducibility of the gas mixer have been determined to be within f0.05% for both Oz and C02 which is the limitation of the GC. We expect that the reproducibility of the gas mixer is significantly less than this; reproducibility should be limited by the uncertainty of the valve opening and closing times, which would place the instrument reproducibility at much less than 0.05%. We would also expect the instrument to remain stable with time without additional calibration, since its calibration depends on the geometry of the common orifice. Because the geometry dependence is only
second order, very little temperature dependence on the flow ratio would be expected. Both expectations have been confirmed. The employment of choked flow across the orifice has been shown to provide the gas mixer with the ability to supply devices having back-pressure requirements up to 10 psi, without affecting the accuracy of the gas mixture. This adds further to the possible applications for this instrument. The versatility provided by having the final gas composition under electronic or microprocessor control makes the gas mixing system ideal for automated gas mixture control applications. One such application is a self-calibrating, continuous in vivo POz and PCOz monitoring system which has been recently reported (5,6). The uniqueness of the principle of operation of the gas mixer gives it the characteristics of (1)high accuracy, (2) selectable mixing ratios, (3) operational convenience, (4) compactness, and (5) automatic control capability. These characteristics represent advantages over present systems which include manifold rotometers, mass flow controllers, volume proportioning pumps, pressure control monitoring, and fixed flow restrictors.
LITERATURE CITED (1) Scaccl, Robert J. Appl. Physiol. 1976, 41, 960-963. (2) DeNevers, Noel "Fluid Mechanics", 1st ed.; Addison-Wesley: Menlo Park, CA, 1970; Chapter 8. (3) Hamming, R. W. "Numerlcai Methods for Scientists and Engineers", 1st ed.; McGraw-HIII: New York, 1962; Chapter 29. (4) Eshbach, Ovid W. "Handbook of Engineering Fundamentals", 3rd ed.; Wiley: New York, 1975; Chapter 8. (5) Clark, Justln S.; et al. "Symposium on Oxygen Transport to TlssueIII", 1st ed.; Plenum Press: New York, 1978; Chapter 1. (6) Clark, Justin S.; et al. Proc. San Diego Biorned. Symp. 1978, 17, 65-71.
RECEIVED for review July 6, 1981. Accepted September 21, 1981. The first prototypes were evaluated by the Pulmonary Laboratory a t the University of Utah Medical Center, Salt Lake City, UT. The gas mixer as used in a stand-alone version for the industrial market has been licensed to Union Carbide, Linde Division, Somerset, NJ.
