Optimum Use of a Differential Pressure Transducer for High-Precision Measurements James C. Holste," Philip T. Eubank, and Kenneth R. Hall Department of Chemical Engineering, Texas A8M University, College Station, Texas 77843
An electronic circuit is presented which increases the usefulness of a diaphragm-type differential pressure transducer that is available commercially. The temperature dependence of the zero setting virtually is eliminated between 100 and 300 K,and the sensitivity at 100 K is increased by a factor of 4. In addition, the output is linear with AP and the unit may be operated with full sensitivity for A P s up to at least f 2 kPa (0.3 psi). A technique for measuring pressures is described and results are presented which demonstrate the extreme precision of the method.
Introduction Conventional high-precision pressure measurements on closed systems at constant temperature generally employ an internal differential pressure transducer (DPT) and an external absolute pressure gauge as shown schematically in Figure 1. Highly accurate pressure gauges generally operate near room temperature and usually are not hermetically sealed. Hence, two fluid systems and the DPT are required. Various types of DPT's are available, but the electronic circuit presented here is relevant only for the diaphragm-types which employ a differential transformer to sense the diaphragm position. Conventional methods require that our DPT operate at the null point, that is A.?' = 0 across the diaphragm. Such a technique is inconvenient when employing a dead weight gauge (DWG) as the external pressure gauge. We present here an electronic circuit with an output that is linear with the pressure difference across the diaphragm to high accuracy and a measurement technique which uses the DPT as an interpolation device between convenient DWG increments. Using the DWG with our technique is much more convenient and more precise. Also, the present method allows in situ calibration of the DPT sensitivity and automatically corrects for volume effects caused by diaphragm displacements from the null point. Experimental Section Apparatus. Figure 2 schematically illustrates the internal arrangement of a typical DPT (within the dashed lines). The small piece of material with high magnetic permeability moves with respect to the upper and lower secondary coils as the diaphragm flexes because of nonzero pressure differentials. The relative coupling of the primary to the two secondary coils changes, and this variable coupling is used to detect movements of the diaphragm. The critical and unique feature of the present method is the use of a ratio transformer to compare outputs from the two secondary coils (illustrated in Figure 2 outside the dashed lines). Other methods may be used to detect the change in coupling, but the ratio method has several important advantages. First, the ratio of secondary outputs depends only on the position of the magnetic material and is essentially independent of the input amplitude to the primary coil. The stability of the driving oscillator therefore is not a critical parameter in this circuit. Second, ratio transformers are suited ideally to this application because of their low cost and high accuracy. Third, the null detector may be used at the highest gain setting even when the DPT is not nulled (AP# 0) so that the same resolution is obtained over the entire range of diaphragm displacements. The linearity of the ratio transformer setting with AP is limited only by the 378
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mechanical properties of the diaphragm. Our particular transducer is linear with high accuracy for P ' s of at least 2 kPa (0.3 psi) on either side of the null point. Fourth, the temperature dependence of the zero setting is reduced greatly for our particular DPT. Figure 2 also presents schematically the complete electronic circuit used for the present method. An oscillator drives the primary coil of the transformer at 5 kHz. This frequency was chosen to match that used by the manufacturer of our DPT. The ratio transformer compares the inductive components of the secondary outputs, while two variable resistors provide coarse and fine balances for the resistive component. Component balances are obtained most conveniently when a phase sensitive detector is used as the null detector, but any ac null detector with 1pV sensitivity would be sufficient. We adjust the ratio transformer and variable resistor settings to achieve null. The resistive component is approximately 2 kfl at 300 K and decreases to nearly zero a t 100 K. The inductive component varies only slightly over the entire temperature range. The 300 K sensitivity of our particular DPT is approximately 30 mV/psi for a primary input of 1 V. The sensitivity of the present circuit a t 100 K is about one-third the room temperature value, but it remains 3-5 times larger than that of the manufacturer's electronics. Five digit resolution in the ratio transformer setting corresponds to 0.6 Pa ( psi) in pressure. The stability and resolution of our measurements appear to be limited solely by the pressure stabilities of the external and internal fluid systems. Indeed, at low system pressures we have obtained resolutions exceeding 0.06 Pa ( psi) with little difficulty. Unfortunately, it is difficult to establish and reproduce the exact zero position with comparable accuracy; therefore such extreme precision is useful only for detecting small changes in the sample pressure with respect to an extremely stable reference pressure. The temperature dependences of the zero settings between 100 and 300 K are shown in Figure 3 both for the circuit described here and for the electronic circuit provided by the manufacturer. The temperature dependence clearly is reduced in the current circuit. This occurs because the predominant temperature dependence is in the resistive component of the core magnetization. The resistance required for balance does vary with temperature, but its value is not required for AP measurements. However, it is important that the resistive component be nulled. The minor temperature dependence remaining in the inductive component may be caused by differential thermal expansions in the transducer or by a small temperature dependence of the inductive part of the core magnetization. The temperature-dependent effect in the present circuit is easily corrected. The separation of the signal into inductive and resistive components also eliminates the
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temperature dependence of the coil resistances as a significant source of error in the pressure measurements. Measurement Technique. The technique we have used to obtain high-precision pressure measurements with the present circuit is illustrated in Figure 4.We adjust the external system pressure to a convenient value and record the external pressure gauge reading (Pex)and the ratio transformer setting ( R ) .The procedure then is repeated for several different external pressures lying within the linear range of the DPT while the sample gas is held a t constant temperature. The sample pressure (PO)then is determined by a least squares fit of
P,, = Po + S ( R - Ro) to the data. Here S is the sensitivity of the ratio transformer setting to the pressure difference across the diaphragm and Ro is the AP = 0 ratio tranformer setting. We determine the null map by exposing both sides of the diaphragm to the pressure transmission fluid and recording Ro as a function of temperature and pressure. The sensitivity is determined independently for each sample pressure and it provides a convenient consistency check. In principle, two external pressures are sufficient to determine Po and S, but for testing the technique we use up to five external pressure settings. Typical fit,s of the above equation to five external pressures have root-mean-square deviations of about 5 parts per million. The value of Po determined from the linear fit corresponds to a pressure reading taken with the diaphragm in the exact null position; therefore no volume correction for diaphragm displacement is necessary. (Diaphragm displacement effects cause an apparent reduction in D P T sensitivity with in-
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Figure 4. Schematic illustration of the pressure measurement technique. The system pressure is determined from a least-squares fit to the external pressures and the corresponding ratio transformer settings. Ro is the ratio transformer setting for zero pressure difference across the diaphragm, and Po is the pressure of sample with zero diaphragm displacement from the null position. creasing pressure, but no change in the zero setting.) The DPT interpolates between the smallest convenient increments of the external gauge. We presently are using an air dead-weight gauge as the external pressure gauge. The smallest convenient increments in our pressure range are 300 P a (0.05 psi) or 600 P a (0.1 psi), for high or low D P T temperatures, respectively. Figure 5 presents an example of the typical precision obtained with this method. Pressure measurements were made as a function of temperature between 100 and 300 K on a sample of helium gas. The deviations of the individual data points from P = a bT cT2 are shown, where a , b , and c have been determined by a least-squares fit. The rootmean-square deviation of this fit is 0.0033%. The scatter in the data is extremely small, but a systematic deviation is observed depending upon whether the measurements were made upon warming or cooling to equilibrium. In fact, the scatter within either the heating or the cooling subset is at least a factor of 2 smaller than the overall fit. This systematic effect occurred consistently in our initial measurements. We have subsequently replaced several fittings and currently do not observe this effect (indicating it was an extremely small leak). In fact, the observed deviations are not much larger than errors expected from temperature measurement imprecision. (Note that 0.001% corresponds to 1 mK a t 100 K.)
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Ind. Eng. Chem., Fundam., Vol. 16, No. 3, 1977
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absolute accuracy of the pressure measurement is obtained, because the absolute accuracy is determined primarily by the external pressure gauge. In many cases, however, extreme precision is of more importance than extreme accuracy, and in these cases the present method should prove definitely superior.
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Figure 5. Deviation of experimental data points between 100 and 300 K from Pcalc= a bT cT* for a sample of helium gas. The rootmean-squaredeviation of this fit is 0.0033%.The origin of the slight systematic dependence on whether the equilibrium temperature was approached by heating or cooling is not understood. The pressures range from 1.0 MPa (140 psi) at 100 K to 2.9 MPa (420 psi) at 300 K. The deviations shown here are typical of those obtained for a series of seven helium isochores at pressures below 5.0 MPa (730 psi).
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For cases where we have held a fixed quantity of gas for extended periods of time a t constant temperature, pressure measurements over a period of several days generally reproduce to a few parts per million after appropriate corrections for very small changes in system temperature are made. Indeed, we have been able to detect leaks in our sample volume which caused relative pressure changes of 2 X lO-5/day or less, although such testing is time-consuming. The interpolation technique described in this section is not restricted solely to the DPT circuitry described in the previous section. This technique may be used with any DPT which has an output that is linear with AP to the required accuracy. I t is important to note that no significant improvement in the
The method presented here has several advantages over existing pressure measurement techniques. The in situ Calibration of the DPT sensitivity at every point, the automatic correction for volume effects caused by diaphragm displacements, and the ability to interpolate between DWG weights lead to very high precision. The extremely small temperature dependence of the ratio transformer setting corresponding to AP = 0 also increases the precision of the measurements. The electronic circuit retains full linearity, resolution, and precision over the entire range for which the mechanical motion of the diaphragm is linear with AP. The wide-range linearity makes the use of an external pressure gauge more convenient, particularly in the case of dead weight gauges. All the components used in the electronic circuit are available commercially, and these components may be useful for other laboratory measurements when not actually required for use with the DPT.
Acknowledgments We gratefully acknowledge financial support for our research from the following sources: NSF Grants ENG 74-23411 and ENG 76-00692,AGA Grants BR-110-1 and BR-110-2, and the donors of the Petroleum Research Fund, administered by the American Chemical Society. We obtained our instruments from RUSKA Instrument Corporation, PO Box 36010, Houston, Texas 77036. This is neither an endorsement nor a disapproval of the manufacturer’s product but only a documentation of source. Received for reuiew October 12,1976 Accepted April 8,1977
A Flow Microreactor for Study of High-pressure Catalytic HydroprocessingReactions Kenneth F. Elierer, Manoj Bhinde, Marwan Houalla, Dennis Broderlck, Bruce C. Gates,’ James R. Katzer, and Jon H. Olson Department of Chemical Engineering, University of Delaware, Newark, Delaware 1971 I
A flow microreactor has been designed for study of kinetics of hydroprocessing reactions and the accompanying catalyst aging. It operates at temperatures up to 450 O C and pressures up to 300 atm. Liquid reactant (containing dissolved hydrogen) can be fed steadily at 0.5 to 600 cm3/h or as pulses injected into a stream of liquid carrier. The design is specified, and the operation is illustrated by conversion data for hydrodesulfurization of dibenzothiophene and of 4-methyldibenzothiophenecatalyzed by sulfided “cobalt molybdate” at 300 O C and 104 atm and for hydrodenitrogenation of quinoline catalyzed by sulfided “nickel molybdate” at 342 OC and 165 atm.
Introduction The understanding of catalytic reaction mechanisms and the design of large-scale catalytic reactors often require reaction kinetic data, and consequently one of the central problems of chemical reaction engineering is the design of 380
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laboratory reactors to provide reaction rate data free from the influence of transport effects (Anderson, 1968; Doraiswamy and Tajbl, 1974). The most appropriate laboratory reactor for a particular application depends on the reaction rate, the phase behavior of the catalyst and reactants, and the rates of
