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A physical model for the interdigitated fuel drivability index sensor
Sensors and Actuators A 116 (2004) 277–283
A physical model for the interdigitated fuel drivability index sensor Simon S. Wang a,∗ , Han S. Lee a,1 , David K. Lambert a,2 , Yingjie Lin b,3 a b
Delphi Research Labs, 51786 Shelby Parkway, Shelby Township, MI 48315, USA Delphi E&C, Mexico Technical Center, 32 Celerity Wagon, El Paso, TX 79906, USA
Received 8 September 2003; received in revised form 11 March 2004; accepted 16 April 2004 Available online 15 June 2004
Abstract An on-board drivability index (DI) sensor has been invented at Delphi Corporation. It is anticipated that the sensor could be used to reduce exhaust emission and improve engine performance during cold starts. During a DI measurement, the initial amount of fuel captured in the sensor declines as the sensor temperature is raised by built-in heating elements. A volatilization curve, a plot of the fuel level versus the sensor temperature, is thus obtained and the DI of the test fuel can be estimated. In this work, a model is proposed that simulates the curves obtained from the DI sensor measurement. This model assumes that the saturated vapor pressure curve for the test fuel determines the shape of its volatilization curve. The model suggests that mass transfer of fuel constituents to the liquid–air interface could be a rate-determining factor for the volatilization process. © 2004 Elsevier B.V. All rights reserved. Keywords: Sensor; Drivability index; Fuel; Model
1. Introduction Control of a gasoline engine’s air-to-fuel ratio during cold starts is important both for its effects on exhaust emission and for its impact on customer satisfaction with engine performance and drivability. If the intake is too rich in fuel, unburned fuel is exhausted to the environment; too lean of an air/fuel mixture can cause: misfire, incomplete combustion, engine stalling, and emission problems. While the engine is cold, only a fraction of the fuel that is injected into the intake manifold promptly evaporates. The variables that control the fraction of the injected fuel that evaporates within an engine cycle include: the engine design, the ambient temperature, the air pressure in the intake manifold, and the drivability index (DI) of the fuel. Of these parameters, DI is presently the only variable that is not measured. Therefore, the implementation of an on-board DI sensor could reduce exhaust emission [1–4] and improve engine performance during cold start. The definition of DI is based on a laboratory test, ASTM D 86 [1]. This test needs a distillation apparatus. The test ∗ Corresponding author. Tel.: +1 586 323 4994; fax: +1 586 323 9898. E-mail address: [email protected] (S.S. Wang). 1 Tel.: +1 586 323 9466; fax: +1 586 323 9898. 2 Tel.: +1 586 323 4433; fax: +1 586 323 9898. 3 Tel.: +1 915 783 7357; fax: +1 915 783 7481.
0924-4247/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2004.04.039
initiates with a 100 mL sample of gasoline, which is to be distilled into a cooled collection container. The sample temperature is raised at a controlled rate. The fraction of fuel distilled is recorded as a function of the sample temperature. The definition of DI relies upon knowledge of the temperatures at which 10, 50, and 90% of the sample volume is distilled, i.e. T10 , T50 , and T90 , respectively [1]. A currently accepted definition for gasoline without oxygenates is: DI = 1.5T10 + 3T50 + T90 . Higher DI corresponds to lower volatility. Under the same conditions, the evaporation rate is lower if the fuel has a higher DI. Several approaches have also been considered to measure the DI of the fuel. Clarke [5,6] proposed the use of an infrared source to measure the fuel spectrum, and compared the spectrum with the known database to determine the fuel DI. Takahashi et al. [7] proposed to measure the sound velocity in the fuel to determine the DI. However, the correlation between the sound velocity and the DI is poor. A DI sensor has been invented at Delphi Corporation [8,9]. This DI sensor is composed of two interdigitated sensing electrodes, 0.6 cm × 0.8 cm in dimension, with a 0.3 mm gap between them (see Fig. 1A). Because of its small size, this DI sensor could be implemented in the fuel tank of a vehicle rather easily. Prior to the measurement, the sensor is brought into contact with the fuel, so that the fuel is loaded in the sensor reproducibly by the capillary effect. Platinum heating elements (see Fig. 1B) are used to heat up the sensor
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found in the ASTM D 86 measurement. In fact, the hydrocarbon components could be vaporized from the sensor at any temperatures as long as the vapor pressure of the fuel in the system is not saturated. We refer to this vaporization process as “volatilization” in this paper in order to distinguish it from the distillation process occurring in the ASTM D 86 method. More investigation is needed to quantitatively describe this volatilization process and simulate the volatilization curves obtained from the DI sensor measurement. In this work, we propose a model based on the saturated vapor pressure of hydrocarbon fuels to simulate the volatilization process that occurs during the DI sensor measurement. Simplified hydrocarbon fuels that contain only one or two components are used to verify this model. The volatilization curves of the test fuels are simulated with the model and compared to those measured by the DI sensor. Several assumptions are made, so that the calculated curves match with those measured. Potential applications of this model, particularly to analyze the DI sensor test results, are also discussed.
2. Model
Fig. 1. (A) Schematic diagram of the interdigitated DI sensor and (B) photo of the DI sensor with heaters and RTD.
and vaporize the fuel sample. The fuel level in the sensor is estimated from the capacitance measured between the two sensing electrodes. The temperature is measured using a resistive temperature detector (RTD). The DI of the test fuel could then be predicted from the temperatures at which 10 and 50% of the test fuel is vaporized plus the temperature at the end of the test. In order to test the sensor in a vehicle, the modular reservoir assembly (fuel delivery system) for the test vehicle was modified to accommodate the sensor [10]. The vehicle test showed a good correlation existing between the sensor output and the fuel DI [8]. The details of the test procedures are also reported previously [8]. Typically, the test results of the DI sensor are presented by plotting the measured fuel level with respect to the sensor temperature. In Fig. 2, the curve thus obtained from a certification gasoline fuel is compared to the distillation curve measured by the ASTM D 86 method for the same fuel. The fuel level measured by the DI sensor declined faster than that measured by the ASTM D 86 method. Since the rate of heating is much faster during the DI sensor measurement, the hydrocarbon components of the fuel loaded in the sensor might not boil or distill at or close to the boiling points
The DI sensor measurements are normally conducted inside a closed system; therefore, the vapor pressure of the fuel should rapidly reach its saturation level. After reaching the fuel vapor saturation level, the fuel loaded into the sensor will not vaporize and the full level within the sensor will be maintained indefinitely as long as the ambient and sensor temperatures remain constant. If the DI sensor is electrically heated, its temperature increases. As the sensor temperature exceeds ambient temperature, the vapor pressure in the vicinity of the sensor is no longer saturated. The fuel sample begins to volatilize to reestablish equilibrium. This volatilization process continues until the end of the measurement. 2.1. Fuels with one component Quantitatively, the driving force for this volatilization process can be illustrated using the saturated vapor pressure curve of a hydrocarbon fuel containing only one component, e.g. heptane. Fig. 3 shows the saturate vapor pressure of heptane at different temperatures. The symbols are the data points collected from a handbook [11] and the lines are obtained by data fitting. If the DI sensor is at an ambient temperature T1 before heating, then the partial pressure of heptane vapor in the closed system is at the saturation level P1 (see Fig. 3). Upon initiating a DI test, the temperature of the sensor will start increasing from T1 to, for example, T2 . The saturated vapor pressure of the heptane will correspondingly increase from P1 to P2 (see Fig. 3). Therefore, heptane is volatilized from the sensor so as to increase the vapor pressure in the vicinity of the sensor from P1 to P2 . When the fuel in the sensor is heated up at a controlled rate
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Fig. 2. The curves of a certified gasoline fuel obtained from the DI sensor measurement and the ASTM D 86 method.
of temperature rise, the amount of heptane volatilized as the sensor temperature increases from T1 to T2 is assumed to be proportional to the area B shown in Fig. 3. This area is calculated by integrating the vapor pressure curve from T1 to T2 . The measurement continues until all the fuel in the sensor is vaporized at a temperature T3 . The total amount of heptane volatilized from the sensor during the measurement is assumed to be proportional to the area A shown in Fig. 3. This area is calculated by integrating the vapor pressure curve from T1 to T3 . Based on these assumptions, the normalized fuel level L in the sensor at the temperature T2 is: L(T2 ) = 1 −
B A
(1)
As presently implemented, the measurement stops when the normalized fuel level drops below a predetermined residual level R to avoid overheating of the fuel [8,9]. If the total amount of heptane volatilized during the measurement is proportional to A, then the amount of heptane
Fig. 3. The saturated vapor pressure of heptane at different temperatures.
originally loaded in the sensor is proportional to A multiplied by a residual factor 1/(1 − R). Eq. (1) is modified accordingly: L(T2 ) = 1 −
B AR
(2)
where R is the residual factor and R = 1/(1 − R). Eq. (2) gives the fuel level at any temperature between T1 and T3 and predicts the volatilization curve. 2.2. Fuels with two or more components Eqs. (1) and (2) can be modified for a hydrocarbon fuel containing two components I and II with their initial concentration at CI and CII in volume percent, respectively. We assume the sensor measurement initiates at a temperature T1 and continues until all the fuel in the sensor is vaporized at a temperature T3 . If one component volatilizes faster than the other, then the concentrations of these two components in the sensor is continuously varied during the measurement. The components in hydrocarbon fuels usually have similar chemical properties. The mixing of two chemicals with similar properties normally approaches an ideal solution. Therefore, it is reasonable to assume that this two-component fuel is an ideal solution, and the partial pressure of each component at its saturation is equal to the vapor pressure for the pure substance multiplied by its mole fraction. The partial pressure curves for components I and II given by ideal solution theory is illustrated in Fig. 4. The amounts of components I and II volatilized as the temperature increases from T1 to T2 are then assumed to be proportional to the areas BI and BII , respectively, as shown in Fig. 4, and the total amounts of components I and II
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Fig. 1B) for the sensor was secured with a rubber stopper. Then, the rubber stopper was placed on the open end of the test tube and sealed with teflon tape. Only a small quantity of test fuel (5 cm3 ) was used to prevent the sensor from being submerged in the fuel. 3.2. DI sensor measurement
Fig. 4. The partial pressure of components I and II at different temperatures.
volatilized during the measurement are assumed to be proportional to the areas AI and AII . The normalized fuel level L in the sensor at the temperature T2 is: BI BII CI − CII (3) L(T2 ) = 1 − AI AII In fact, Eq. (3) could be generalized for a hydrocarbon fuel containing n components: n Bi (4) Ci L(T2 ) = 1 − Ai i=1
Going back to the two component system, the measurement stops as the normalized fuel level drops below a predetermined residual level R to avoid overheating of the fuel [8,9]. We assume the boiling point for component II is much higher than that for I, and the fuel sample left in the sensor at the end of the measurement is predominated by component II. If the total amount of component II volatilized during the measurement is proportional to AII , then the amount of component II originally loaded in the sensor is proportional to AII multiplied by a residual factor CII /(CII − R). Eq. (4) is modified accordingly: BI BII CI − CII (5) L(T2 ) = 1 − AI AII R
After loading the sensor with the fuel sample by the capillary effect, the fuel level in the sensor was monitored as a function of time. If the vapor pressure of the test fuel was at saturation, the sensor remained full indefinitely. Before operating the sensor, the test tube was inverted so that the connection wires were below the sensor. This prevented fuel from dripping down the wires and back into the sensor (see Fig. 1). The heaters were then turned on to vaporize the fuel loaded in the sensor. Both the fuel level (capacitance) and the sensor temperature were measured once per second and recorded using a laptop computer. To avoid overheating, the measurement terminated if the normalized fuel level dropped below a predetermined residual level R. In this work, the R-value for all the test fuels was around 25%. The measurement was conducted inside an exhaust hood. The ambient temperature surrounding the test tube was adjusted either using an oven or a cooling system so that the measurements could be initiated at a temperature between 5 and 67 ◦ C. The details of the measurement procedures have been reported previously [9].
4. Results and discussion 4.1. Fuels with one component The model prediction was first compared with the DI sensor output measured with a simplified fuel containing only one component, i.e. heptane. The DI sensor was tested with an initial ambient temperature, which was varied from 5 to 49 ◦ C as shown in Fig. 5. It is seen in Fig. 5 that as the initial temperature of the measurement was changed from
where R is the residual factor and R = CII /(CII − R). Eq. (5) gives the fuel level at any temperature between T1 and T3 and predicts the volatilization curve.
3. Experimental 3.1. Test fuels Three fuels: neat-heptane, nonane, and a 1:1 mixture of heptane and nonane, were tested in this work to verify the model. The test was conducted inside a test tube, 40 cm3 in volume. For each measurement, about 5 cm3 of test fuel was poured into the test tube. The connection wires (see
Fig. 5. The volatilization curves of heptane measured by the DI sensor as compared to those calculated from the model.
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curves for nonane were then calculated using Eq. (2) and are shown in Fig. 6 for comparison. It is seen in Fig. 6 that the curves calculated from the model agree with those measured by the sensor. As the initial temperature increases from 8 to 67 ◦ C, the temperature at the end for the curves also shifts from 107.5 to 120 ◦ C, respectively. Again, the shift to higher temperature of the volatilization curves with increasing initial temperature is believed to be intrinsic to this DI sensor measurement. 4.2. Fuel with two components
Fig. 6. The volatilization curves of nonane measured by the DI sensor as compared to those calculated from the model.
5 to 49 ◦ C, the temperature at the end also shifted from 78 to 87 ◦ C, respectively. The volatilization curves for heptane were then calculated using Eq. (2) and are shown in Fig. 5 for comparison. It is seen in Fig. 5 that the curves calculated from the model indeed match those measured by the DI sensor. In addition, the model also predicts that as the initial temperature increases, the volatilization curves shift toward higher temperature. Therefore, it is believed that the shift of the volatilization curves with initial temperature is intrinsic to this DI sensor measurement. This shift would make the DI number estimated from the volatilization curve higher than its true value. Algorithms based on this model could thus be developed to account for measurement initiated at different temperatures. The model prediction was then compared with the DI sensor output measured with pure nonane (see Fig. 6). Since the boiling point for nonane (150.8 ◦ C) is higher than that for heptane (98.5 ◦ C), the ambient temperatures chosen to begin the measurements with nonane were also higher than for heptane, i.e. varying from 8 to 67 ◦ C. The volatilization
Subsequently, this model prediction was compared with the sensor output measured with a fuel containing two components, i.e. 1:1 mixture of heptane and nonane. The DI sensor was tested in this fuel with an ambient temperature, which was varied from 8 to 53 ◦ C. To simulate these curves with the model, two assumptions were made. Because the boiling point for nonane (150.8 ◦ C) is much higher than that for heptane (98.5 ◦ C), it was assumed that the fuel left in the sensor at the end of the measurement was predominantly nonane. In addition, it was assumed that heptane loaded in the sensor had completely volatilized at its boiling point. Since the boiling point for nonane is much higher than that for heptane, heptane should volatilize faster and the concentrations of these two components in the sensor continuously varied during the measurement. In the initial simulation using our model, however, it was tentatively assumed that these concentrations remained approximately constant. The volatilization curves for the fuel were calculated using Eq. (5). Since the concentrations of heptane and nonane actually varied during the measurement, the volatilization curves calculated with constant concentration did not match well with the measured ones, as expected. From our initial simulation, the concentrations of heptane and nonane in the sensor during the measurement could be
1.2
Level (Normalized)
1 0.8 Measured (Init. Temp. 8C)
0.6
Calculated (Init. Temp. 8C) Measured (Init. Temp. 22C) Calculated (Init. Temp. 22C)
0.4
Measured (Init. Temp. 35C) Calculated (Init. Temp. 35C) Measured (Init. Temp. 45C)
0.2
Calculated (Init. Temp. 45C) Measured (Init. Temp. 53C) Calculated (Init. Temp. 53C)
0 0
20
40
60
80
100
120
Temperature (C) Fig. 7. The volatilization curves of 1:1 mixture of heptane and nonane measured by the DI sensor as compared to those calculated from the model with the concentrations of heptane and nonane calculated from the first simulation.
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350 Init. Temp. 8C
Partial pressure (mm Hg)
300
Mass transfer control Init. Temp. 22C
250
Mass transfer control Init. Temp. 35C Mass transfer control
200
Init. Temp. 45C Mass transfer control
150
Init. Temp. 53C Mass transfer control
100 50 0 0
20
40
60
80
100
120
Temperature (C) Fig. 8. The partial pressure of heptane and the mass transfer control region during the DI sensor measurement.
estimated. These concentrations were then used to calculate the partial pressure of heptane and nonane with ideal solution theory as illustrated in Fig. 4. The volatilization curves for the fuel were then calculated again with the modified partial pressure and are shown in Fig. 7. Fig. 7 shows a good agreement between the calculated and the measured curves. In this simulation, it was also assumed that the volatilization of heptane entered the mass transfer control region toward the end of the measurement as shown by the dotted lines in Fig. 8. In fact, heptane in a two-component fuel does not volatilize as easily as in pure heptane, because the heptane molecules must transfer through the medium to reach the fuel–air interface to volatilize. As the mass transfer within the liquid becomes the rate-determining factor for the volatilization process, its rate approaches a constant and the increase of partial pressure with temperature is no longer the driving force.
temperature of sensor and fuel) increased, the volatilization curve shifted toward higher temperature. This shift would make the DI number estimated from the volatilization curve higher than its true value. Therefore, algorithms need to be developed to account for measurement initiated at different temperatures.
Acknowledgements The authors like to thank Ken Rahmoeller and Kapila Wadu-Mesthride for providing the fuel samples. The authors also thank Michel F. Sultan, Joe Mantese, and Lorenzo Rodriguez for their support and valuable suggestions in completing this work.
References 5. Conclusions A model is proposed to simulate the volatilization curves obtained from the DI sensor measurements conducted in a test tube using simplified hydrocarbon fuels containing one or two components. This model, verified experimentally, assumes that the saturated vapor pressure curve for the test fuel determines the shape of its volatilization curve measured from the DI sensor. During the measurement, the volatilization of the test fuel to saturate the vapor pressure in the system is the driving force in determining the fuel level in the DI sensor and drives its decline. The model also suggests that mass transfer within the liquid could be a rate-determining factor for the volatilization process with fuels containing more than one component. Therefore, this model could help us analyze vehicle test results obtained from an on-board DI sensor using commercial gasoline fuels. Furthermore, this model predicts that as the ambient temperature (or the initial
[1] Standard Test Method for Distillation of Petroleum Products at Atmospheric Pressure, Designation: D 86–00, American Society for Testing and Materials, West Conshohocken, PA. [2] Low- and Intermediate-Temperature Drivability Program using Gasoline–Alcohol Blends, CRC Report 568, Coordinating Research Council, 1990. [3] Effect of Volatility and Oxygenates on Drivability at Intermediate Ambient Temperatures, CRC Report 578, Coordinating Research Council, 1992. [4] B. Evans, S. Jorgensen, G. Nusser, K. Eng, M. McNally, C. Richardson, D. Whelan, E. Ziegel, New fuel volatility indices, Automotive Eng. (February 2000) 175. [5] R.H. Clarke, Portable Fuel Analyzer for the Diagnosis of Fuel-Related Problems On-Site at the Vehicle Service Bay, US Patent 5,569,922 (October 1996). [6] R.H. Clarke, Method and Devices for Fuel Characterization and Optimal Fuel Identification On-Site at a Fuel Delivery Dispenser, US Patent 5,750,995 (May 1998). [7] T. Takahashi, T. Kondo, H. Saitou, T. Okazaki, M. Ishikiriyama, Method and Apparatus for Determining Gasoline Characteristics by using Ultrasonic Wave, US Patent 6,032,516 (March 2000).
S.S. Wang et al. / Sensors and Actuators A 116 (2004) 277–283 [8] H.S. Lee, S.S. Wang, D.K. Lambert, C.R. Harrington, J. Lin, An on-vehicle DI sensor: initial results, IEEE Sens. J. Scheduled for publication in December, 2004. [9] Y.J. Lin, H.S. Lee, S.S. Wang, D.K. Lambert, Drivability Index Sensor Sensing Element and Signal Processing Circuit Design, US Patent 6,564,624 (May 2003). [10] D.K. Lambert, C.R. Harrington, R. Kerr, H.S. Lee, Y.J. Lin, D.Y. Wang, S.S. Wang, Fuel Drivability Index Sensor, SAE Paper, 2003-01-3238, 2003. [11] R.H. Perry, C.H. Chilton, Chemical Engineers’ Handbook, fifth ed., McGraw Hill Book Company, 1973 (Chapter 3).
Biographies Dr. Simon S. Wang received his MS and PhD degree in Chemical Engineering from the University of California at Los Angeles in 1977 and 1979, respectively. He is presently a Senior Staff Research Engineer at Delphi Research Labs. Dr. Wang has received 17 US patents and published 70 papers on: fuel cell, engine oil condition sensor and sensing algorithm, microsensors, fretting corrosion in electrical connectors, electrochemical etching of silicon, electrochemical phenomena in lubricants, sensor modeling, microelectronic fabrication technologies, battery, and novel surface
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coatings. His research interests include: fuel cell, microsensors, microelectronic fabrication, triboelectrochemistry, energy storage systems and surface science. Han-Sheng Lee received his PhD in Electrical Engineering from Princeton University in 1976. In the same year, he joined the GM Research Labs. He was transferred to Delphi Research Labs, Delphi Systems in 1999. His technical interests are in the general area of physics, technology and applications of sensors and semiconductor devices. David K. Lambert received the BA and PhD degrees in physics, both from the University of California at Berkeley. He is currently Senior Staff Research Scientist at Delphi Research Labs. He has also served as adjunct Professor in the Department of Physics and Astronomy at Michigan State University. His research interests include chemical sensors, and sensors that involve infrared spectroscopy or heat transfer. He has published over 40 papers and holds 17 US patents. Yingjie Lin has his Bachelor Degree in Engineering Mechanics from Tsinghua University; his Master Degree in Mechanical Engineering and Ph.D. in Electrical and Computer Engineering from The University of Texas at El Paso. He joined Delphi in 1997 and is Staff Research Engineer of Delphi Dynamics and Propulsion (D&P) Innovation Center. Currently, he responses for advanced sensor/actuator technology research and new product development.
A physical model for the interdigitated fuel drivability index sensor Simon S. Wang a,∗ , Han S. Lee a,1 , David K. Lambert a,2 , Yingjie Lin b,3 a b
Delphi Research Labs, 51786 Shelby Parkway, Shelby Township, MI 48315, USA Delphi E&C, Mexico Technical Center, 32 Celerity Wagon, El Paso, TX 79906, USA
Received 8 September 2003; received in revised form 11 March 2004; accepted 16 April 2004 Available online 15 June 2004
Abstract An on-board drivability index (DI) sensor has been invented at Delphi Corporation. It is anticipated that the sensor could be used to reduce exhaust emission and improve engine performance during cold starts. During a DI measurement, the initial amount of fuel captured in the sensor declines as the sensor temperature is raised by built-in heating elements. A volatilization curve, a plot of the fuel level versus the sensor temperature, is thus obtained and the DI of the test fuel can be estimated. In this work, a model is proposed that simulates the curves obtained from the DI sensor measurement. This model assumes that the saturated vapor pressure curve for the test fuel determines the shape of its volatilization curve. The model suggests that mass transfer of fuel constituents to the liquid–air interface could be a rate-determining factor for the volatilization process. © 2004 Elsevier B.V. All rights reserved. Keywords: Sensor; Drivability index; Fuel; Model
1. Introduction Control of a gasoline engine’s air-to-fuel ratio during cold starts is important both for its effects on exhaust emission and for its impact on customer satisfaction with engine performance and drivability. If the intake is too rich in fuel, unburned fuel is exhausted to the environment; too lean of an air/fuel mixture can cause: misfire, incomplete combustion, engine stalling, and emission problems. While the engine is cold, only a fraction of the fuel that is injected into the intake manifold promptly evaporates. The variables that control the fraction of the injected fuel that evaporates within an engine cycle include: the engine design, the ambient temperature, the air pressure in the intake manifold, and the drivability index (DI) of the fuel. Of these parameters, DI is presently the only variable that is not measured. Therefore, the implementation of an on-board DI sensor could reduce exhaust emission [1–4] and improve engine performance during cold start. The definition of DI is based on a laboratory test, ASTM D 86 [1]. This test needs a distillation apparatus. The test ∗ Corresponding author. Tel.: +1 586 323 4994; fax: +1 586 323 9898. E-mail address: [email protected] (S.S. Wang). 1 Tel.: +1 586 323 9466; fax: +1 586 323 9898. 2 Tel.: +1 586 323 4433; fax: +1 586 323 9898. 3 Tel.: +1 915 783 7357; fax: +1 915 783 7481.
0924-4247/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2004.04.039
initiates with a 100 mL sample of gasoline, which is to be distilled into a cooled collection container. The sample temperature is raised at a controlled rate. The fraction of fuel distilled is recorded as a function of the sample temperature. The definition of DI relies upon knowledge of the temperatures at which 10, 50, and 90% of the sample volume is distilled, i.e. T10 , T50 , and T90 , respectively [1]. A currently accepted definition for gasoline without oxygenates is: DI = 1.5T10 + 3T50 + T90 . Higher DI corresponds to lower volatility. Under the same conditions, the evaporation rate is lower if the fuel has a higher DI. Several approaches have also been considered to measure the DI of the fuel. Clarke [5,6] proposed the use of an infrared source to measure the fuel spectrum, and compared the spectrum with the known database to determine the fuel DI. Takahashi et al. [7] proposed to measure the sound velocity in the fuel to determine the DI. However, the correlation between the sound velocity and the DI is poor. A DI sensor has been invented at Delphi Corporation [8,9]. This DI sensor is composed of two interdigitated sensing electrodes, 0.6 cm × 0.8 cm in dimension, with a 0.3 mm gap between them (see Fig. 1A). Because of its small size, this DI sensor could be implemented in the fuel tank of a vehicle rather easily. Prior to the measurement, the sensor is brought into contact with the fuel, so that the fuel is loaded in the sensor reproducibly by the capillary effect. Platinum heating elements (see Fig. 1B) are used to heat up the sensor
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found in the ASTM D 86 measurement. In fact, the hydrocarbon components could be vaporized from the sensor at any temperatures as long as the vapor pressure of the fuel in the system is not saturated. We refer to this vaporization process as “volatilization” in this paper in order to distinguish it from the distillation process occurring in the ASTM D 86 method. More investigation is needed to quantitatively describe this volatilization process and simulate the volatilization curves obtained from the DI sensor measurement. In this work, we propose a model based on the saturated vapor pressure of hydrocarbon fuels to simulate the volatilization process that occurs during the DI sensor measurement. Simplified hydrocarbon fuels that contain only one or two components are used to verify this model. The volatilization curves of the test fuels are simulated with the model and compared to those measured by the DI sensor. Several assumptions are made, so that the calculated curves match with those measured. Potential applications of this model, particularly to analyze the DI sensor test results, are also discussed.
2. Model
Fig. 1. (A) Schematic diagram of the interdigitated DI sensor and (B) photo of the DI sensor with heaters and RTD.
and vaporize the fuel sample. The fuel level in the sensor is estimated from the capacitance measured between the two sensing electrodes. The temperature is measured using a resistive temperature detector (RTD). The DI of the test fuel could then be predicted from the temperatures at which 10 and 50% of the test fuel is vaporized plus the temperature at the end of the test. In order to test the sensor in a vehicle, the modular reservoir assembly (fuel delivery system) for the test vehicle was modified to accommodate the sensor [10]. The vehicle test showed a good correlation existing between the sensor output and the fuel DI [8]. The details of the test procedures are also reported previously [8]. Typically, the test results of the DI sensor are presented by plotting the measured fuel level with respect to the sensor temperature. In Fig. 2, the curve thus obtained from a certification gasoline fuel is compared to the distillation curve measured by the ASTM D 86 method for the same fuel. The fuel level measured by the DI sensor declined faster than that measured by the ASTM D 86 method. Since the rate of heating is much faster during the DI sensor measurement, the hydrocarbon components of the fuel loaded in the sensor might not boil or distill at or close to the boiling points
The DI sensor measurements are normally conducted inside a closed system; therefore, the vapor pressure of the fuel should rapidly reach its saturation level. After reaching the fuel vapor saturation level, the fuel loaded into the sensor will not vaporize and the full level within the sensor will be maintained indefinitely as long as the ambient and sensor temperatures remain constant. If the DI sensor is electrically heated, its temperature increases. As the sensor temperature exceeds ambient temperature, the vapor pressure in the vicinity of the sensor is no longer saturated. The fuel sample begins to volatilize to reestablish equilibrium. This volatilization process continues until the end of the measurement. 2.1. Fuels with one component Quantitatively, the driving force for this volatilization process can be illustrated using the saturated vapor pressure curve of a hydrocarbon fuel containing only one component, e.g. heptane. Fig. 3 shows the saturate vapor pressure of heptane at different temperatures. The symbols are the data points collected from a handbook [11] and the lines are obtained by data fitting. If the DI sensor is at an ambient temperature T1 before heating, then the partial pressure of heptane vapor in the closed system is at the saturation level P1 (see Fig. 3). Upon initiating a DI test, the temperature of the sensor will start increasing from T1 to, for example, T2 . The saturated vapor pressure of the heptane will correspondingly increase from P1 to P2 (see Fig. 3). Therefore, heptane is volatilized from the sensor so as to increase the vapor pressure in the vicinity of the sensor from P1 to P2 . When the fuel in the sensor is heated up at a controlled rate
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Fig. 2. The curves of a certified gasoline fuel obtained from the DI sensor measurement and the ASTM D 86 method.
of temperature rise, the amount of heptane volatilized as the sensor temperature increases from T1 to T2 is assumed to be proportional to the area B shown in Fig. 3. This area is calculated by integrating the vapor pressure curve from T1 to T2 . The measurement continues until all the fuel in the sensor is vaporized at a temperature T3 . The total amount of heptane volatilized from the sensor during the measurement is assumed to be proportional to the area A shown in Fig. 3. This area is calculated by integrating the vapor pressure curve from T1 to T3 . Based on these assumptions, the normalized fuel level L in the sensor at the temperature T2 is: L(T2 ) = 1 −
B A
(1)
As presently implemented, the measurement stops when the normalized fuel level drops below a predetermined residual level R to avoid overheating of the fuel [8,9]. If the total amount of heptane volatilized during the measurement is proportional to A, then the amount of heptane
Fig. 3. The saturated vapor pressure of heptane at different temperatures.
originally loaded in the sensor is proportional to A multiplied by a residual factor 1/(1 − R). Eq. (1) is modified accordingly: L(T2 ) = 1 −
B AR
(2)
where R is the residual factor and R = 1/(1 − R). Eq. (2) gives the fuel level at any temperature between T1 and T3 and predicts the volatilization curve. 2.2. Fuels with two or more components Eqs. (1) and (2) can be modified for a hydrocarbon fuel containing two components I and II with their initial concentration at CI and CII in volume percent, respectively. We assume the sensor measurement initiates at a temperature T1 and continues until all the fuel in the sensor is vaporized at a temperature T3 . If one component volatilizes faster than the other, then the concentrations of these two components in the sensor is continuously varied during the measurement. The components in hydrocarbon fuels usually have similar chemical properties. The mixing of two chemicals with similar properties normally approaches an ideal solution. Therefore, it is reasonable to assume that this two-component fuel is an ideal solution, and the partial pressure of each component at its saturation is equal to the vapor pressure for the pure substance multiplied by its mole fraction. The partial pressure curves for components I and II given by ideal solution theory is illustrated in Fig. 4. The amounts of components I and II volatilized as the temperature increases from T1 to T2 are then assumed to be proportional to the areas BI and BII , respectively, as shown in Fig. 4, and the total amounts of components I and II
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Fig. 1B) for the sensor was secured with a rubber stopper. Then, the rubber stopper was placed on the open end of the test tube and sealed with teflon tape. Only a small quantity of test fuel (5 cm3 ) was used to prevent the sensor from being submerged in the fuel. 3.2. DI sensor measurement
Fig. 4. The partial pressure of components I and II at different temperatures.
volatilized during the measurement are assumed to be proportional to the areas AI and AII . The normalized fuel level L in the sensor at the temperature T2 is: BI BII CI − CII (3) L(T2 ) = 1 − AI AII In fact, Eq. (3) could be generalized for a hydrocarbon fuel containing n components: n Bi (4) Ci L(T2 ) = 1 − Ai i=1
Going back to the two component system, the measurement stops as the normalized fuel level drops below a predetermined residual level R to avoid overheating of the fuel [8,9]. We assume the boiling point for component II is much higher than that for I, and the fuel sample left in the sensor at the end of the measurement is predominated by component II. If the total amount of component II volatilized during the measurement is proportional to AII , then the amount of component II originally loaded in the sensor is proportional to AII multiplied by a residual factor CII /(CII − R). Eq. (4) is modified accordingly: BI BII CI − CII (5) L(T2 ) = 1 − AI AII R
After loading the sensor with the fuel sample by the capillary effect, the fuel level in the sensor was monitored as a function of time. If the vapor pressure of the test fuel was at saturation, the sensor remained full indefinitely. Before operating the sensor, the test tube was inverted so that the connection wires were below the sensor. This prevented fuel from dripping down the wires and back into the sensor (see Fig. 1). The heaters were then turned on to vaporize the fuel loaded in the sensor. Both the fuel level (capacitance) and the sensor temperature were measured once per second and recorded using a laptop computer. To avoid overheating, the measurement terminated if the normalized fuel level dropped below a predetermined residual level R. In this work, the R-value for all the test fuels was around 25%. The measurement was conducted inside an exhaust hood. The ambient temperature surrounding the test tube was adjusted either using an oven or a cooling system so that the measurements could be initiated at a temperature between 5 and 67 ◦ C. The details of the measurement procedures have been reported previously [9].
4. Results and discussion 4.1. Fuels with one component The model prediction was first compared with the DI sensor output measured with a simplified fuel containing only one component, i.e. heptane. The DI sensor was tested with an initial ambient temperature, which was varied from 5 to 49 ◦ C as shown in Fig. 5. It is seen in Fig. 5 that as the initial temperature of the measurement was changed from
where R is the residual factor and R = CII /(CII − R). Eq. (5) gives the fuel level at any temperature between T1 and T3 and predicts the volatilization curve.
3. Experimental 3.1. Test fuels Three fuels: neat-heptane, nonane, and a 1:1 mixture of heptane and nonane, were tested in this work to verify the model. The test was conducted inside a test tube, 40 cm3 in volume. For each measurement, about 5 cm3 of test fuel was poured into the test tube. The connection wires (see
Fig. 5. The volatilization curves of heptane measured by the DI sensor as compared to those calculated from the model.
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curves for nonane were then calculated using Eq. (2) and are shown in Fig. 6 for comparison. It is seen in Fig. 6 that the curves calculated from the model agree with those measured by the sensor. As the initial temperature increases from 8 to 67 ◦ C, the temperature at the end for the curves also shifts from 107.5 to 120 ◦ C, respectively. Again, the shift to higher temperature of the volatilization curves with increasing initial temperature is believed to be intrinsic to this DI sensor measurement. 4.2. Fuel with two components
Fig. 6. The volatilization curves of nonane measured by the DI sensor as compared to those calculated from the model.
5 to 49 ◦ C, the temperature at the end also shifted from 78 to 87 ◦ C, respectively. The volatilization curves for heptane were then calculated using Eq. (2) and are shown in Fig. 5 for comparison. It is seen in Fig. 5 that the curves calculated from the model indeed match those measured by the DI sensor. In addition, the model also predicts that as the initial temperature increases, the volatilization curves shift toward higher temperature. Therefore, it is believed that the shift of the volatilization curves with initial temperature is intrinsic to this DI sensor measurement. This shift would make the DI number estimated from the volatilization curve higher than its true value. Algorithms based on this model could thus be developed to account for measurement initiated at different temperatures. The model prediction was then compared with the DI sensor output measured with pure nonane (see Fig. 6). Since the boiling point for nonane (150.8 ◦ C) is higher than that for heptane (98.5 ◦ C), the ambient temperatures chosen to begin the measurements with nonane were also higher than for heptane, i.e. varying from 8 to 67 ◦ C. The volatilization
Subsequently, this model prediction was compared with the sensor output measured with a fuel containing two components, i.e. 1:1 mixture of heptane and nonane. The DI sensor was tested in this fuel with an ambient temperature, which was varied from 8 to 53 ◦ C. To simulate these curves with the model, two assumptions were made. Because the boiling point for nonane (150.8 ◦ C) is much higher than that for heptane (98.5 ◦ C), it was assumed that the fuel left in the sensor at the end of the measurement was predominantly nonane. In addition, it was assumed that heptane loaded in the sensor had completely volatilized at its boiling point. Since the boiling point for nonane is much higher than that for heptane, heptane should volatilize faster and the concentrations of these two components in the sensor continuously varied during the measurement. In the initial simulation using our model, however, it was tentatively assumed that these concentrations remained approximately constant. The volatilization curves for the fuel were calculated using Eq. (5). Since the concentrations of heptane and nonane actually varied during the measurement, the volatilization curves calculated with constant concentration did not match well with the measured ones, as expected. From our initial simulation, the concentrations of heptane and nonane in the sensor during the measurement could be
1.2
Level (Normalized)
1 0.8 Measured (Init. Temp. 8C)
0.6
Calculated (Init. Temp. 8C) Measured (Init. Temp. 22C) Calculated (Init. Temp. 22C)
0.4
Measured (Init. Temp. 35C) Calculated (Init. Temp. 35C) Measured (Init. Temp. 45C)
0.2
Calculated (Init. Temp. 45C) Measured (Init. Temp. 53C) Calculated (Init. Temp. 53C)
0 0
20
40
60
80
100
120
Temperature (C) Fig. 7. The volatilization curves of 1:1 mixture of heptane and nonane measured by the DI sensor as compared to those calculated from the model with the concentrations of heptane and nonane calculated from the first simulation.
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350 Init. Temp. 8C
Partial pressure (mm Hg)
300
Mass transfer control Init. Temp. 22C
250
Mass transfer control Init. Temp. 35C Mass transfer control
200
Init. Temp. 45C Mass transfer control
150
Init. Temp. 53C Mass transfer control
100 50 0 0
20
40
60
80
100
120
Temperature (C) Fig. 8. The partial pressure of heptane and the mass transfer control region during the DI sensor measurement.
estimated. These concentrations were then used to calculate the partial pressure of heptane and nonane with ideal solution theory as illustrated in Fig. 4. The volatilization curves for the fuel were then calculated again with the modified partial pressure and are shown in Fig. 7. Fig. 7 shows a good agreement between the calculated and the measured curves. In this simulation, it was also assumed that the volatilization of heptane entered the mass transfer control region toward the end of the measurement as shown by the dotted lines in Fig. 8. In fact, heptane in a two-component fuel does not volatilize as easily as in pure heptane, because the heptane molecules must transfer through the medium to reach the fuel–air interface to volatilize. As the mass transfer within the liquid becomes the rate-determining factor for the volatilization process, its rate approaches a constant and the increase of partial pressure with temperature is no longer the driving force.
temperature of sensor and fuel) increased, the volatilization curve shifted toward higher temperature. This shift would make the DI number estimated from the volatilization curve higher than its true value. Therefore, algorithms need to be developed to account for measurement initiated at different temperatures.
Acknowledgements The authors like to thank Ken Rahmoeller and Kapila Wadu-Mesthride for providing the fuel samples. The authors also thank Michel F. Sultan, Joe Mantese, and Lorenzo Rodriguez for their support and valuable suggestions in completing this work.
References 5. Conclusions A model is proposed to simulate the volatilization curves obtained from the DI sensor measurements conducted in a test tube using simplified hydrocarbon fuels containing one or two components. This model, verified experimentally, assumes that the saturated vapor pressure curve for the test fuel determines the shape of its volatilization curve measured from the DI sensor. During the measurement, the volatilization of the test fuel to saturate the vapor pressure in the system is the driving force in determining the fuel level in the DI sensor and drives its decline. The model also suggests that mass transfer within the liquid could be a rate-determining factor for the volatilization process with fuels containing more than one component. Therefore, this model could help us analyze vehicle test results obtained from an on-board DI sensor using commercial gasoline fuels. Furthermore, this model predicts that as the ambient temperature (or the initial
[1] Standard Test Method for Distillation of Petroleum Products at Atmospheric Pressure, Designation: D 86–00, American Society for Testing and Materials, West Conshohocken, PA. [2] Low- and Intermediate-Temperature Drivability Program using Gasoline–Alcohol Blends, CRC Report 568, Coordinating Research Council, 1990. [3] Effect of Volatility and Oxygenates on Drivability at Intermediate Ambient Temperatures, CRC Report 578, Coordinating Research Council, 1992. [4] B. Evans, S. Jorgensen, G. Nusser, K. Eng, M. McNally, C. Richardson, D. Whelan, E. Ziegel, New fuel volatility indices, Automotive Eng. (February 2000) 175. [5] R.H. Clarke, Portable Fuel Analyzer for the Diagnosis of Fuel-Related Problems On-Site at the Vehicle Service Bay, US Patent 5,569,922 (October 1996). [6] R.H. Clarke, Method and Devices for Fuel Characterization and Optimal Fuel Identification On-Site at a Fuel Delivery Dispenser, US Patent 5,750,995 (May 1998). [7] T. Takahashi, T. Kondo, H. Saitou, T. Okazaki, M. Ishikiriyama, Method and Apparatus for Determining Gasoline Characteristics by using Ultrasonic Wave, US Patent 6,032,516 (March 2000).
S.S. Wang et al. / Sensors and Actuators A 116 (2004) 277–283 [8] H.S. Lee, S.S. Wang, D.K. Lambert, C.R. Harrington, J. Lin, An on-vehicle DI sensor: initial results, IEEE Sens. J. Scheduled for publication in December, 2004. [9] Y.J. Lin, H.S. Lee, S.S. Wang, D.K. Lambert, Drivability Index Sensor Sensing Element and Signal Processing Circuit Design, US Patent 6,564,624 (May 2003). [10] D.K. Lambert, C.R. Harrington, R. Kerr, H.S. Lee, Y.J. Lin, D.Y. Wang, S.S. Wang, Fuel Drivability Index Sensor, SAE Paper, 2003-01-3238, 2003. [11] R.H. Perry, C.H. Chilton, Chemical Engineers’ Handbook, fifth ed., McGraw Hill Book Company, 1973 (Chapter 3).
Biographies Dr. Simon S. Wang received his MS and PhD degree in Chemical Engineering from the University of California at Los Angeles in 1977 and 1979, respectively. He is presently a Senior Staff Research Engineer at Delphi Research Labs. Dr. Wang has received 17 US patents and published 70 papers on: fuel cell, engine oil condition sensor and sensing algorithm, microsensors, fretting corrosion in electrical connectors, electrochemical etching of silicon, electrochemical phenomena in lubricants, sensor modeling, microelectronic fabrication technologies, battery, and novel surface
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coatings. His research interests include: fuel cell, microsensors, microelectronic fabrication, triboelectrochemistry, energy storage systems and surface science. Han-Sheng Lee received his PhD in Electrical Engineering from Princeton University in 1976. In the same year, he joined the GM Research Labs. He was transferred to Delphi Research Labs, Delphi Systems in 1999. His technical interests are in the general area of physics, technology and applications of sensors and semiconductor devices. David K. Lambert received the BA and PhD degrees in physics, both from the University of California at Berkeley. He is currently Senior Staff Research Scientist at Delphi Research Labs. He has also served as adjunct Professor in the Department of Physics and Astronomy at Michigan State University. His research interests include chemical sensors, and sensors that involve infrared spectroscopy or heat transfer. He has published over 40 papers and holds 17 US patents. Yingjie Lin has his Bachelor Degree in Engineering Mechanics from Tsinghua University; his Master Degree in Mechanical Engineering and Ph.D. in Electrical and Computer Engineering from The University of Texas at El Paso. He joined Delphi in 1997 and is Staff Research Engineer of Delphi Dynamics and Propulsion (D&P) Innovation Center. Currently, he responses for advanced sensor/actuator technology research and new product development.