1. VESSEL DECOMPRESSION MODEL Prepared by Catalina Alupoaei December 9, 2001

2. INTRODUCTION TO VACUUM TECHNOLOGY Some of the applications: 1.An early application of vacuum technology came around 1900 when the first major industrial use was for light bulbs and TV tube production (later on). 2.The second major application is in the electronic industry. Many processes that occur in a semiconductor fabrication facility require vacuums of different levels, including the deposition of thin films of material on computer chips. 3.Another major application is in space technology. The main issue in space technology is how to design the space station or shuttle in order to maintain a pressurized cabin. Also, it is important to design safe space-suits to protect astronauts during their missions in open space. The vacuum environment plays a basic and indispensable role in present day technology It has an extensive range of applications in industrial production, and in research and development laboratories, where it is used by engineers, scientists and technologists for a variety of purposes.

3. EXPERIMENTAL PROTOCOL  The experiments were conducted at HCC’s Vacuum Technology Laboratory to develop a model for a vacuum system  The system used for conducting the experiments consists of a chamber with a single vacuum pump connected to it. The pump removes the gas from the chamber as function of time  The vacuum station allow to automatically monitor the drop in the vacuum chamber pressure as function of time. In addition, the station has a mass flow controller that precisely meters gas into the chamber at various desired mass flow rates  Experiments were conducted at different percentage of mass flow (between 10- 100%)

4. MATHEMATICAL MODEL S = pumping speed V = volume of gas removed t = time p = pressure at the inlet Q = throughput Assumptions:  constant pumping speed, S  no additional gas load to that in volume V, at ant time Q = pS  the process is isothermal  Is based on on the ideal gas law

5. MATHEMATICAL MODEL For initial condition:  t = 0  p = po A program has been written in Matlab for fitting the exponential function for pressure (P/Po) as function of time. Results the measured vacuum chamber pressure change as function of time is given by:

6. Measured vacuum pressure versus time (at different % mass flow)

7. DATA PROCESSING  The region selected for the fitting : From time corresponding to P maximum to time = 30 seconds  The selected region of data for each experiment was shifted to the origin, so the time corresponding to the P maximum is now considered time zero  The pressure data were normalized (P/Po)  The estimation of the time constant (S/V) was accomplished solving the corresponding linear least square problem  The measured and calculated data for the selected range have been plotted together for each experiment

8. Comparison between measured and calculated vacuum chamber pressure versus time 10% mass flow rate 100% mass flow rate

9. Estimates for the time constant (S/V) and for the standard deviations

10. The pump time constant (S/V) versus different percentage of mass flow rate together with ± 2 standard deviations

11. The pump-down time The time required to pump-down a vacuum system from atmospheric pressure to a specified pressure is called the time of evacuation or pump-down time The pump-down time Tf estimated from the model as 99% of the pressure drop corresponds to,

12. Pumping speed versus pump-down time for various volumes [3]

13. The pump-down estimates from the model  could be used with Figure above to obtain the volume or the speed to specify a pump

14. CONCLUSIONS  There is a significant variability in the experimental data relative to the time interval required to reach the maximum pressure and in the order of the experiments relative to the percent of mass flow rate  The parameter values reported in Table above also reflect this variability  Nevertheless, the estimates of the variance of the model lack of fit (calculated from the residual sum of squares) suggest that the parameters are statistically different  The model gives an adequate representation of the trend of the pressure versus time data, but is clearly not complete  The data appears to have an exponential decay, followed by a plateau (probably the rate of mass flow decreases), continued by a second exponential decay  This behavior could be explained on the basis of temperature. Initially the system is isothermal, as the gas is extracted, the temperature drops, reducing the pressure and the mass flow, as the temperature equilibrates, the rate of mass flow increases again. Temperature data would be very helpful to improve the reproducibility and the control of the system.

15. REFERENCES 1.Rajka Krstic, Jennifer Trelewicz and Veena Mahesh, Introduction to Vacuum Technology 2.Chambers, A., Basic vacuum technology, 1998 3.Andrew Guthrie, Vacuum Technology, Alameda State College, California, John Wiley and Sons, Inc. 1965 4.L. Holland, W. Steckelmacher and J. Yarwood, Vacuum Manual, E. & F. N. Spon London, 1974

16. NOTE The document in Word provides the program that has been written in Matlab for fitting the exponential function for pressure (P/Po) as function of time omparison between measured and calculated vacuum chamber pressure versus time for the different range of mass flow rate Also, it provides all the figures with the comparison between measured and calculated vacuum chamber pressure versus time for the different range of mass flow rate