Ind. Eng. Chem. Res. 1989,28, 371-375 Murray, J. D. Initial Motion of a Bubble in a Fluidized Bed: Part 1. Theory. J . Fluid Mech. 1967,28, 417-428. Partridge, B. A.; Lyall, E. Initial Motion of a Bubble in a Fluidized Bed: Part 1. Experiment. J . Fluid Mech. 1967, 28, 429-431. Pritchett, J. W.; Blake, T. R.; Garg, S. K. A Numerical Model of Gas Fluidized Beds. AIChE S y m p . Ser. 1978, 74(176), 134-148. Ransom, V. H. Hyperbolic Two-Pressure Models for Two-Phase Flow. J . Comput. Phys. 1984,53, 124-151. Rivard, W. C.; Torrey, M. D. K-FIX: A Computer Program for Transient, Two Dimensional Two Fluid Flow. LA-NUREG-6623, Los Alamos, 1977. Roache, P. J. A New Direct Method for the Discreted Poisson Equation. In Proceedings of the Second International Conference on Numerical Methods in Fluid Dynamics; Springer-Verlag: New York, 1971; pp 48-53. Sod, G. A. Numerical Methods i n Fluid Dynamics: Initial and Boundary Value Problems; Cambridge University Press: New York, 1985.
371
Stewart, H. B. Stability of Two-Phase Flow Calculation Using Two-Fluid Models. J. Comput. Phys. 1979, 33, 259-270. Stewart, H. B.; Wendroff, B. Two-Phase Flow: Models and Methods. J. Comput. Phys. 1984,56,363-409. Von Neumann, J.; Richtmyer, R. D. A Method for the Numerical Calculation of Hydrodynamic Shocks. J. Appl. Phys. 1950,21, 232-237. Wallis, G. B. One-Dimensional Two-Phase Flow; McGraw-Hill: New York, 1969. Wang, Y. Numerical Modeling of the Hydrodynamics of Gas Fluidized Beds. Ph.D. Dissertation, Oregon State University, Corvallis, 1987. Wylie, R. C. Advanced Engineering Mathematics, 4th ed.; McGraw-Hill: New York, 1975. Received for review February 22, 1988 Revised manuscript received September 13, 1988 Accepted October 3, 1988
COMMUNICATIONS Detection of High-pressure Dew and Bubble Points Using a Microwave Technique An apparatus for automatic experimental determination of dew and bubble points of oils and gases under reservoir conditions, 50-500 bar and 50-200 "C, is described. A 10-mL stainless steel equilibrium cell is part of an X-band (8-12-GHz) microwave circuit. Formation of new phases in a sample confined within the cell creates characteristic changes in the dielectric properties of the sample and thereby in the quality factor of the microwave circuit. This allows the detection of dew and bubble points. A binary mixture of ethane and n-octane is used t o test the performance of the apparatus. The natural gas and petroleum industries increasingly demand accurate high-pressure phase equilibrium data of petroleum fluids, i.e., multicomponent hydrocarbon mixtures. The data are needed for effective reservoir management and enhanced recovery techniques, and they comprise among others the saturation properties (dew and bubble points) of the petroleum fluids at reservoir conditions, 50-500 bar and 50-200 "C. Saturation pressures of petroleum fluids at reservoir conditions are usually determined at constant temperature in high-pressure steel vessels (equilibrium cells) with windows. The sample volume/pressure is varied by injection or removal of mercury, and the saturation point is observed visually as the formation or the disappearance of a phase. Bubble points can sometimes be detected as a break point in a pressure versus volume curve. The relatively large sample volumes (200-2000 mL) that are used in such cells make the establishment of equilibrium time excessive after a temperature or pressure change, and the visual detection technique is in itself operator dependent and difficult to automate. The apparatus described in this paper permits determination of phase boundaries from measurements of sample interaction with microwave energy and is based on the principles described by Rogers et al. (1985). The size of the equilibrium cell is -10 mL, and the apparatus is completely automated. The sample is made part of a microwave circuit that is sensitive to changes in the dielectric properties of the sample. The microwave properties of the sample are in this way monitored while the
pressure is reduced along an isotherm, beginning with a single-phase sample. Upon reaching a phase boundary, the dielectric properties of the sample change because the sample is no longer a homogeneous dielectric and the interfaces between the phases introduce reflections that were not present in the single-phase sample. This produces a shift in the response of the microwave circuit that is indicative of a phase boundary.
Apparatus The apparatus was designed to measure high-pressure dew and bubble points in the temperature range 50-200 " C and in the pressure range 50-500 bar. A block diagram of the apparatus is shown in Figure 1. The microwave/ sample interface is located in the phase detector, which consists of a high-pressure equilibrium sample cell and a microwave resonance cavity. The phase detector is mounted in a thermostated air bath together with a magnetically activated circulation pump. An external servocontrolled volume is used to vary the pressure of the sample. The sample is loaded into the thermostated phase detector and brought to a pressure that is high enough to assure that the sample is in a single-phase region at a given temperature. The sample is mixed simultaneously by the mixing pump to produce a homogeneous sample. During an experiment, the sample pressure is reduced slowly along an isotherm by increasing the servocontrolled volume until a dew or bubble point is determined. The microwave resonance cavity is connected to a microwave source and
0888-5885/89/2628-0371~~1.50/00 1989 American Chemical Society
372 Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989
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a high electrical conductivity as required for an end wall of the microwave resonance cavity. The microwave resonance cavity is a standard X-band TEoll resonance cavity with an adjustable resonant frequency. The resonant frequency is adjusted by means of a plunger micrometer arrangement. The static seal between the sapphire disk and the sample volume is made by a VITQN 0 ring, and the sample volume is accessible through three high-pressure connection ports. Two ports are diametrically opposite each other in the sapphire disk end of the sample volume, and the third port is located a t the bottom.
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a diode detector to form an X-band (8-12-GHz) microwave circuit that is sensitive to dielectric changes of the sample in the equilibrium cell. The detectable dielectric properties of the sample change abruptly a t a dew or bubble point. Temperatures are measured with PtlWresistance thermometers and pressures with strain gauge type pressure transducers. Data acquisition and apparatus control are provided by a control computer.
Phase Detector The high-pressure equilibrium cell was designed for use with noncorrosive hydrocarbon mixtures without significant amounts of H,S. Figure 2 is an assembly drawing of the phase detector. The cell was manufactured from a cylindrical piece of stainless steel (SS 316, diameter 64 mm, length 70 mm) in which a blind hole (diameter 20 mm, length 50 mm) is the sample volume. The open end of the sample volume is covered by a sapphire disk (diameter 25 mm, thickness 5 mm), which is supported by a BERYLCO 25 plate (Cu-Be alloy, diameter 64 mm, thickness 10 mm) held in place by six bolts penetrating through the cell body. Sapphire is almost transparent to microwave energy, and disk shapes can withstand high pressures with proper support. A slit (1 mm X 16 mm) in the support plate allows energy from the microwave resonance cavity to be transmitted through the support plate and the sapphire disk and into the sample cell. BERYLCO 25 was used for the support plate, because it is strong and ductile and has
Microwave Circuit The X-band (8-12-GHz) microwave circuit consists of a microwave source, a Schottky diode detector, and the microwave resonance cavity. A microwave circulator and transmission lines (coaxial cables or TEolmode rectangular waveguides) used to connect these items in a circuit are shown in Figure 3. The circulator acts as a microwave roundabout that allows transmission of microwave power in only one direction, as indicated by the arrows in Figure 3. If we denote the connection ports as 1, 2, and 3, microwave power admitted to port l will be transmitted to port 2 almost without losses, but it is blocked from port 3. Similar relations hold for ports 2 and 3. The microwave source is a power-leveled, high-stability (better than 100-Hz) sweepable microwave source. It covers the frequency range 5.9-12.4 GHz (vacuum wavelengths 2.4-5.1 cm). The power available at the microwave source output is approximately 1 mW. The microwave power is measured with a Schottky diode, which is a fast-responding detector that is suitable for relative measurements. The microwave resonance cavity, which is part of the phase detector, is a standard X-band TEoll resonance cavity. It is a cylinder manufactured from a high electrical conducting material and fitted with a movable plunger at one end and the support plate of the phase detector at the other end. Microwave energy is admitted to the cavity through a rectangular TEol mode X-band waveguide and a hole in the cylinder wall. Microwave energy is admitted to the resonance cavity only for plunger positions corresponding to resonance frequencies. At this frequency, a standing wave is supported in the resonance cavity, and most of the energy admitted to the resonance cavity will be stored in it. The slit in the support plate permits microwave energy to interact with the sample in the sample volume of the phase detector. This coupling between the resonating microwave field in the resonance cavity and the sample in the sample volume is the basis for the detection of dew and bubble points by means of the dielectric changes of the sample that accompany the formation of a dew or bubble point.
Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989 373 l R e f l e c t e d power
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Microwave Circuit Properties The microwave circuit transmits microwave energy from the microwave source through the circulator to the microwave resonance cavity. Microwave power reflected from the resonance cavity is transmitted back through the circulator to the Schottky diode detector, where the reflected power is detected. Figure 4 shows the amount of reflected power from the resonance cavity (empty sample volume) as a function of the microwave source frequency for a fixed plunger position of the resonance cavity. The position of the resonance peak is related to the plunger position. Pushing the plunger further into the resonance cavity, Le., reducing the resonance volume, will move the resonance peak toward higher frequencies and vice versa. The position and shape of the resonance peak are of major interest, because it is within the frequency range covered by the resonance peak that microwave energy is stored in the resonance cavity and can interact with the sample. Upon formation of a phase boundary, there is a shift in the dielectric properties of the sample, because the sample is no longer a homogeneous dielectric and the interfaces between the two phases introduce reflections that were not present in the single-phase sample. These reflections are the result of the difference in dielectric constant (€) of the two phases (evapor 1and €liquid -2-3 for hydrocarbons). This alters the shape and location of the resonance pattern in Figure 4. The resonance peak can be characterized by four parameters indicated in Figure 4 and described as follows: Fc/MHz, the resonant frequency, i.e., the frequency corresponding to the minimum amount of reflected power; H/mW, the peak height, i.e., the difference between the reflected power at the base line (6 MHz below F,) and the reflected power a t resonance; F] and Fh/MHz, lower and upper half power frequencies, i.e., the frequencies below and above F, where the reflected power is the mean of the base line and the resonance levels, respectively. Another useful parameter to characterize the microwave resonance peak is the quality factor (8)defined by
-
Q = Fc/@ where hF = Fh - F,. The quality factor is a measure of the sharpness of the resonance peak, and it represents the inverse of the energy dissipation of the resonance cavity, i.e., represents the loss through the coupling slit and Joule losses in the cavity walls (Sucher and Fox, 1963; Fogh, 1988a). The quality factor is convenient for expressing the relative changes in the energy dissipation of the sample. Since formation of a second phase will always change the energy dissipation of the sample, it is possible to detect phase transitions.
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The coupling between the microwave resonance cavity and the sample volume is almost negligible, because the wavelength of the microwaves (2.5-4 cm) is large compared to the slit size (16 X 1mm) and thickness of the support plate (10 mm). The slit coupling is enhanced by reducing the effective wavelength of the microwaves in the coupling slit by partially filling the coupling slit with a high dielectric constant ceramic material (see Figure 2). The coupling is also a strong function of the resonance frequency, and it can be evaluated through the quality factor (Q)of the microwave circuit. A decrease in Q corresponds to an increased energy dissipation, which in turn represents an increased coupling. The coupling can be evaluated by measuring the quality factor ( Q ) as a function of the resonance frequency (F,) with and without the coupling slit. A reference experiment is conducted with a metal (electrical conducting) disk in place of the sapphire disk in the phase detector. Figure 5 shows a typical result with an effective sample coupling in the frequency range 9100-9500 mHZ. The periodic variation is caused by a misalignment in the micrometer positioned plunger. The coupling range and minimum in Q is sample dependent, and an appropriate resonance frequency (F,) for use during a dew or bubble point experiment is found by recording the Fc-Q curve similar to the one shown in Figure 5 with a single-phase sample in the sample cell.
Control and Data Retrieval System The apparatus has an extensive control and data retrieval system, which is needed to make the microwave measurements and is used to automate the experiments and to retrieve and store data. The control and data retrieval system hardware is schematically presented in Figure 6. Communications with the data retrieval hardware are made through the HP-IB (IEEE 488) instrument bus. The
374 Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989
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instruments on the bus are divided into three groups. The first group consists of the sweep oscillator and the synthesizer, which are part of the microwave source. The second group consists of the relay box and the digital voltmeter and is the process input to the control and data retrieval system. The relay box switches various signals to the digital voltmeter, which in turn measures the signals and makes them available for the control computer. The third group consists of the ordinary data presentation units, the printer and plotter, and the devices for data and program storage. A general purpose digital input-output interface (GPIO) is used to control the servovolume, and a serial line is used to transmit data to a remote computer for detailed analysis. Further details about the control and data retrieval system, the specific instruments, and the layout of the microwave source are given elsewhere (Fogh, 1988a,b).
Experimental Procedure The sample is loaded to the thermostated phase detector and brought to a pressure that is high enough to assure that the sample is in a single-phase state at the desired temperature. The sample is simultaneously mixed by means of the magnetic mixing pump to facilitate equilibration, The microwave parameters are then monitored as a function of the pressure, which is slowly reduced by means of the external servocontrolled volume until a dew or bubble point is determined. The entire experiment is controlled by a program named MCCP (Microwave Circuit Control Program), which is represented by a simple flow diagram in Figure 7. The rate of pressure/volume change is controlled within the program cycle. The monitored microwave parameters are, with reference to Figure 4,the resonance frequency ( F J , the lower and upper half power frequencies (Fl and Fh), and the peak height ( H ) . These values are measured every 30 s together with temperatures and pressures and are stored for later analysis. The data analysis is performed on a remote computer with extensive data handling and data representation capabilities. The apparatus can therefore be
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used immediately for another experiment and allows standard software to be applied for data handling and data representation.
Experimental Results The performance of the microwave apparatus was tested extensively in an experimental program, which established the feasibility of the microwave detection technique as it is implemented in the apparatus. Also deficiencies and limitations in the setup were discovered, and procedures for the optimal choice of experimental parameters were developed. A detailed description of the experiments and results is given elsewhere (Fogh, 1988a), whereas only results from a binary mixture of ethane (C,) and n-octane (nC,) are given here to illustrate the performance of the apparatus and the feasibility of the microwave detection technique. A binary mixture of C2and nC8 with 0.922 mole fraction C2 was used because the calculated critical point of this mixture (91.3 "C and 86.4 bar (Fogh, 1988a; Michelsen, 1980)) lies within the temperature range of the apparatus, thus permitting dew and bubble point determinations by simply changing the temperature. Figure 8 shows the pressure ( P )and quality factor (Q) traces (versus time) for a bubble point experiment at 59.5 "C, where a resonance frequency of 9270 MHz was used. The quality factor (Q) trace shows a bubble point at approximately 90 min of a scan a t constant rate of volume change. There is a steady drift in the quality factor (Q) above and below the bubble point, but the phase transition point is marked by a large shift in the quality factor (8). The bubble point determination can in this case be cross-checked by means of the pressure (PI trace, where the bubble point as determined from the break point in the pressure curve occurs at the same time as the shift in the quality factor. The saturation points are normally found directly from the Q-P cross plots that eliminate the time. Figure 9 shows the Q-P cross plot that corresponds to the P and Q traces shown in Figure 8. The bubble point
Ind. Eng. Chem. Res., Vol. 28, No. 3, 1989 375 l0500$
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Conclusions An apparatus using microwave energy for the detection of phase transitions in high-pressure (50-500-bar) petroleum mixtures has been described. It has enabled a considerable reduction of the sample volume compared to conventional methods, and a high degree of automation has been incorporated. The performance of the microwave detection technique is illustrated by results from experiments with a binary mixture of 0.922 mole fraction ethane (C,)in n-octane (C,)that exhibits dew and bubble points in the temperature range 50-200 “C. Acknowledgment
Figure 9. Pressure (P)and quality factor (Q)cross plot from a bubble point experiment with a C2-nC8 binary mixture at 59.5 “C. 100
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The authors are grateful for the generous financial support provided by “Energiministeriet” (The Danish Ministry of Energy) through “aktstykke 118”and “EFP85”. The authors also acknowledge the careful and expert work of our workshop, especially P. K. Nielsen, in the construction of many parts of the apparatus. Finally the collaboration with W. J. Rogers from Texas A&M University has been of invaluable importance in the design of the apparatus, as have many fruitful discussions with our colleagues a t Instituttet for Kemiteknik, particularly Professor Aa. Fredenslund and at the Norwegian Oil Company, STATOIL. Registry No. C z , 74-84-0; n-Cs, 111-65-9.
Literature Cited
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at -66 bar is easily detectable from the break point in the quality factor (8)curve. The results from the bubble and dew point experiments with the 0.922 mole fraction C2 in nC8 mixture are shown in Figure 10 together with the calculated phase envelope. The calculations were made with the TERM (Michelsen, 1980) program using the SRK equation of state option with standard binary interaction parameters. There is a reasonable agreement between the calculated and measured saturation points, although the measured dew points all lie within the calculated phase envelope.
Fogh, F. Experimental Determination of High Pressure Dew and Bubble Points Using a Microwave Technique. Ph.D. Thesis, Instituttet for Kemiteknik, Lyngby, 1988a. Fogh, F. Computer Listings for the Microwave Apparatus Programs. Instituttet for Kemiteknik, Lyngby, 1988b. Michelsen, M. L. (TERM program MAN 8108 based on) Calculation of Phase Envelopes and Critical Points for Multicomponent Mixtures. Fluid Phase Equilibr. 1980, 4,1-10. Rogers, W. J.; Holste, J. C.; Eubank, P. T.; Hall, K. R. Microwave Apparatus for Phase Transition Studies of Corrosive Fluids to 1.7 kbar and 588 K. Rev. Sci. Znstrum. 1985, %(lo), 1907-1912. Sucher, M.; Fox, J. Handbook of Microwave Measurements, 3rd ed.; Wiley: New York and London, 1963; Vol. 11.
Folmer Fogh, Peter Rasmussen* Instituttet for Kemiteknik Technical University o f Denmark DK-2800 Lyngby, Denmark Received for review April 26, 1988 Accepted December 20, 1988
