A. K. Coker
Davy Energy & Environmental Ltd.
Cleveland, U.K.
Equilibrium flash calculations can be computed quickly by an interactive Fortran program developed for personal computers. The program determines the equilibrium separation of a stream for multicomponent mixtures in oil, gas, and chemical processes, resulting in a liquid-vapor equilibrium mixture.
Results are obtained much faster than with previously published programs. 1-4
Flash vaporization calculations involving multicomponent mixtures are essential to the design and successful operation of many processes. These calculations are often required to determine the condition of the feed to a fractionation column or to determine the flow of vapor from a reboiler or condenser.
Flash calculations often involve trial-and-error solutions which are time consuming, tedious, and subject to error if performed manually. Previous calculation procedures involved the use of programmable calculators which, with the growing use of personal computers, are becoming obsolete.
Multicomponent flash (isothermal and adiabatic) computations are incorporated as part of overall process simulation and equipment design. However, single-stage flash fractionation processes are also employed to obtain a separation of the light components in a feed and as a preliminary step before a multicomponent fractionation column, such as crude distillation.
Table 1 lists ways of producing two-phase mixtures from a single phase at appropriate conditions. The last process in the table typifies the well-head separation that takes place in an oil field. It is termed a flash process because vapor forms as a result of rapidly dropping the pressure.
FUNDAMENTALS
To carry out an appropriate flash calculation, the pressure, P, and the temperature, T, must be known. If the values of P and T in the separating vessel are fixed, the value of P must not be so high that two phases cannot exist at any value of T.
Nor must T lie outside of the bubble point and dew point range corresponding to P. For a valid two-phase equilibrium calculation, the following relationship must be satisfied:
Tbp < Ts < Tdp
where: Tbp is the bubble point temperature, Ts is the specified temperature, and Tdp is the dew point temperature.
The existence of a valid two-phase flash can be verified with the design equations for the bubble point, dew point, and equilibrium data calculated at the specified pressure and temperature.
The design equations for the bubble and dew points are:
Bubble point:
[SEE FORMULAS 1 AND 2]
Table 2 illustrates the phase condition using the liquid-vapor data associated with the specified pressure and temperature.
From Table 2, the condition for a valid two-phase equilibrium flash is (see box for nomenclature):
[SEE FORMULAS 3 AND 4]
Feed analyses in terms of component concentrations are normally not available for complex hydrocarbon mixtures with a final boiling point more than about 38 C. (e.g., n-pentane) unless such a feed is broken down into pseudo components (narrow boiling fractions). This enables the mole fraction and equilibrium constant, K, to be estimated and, consequently, flash calculation of the mixture can be carried out.5 A continuous equilibrium flash fractionation process is shown in Fig. 1.
Efficient techniques for the solution of the trial-and-error calculations necessary in multicomponent flash computations are given by Smith, Hengstebeck, King, and Oliver.6-9 However, the iterative convergence method first suggested by Oliver, and later modified by Kostecke, is employed in the program.1 2
FLASH CALCULATION EQUATIONS
The equations used in the program for multicomponent equilibrium flash calculations are:
[SEE FORMULAS 5, 6 AND 7]
where: R = the liquid-vapor (LN) ratio.
The new LN ratio for each iterative calculation, R', is determined from:
R' - [FR - E(R + 1)]/[F + E(R + 1)] (8)
where the constants E and F are determined from:
[SEE FORMULAS 9 AND 10]
The computation then determines whether E < 0.001. If E is not less than 0.001, R is set equal to R' and the calculations of Equations 7, 8, 9, and 10 are repeated until E < 0.001.
Once E < 0.001, the calculation proceeds to Equations 11 and 12:
Li = MiR/(Ki + R) (11)
= Mi - Li (12)
The mole fractions of components in the feed and the liquid and vapor phases are evaluated as follows:
[SEE FORMULAS 13, 14, 15, AND 16]
THE PROGRAM
The Fortran program developed for the flash calculations is named FLASH and can be run on IBM or IBM compatible personal computers with the MS DOS operating system. The program is based on the vapor-liquid equilibrium relationships given in handbooks available from the Gas Processors Suppliers Association, Tulsa, and other literature.
The program will handle flash calculations with feed streams containing up to 15 components. As an added feature, the calculation will check the feed composition at flash conditions for dew point and bubble point (i.e., whether the feed is either all vapor or all liquid).
These checks are performed before the flash calculations are started. If the feed is above the dew point or below the bubble point, an appropriate message is displayed on the screen. A default value for R (L/V ratio) 1 is incorporated in the program to start the iterative process. Report-quality outputs are generated by the program, and the program can be operated either from a floppy diskette or it can be loaded onto a hard disk.
To operate the program, simply log onto the appropriate drive and type "FLASH.EXE" or "FLASH". If printed results are required, simply press the PrtSc key on the keyboard.
The program is not applicable to an adiabatic flash process when the feed stream is at a higher pressure than the flash pressure, and the heat for vaporization is provided by the enthalpy of the feed. In this situation, the flash temperature will be unknown and must be obtained by trial and error.
A temperature must be found at which both the material and energy balances are satisfied.
EXAMPLES
Four examples demonstrate the use of the program and the results computed by it.
The first example is a 9-component still product accumulator stream that is compressed to 370 psia and cooled to 90 F.4 The program is used to determine the amount of liquid and vapor produced at these conditions. Feed stream data and the program's results are shown in Table 3.
The second example flashes a feed stream to a natural gas liquefaction plant. The feed is flashed at 600 psia and 20 F.3 The program determines the flow rates of the liquid and vapor streams at a feed flowrate of 1,000 moles/hr.
Feed stream data and the program's results are shown in Table 4.
A 12-component mixture is flashed at 860 psia and -65 F. for the third example.1 Feed stream data and results are shown in Table 5.
Finally, the fourth example determines the equilibrium separation of a 5-component mixture at equilibrium conditions of 100 psia and 160 F.10 Table 6 gives the feed stream data and results.
Editor's note: OGJ subscribers may obtain a free copy of the complete operating program on diskette by sending a blank, 5 1/4 in. floppy diskette, formatted to MS DOS, and a self-addressed, postage-paid or stamped return diskette mailer to: Refining/Petrochemical Editor, Oil & Gas Journal, P.O. Box 1941, Houston, TX, U.S.A., 77251.
Subscribers outside of the U.S. send the diskette and return mailer without return postage to the same address. This offer will expire Mar. 31, 1991.
ACKNOWLEDGMENT
The author thanks Dr. C. J. Mumford, senior lecturer, Aston University, U.K., for the review of this work, and the management of H&G Engineering, Glasgow, U.K., for permission to publish this article.
REFERENCES
- Oliver, I.H., "Hand calculator program speeds flash calculations," OGJ, Mar. 31, 1980, p. 130.
- Kostecke, S.T., "Speed of hand calculator programs can be improved," OGJ, Aug. 11, 1980, p. 107.
- Mansouri, S.. "Flash Computations," Chemical Engineering, Aug. 27, 1979.
- Blackwell, W.W., Chemical Process Design on a Programmable Calculator, McGraw Hill Inc., New York, 1984.
- Perry, R.H., and Green, D., Chemical Engineers' Handbook, McGraw Hill Inc., New York, 1984.
- Smith, B.D., Design of Equilibrium Stage Processes, McGraw Hill Inc., New York, 1963.
- Hengstebeck, R.J. Distillation: Principles and Design Procedures, Reinhold Publishing Co., 1961.
- King, C.J., Separation Processes, McGraw Hill Inc., New York, 1971.
- Oliver, E.D., Diffusional Separation Processes, John Wiley & Sons, 1966.
- Schweitzer, P.A., Handbook of Separation Techniques for Chemical Engineers, McGraw Hill Inc., New York, 2nd Edition, 1988.
Copyright 1991 Oil & Gas Journal. All Rights Reserved.
