US2721696A - Phase equilibrium computer - Google Patents

Description

Oct. 25, 1955 J. D. EISLER ET AL PHASE EQUILIBRIUM COMPUTER 2 Sheets-Sheet 1 Filed Aug. 20. 1952 m YRm mam 3 05V MWEW .D 2 H M w m ww p F L E&

Y B .I K m L .L A m N A m m E M 4 AIM T F N I Q L E Du R U C I l B R W M m ATTORNEY 25, 1955 J. D. EISLER ETAL PHASE EQUILIBRIUM COMPUTER 2 Sheets-Sheet 2 Filed Aug. 20. 1952 I8 lOO.n.

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Q\ lo lOO.n INVENTORS ELIHU H. COOLEY IZSOSEPH D. EISLER BY 1 & v I

mohuwhmo 152 AT TORNE Y U d States Patent k PHASE EQUILIBRIUM COMPUTER Joseph D. Eisler and Elihu H. Cooley, Tulsa, Okla., assignors to Stanolind Oil and Gas Company, Tulsa, Okla., a corporation of Delaware Application August 20, 1952, Serial No. 305,322

5 Claims. (Cl. 235-61) This invention relates to a special .type of electrical computer of particular application to problems involving phase-equilibrium data in chemical engineering computations.

In many aspects of the crude oil producing and refining industries, the physical behavior of petroleum fluids under various conditions of pressure and temperature is of great importance. The liquid-vapor phase relationships are of controlling interest in the design of fractionators, absorbers, surface separator systems, analysis of reservoir fluids with pressure decline, recovery problems, etc. j p

In fractionators and absorbers, the quantitative interactions of the gas and liquid phases are important as functions of the pressure variation throughout the columns, or as functions of the absolute pressure and temperature operating variables. In oil production operations, the nature and amount of gas developed in the reservoir with pressure decline depends on the basic liquid-vapor relationships. The bubble points and dew points of hydrocarbon fluids determine conditions of pressure and temperature at which the first bubble of vapor, or the first drop of liquid, will form, respectively. The amount of gas in solution per barrel of residual oil at 60 F. and one atmosphere, commonly known as the gas-oil ratio, is of importance in estimating the behavior of reservoir fluids as the reservoir pressure declines, and in material balance calculations. One of the best ways to follow the process of changing oil and gas compositions and amounts with reservoir pressure decline is by means of pressure-temperature diagrams of the fluids, or the so-called phase diagrams.

Surface-separator systems may be designed using proper mathematical relations expressing the liquid-vapor phase interactions. Optimum operating pressures and temperatures for maximum recovery of the desirable constituents can be computed, together with the stock tank losses.

The physical phenomena associated Withthe vaporliquid relationships can, in each instance, be evaluated by appropriate experimental methods which are both laborious and time-consuming. However, by ascribing to each individual component certain characteristics describing the vapor-liquid behavior, the phase properties of the composite mixtures can be mathematically expressed and computed.

The fundamental mathematical relationships involved in problems in phase-equilibrium data are given below:

x1t=mol fraction of any constituent in liquick=Orm;.';j,

r, 2,721,696 Patented Oct. 25, 1955 For material balance for any constituent,

Zn= Vyn-I-Lxn The equilibrium vaporization factor for any constit uent equals the ratio of ya to xn and its value at any given temperature and pressure is given in published tables. Thus,

in which Q is a factor convenient for use in the computer arrangement, as will appear below.

By substituting Equations 6 and 7 into Equation 5 and summing for n constituents,

n ZVx -V-Z Q .(8l From Equation 4 and Equation 7, l

V- Combining Equations 8 and 9,

1 z l +Q lmo 0) This equation is the basic computer equation. 7 p

In solving a given problem, the values of Zn and kn are introduced into the computer and a value of Q is found by electrical balance which satisfies Equation 10. Once the value of Q is determined, the value of V is obtained by another electrical balance based on Equation 9. The value of am for each individual constituent may be obtained by an electrical balance based on the individual terms of Equation 8. The value of L and the individual values of ya can be determined from Equations 4 and 6 respectively by calculation.

It will be shown that by use of the Equation 10, it is possible to set up a multiple bridge circuit which permits determining the unknown factors (usually am and V) in a given problem, in a time much less than that required for the previous tedious cut-and-try approximations now in use.

In order to illustrate the design and operation of the invention, certain figures are attached, which form apart of this specification. In these figures, the same reference numeral in different figures refers to the same or a corresponding part.

Figure '1 shows a circuit used to obtain a voltage proportional to the quantity to the sum lmo equal to the right side of Equation 8 or 10. Only part of the circuit is shown; that not shown consists of further units of the type given in Figure 1.

Figure 3 shows a circuit used to obtain a voltage pr'or portional to I 1 Q he lefts de f. quation. .10,

Figure 4 shows a circuit involving those of Figures 2 and 3 for solving Equation 10. As in Figure 2, only part of the circuit is shown, that not shown consisting of further units of the type given in Figure 2.

Figure' 5 shows the circuits of one complete computer arranged in accordance with this invention.

The choice of the. form of phase equilibrium relationship, as given above, permits the design of a suitable network of resistors which together with a null indicator forms the computer. For convenience of operation, each factor in the equation may be represented by a decade variable precision resistance. The resistances possess the necessary stability in order to achieve the required accuracy of the final solution.

In tracing the correspondence between the liquid-vapor system and the computer circuit, the portion of the circuit representing one term of the sum given by the right-hand part of Equation 10, is given in Figure 1. The two factors Zn and n are represented by a resistance and a current respectively, so that their product becomes a voltage. In the term the two variables in the denominator are represented by two variable resistors kn (12) and Q (13) connected in series. The current in this path is per volt applied to that path. A convenient resistance scale factor of 10,000 ohms may be chosen, for example, to represent unity in the equation. The factor Zn is introduced into this relationship by tapping a portion of the resistance representing Q. While the total value of Q remains unchanged, the tap 15 on the potential divider provides control for Zn. The resistance from the bottom of this potentiometer 16 up to the tap 15 is made proportional to. Zn, using the scale factor mentioned. Thus, the voltage era- 16 across Zn is proportional to the prodnot required by Equation 10. The right-hand part of Equation is a sum of terms representing all the constituents in a givensystem, and additional similar paths are set up in the computer, in parallel, to represent the other constituents. While the setting values of kn and Zn may be different in each of these branches, the value of Q is the same in all paths and the Q controls for all paths are mechanically. coupled to one set of control knobs, for example, by means of sprockets and chains. Thus, all Q resistors 13 are simultaneously changed at the same rate by the same amount.

To .obtain the sum of all constituents as given by the right-hand side of Equation 10, voltages from all the Zn taps are added electrically by employing substantially identical high resistances S (19) connected to a common mixer point 20. The voltage to ground at this common point 20 represents the entire right-hand side of Equation 10. The schematic connection of that portion of the equation is given in Figure 2. In this figure, resistances 17 and total potentiometer resistances 18 in series make up the Q resistors.

The requirements on the values of the high resistances S in order that the voltage 620-16 across the points 20 to 16 of Figure 2 shall be proportional to the sum that the value of the resistances be large compared with the total resistance connected in series with each such resistance, at least about 100 times and preferably 1,000

4 ments, vol. 19, No. 7, July 1946, pp. 396-7, or U. S. 2,557,070 Berry.)

It should be pointed out that it is immaterial whether the Q resistor or the kn resistor is tapped at the value proportional to Zn. In both cases, the voltage produced will be proportional to The bridge circuit is completed by providing a path corresponding to the left-hand portion of the equation; namely,

The circuit for this path is given in Figure 3. The denominator of the equation is represented by two resistors Q (13) and R (23) (R being equal to unity on the scale chosenin the example given, equal to 10,000 ohms). The- Q resistor 13 is mechanically coupled to the gang of resistances for the Q on the other side of the bridge. The current through this path per volt applied to the bridge is and the voltage across the unity portion R from 21 to 16 is thus equal to the current.

To achieve the equa sign in the Equation 10, the voltage,

must be reduced by an appropriate scale factor m. It is apparent that when point 22 is eventually connected to the. null balance detector 24 shown in Figures 4 and 5 and final balance is obtained by suitable manipulation of the Q resistors, the voltage drop e across points 20 to 16 is balanced by 2 across 22 to 16, and no current flows through point 20. At this point, the current flow due to the voltage across the Z1 resistance must return to ground through n 1 S resistances 19 in parallel. The voltage component e across 20-16 at this time due to that across Z1 is thus across avoltage divider of n-1 S resistors 19 inparallel, in series with one S resistor, so the voltage component across, 2016 is that across 21. Since this applied to all such components, the voltagee across 20-16 is thus log-H2 In this case, the appropriate scale factor In is numerically equal to n..

However, a further improvement can be made. This results from the fact that Q should desirably have values less than, 1, in fact down to about 0.01. This can be accomplishedby making the Zn resistances 13 proportionally less than would be indicated by the circuit of Figure 1. If, for example, the maximum value of Zn is 0.01 of the value -it-nominally should have, then Q can have a minimum-value of 0.01,,sincethe minimum value. of the Q resistances is the maximum value of a Zn potentiometer. In this case, the voltage n 2 k.+Q

and the appropriate scale factor m is numerically equal to n. Other values for the Zn Potentiometers obviously co uld"be-used;' the example. given-is merely illustrative.-

reference to Equation 8 When. m has been determined in the design, a tap 22 can be established on the resistor 23 at A null detector 24 (voltmeter, galvanometer, etc.) preferably with adjustable sensitivity is connected from point 20 to point 22. When by simultaneous manipulation of all the Q resistors the voltage across the null detector 24 becomes zero, e is equal to e, or

By reference to Equation 10.it is seen that this was the equation to be solved, and the true value for Q has been found. At any other value of Q, the null indicator 24 will show a voltage across it.

The problem is introduced into the computer by setting the proper value for the Zn potentiometers 18 and kn resistors 12 for all constituents. The problem is solved by varying the ganged Q resistances until the potential across the null indicator 24 is zero. The value of Q at balance may be head from dials on a panel (e. g., by adding the value 0.01, the minimum, to the dial reading of the decade Q resistors 17). Convenient ranges for the zn potentiometers 18 are four decades and for the kn resistors 12, seven decades. The values of kn are adjusted to literature values by setting the appropriate decades. The values for Zn (or proportional part, as discussed above) are similarly adjusted to the mol fraction of the feed for the particular constituent.

While the balancing of Q resistors represents the solution to a given problem, there are voltages at the various points in the circuit which yield additional required answers. The voltage across unity resistance 23 (R) on the right-hand side of the bridge corresponds to V in terms of the bridge voltage (see Figure 3); and the voltage across each Zn corresponds to Xn in terms of the V voltage. The values of V and xn are evaluated by balancing these voltages against calibrated potential divider circuits.

This is explained in more detail by reference to Figure 5. In Equation 9 the value V is shown to be 1 Q The voltage at point 25 for a constituent computer, that is, 11:10, is

e -0.001 E Since a null detector 24 is available, it is only necessary to employthis'detector and a suitable potentiometer circuit to measure V. This potentiometer circuit is made up of potentiometer 26 and series resistor 27, arranged of such values that the voltage across 26 is 0.001 B. By suitable manipulation of multipoint selector switch 28 to position 11 at the left, the-voltage on the tap of potentiometer 26 is applied in series opposition to that from point 25. By changing this tap on potentiometer, 26 (usually but not necessarily by making 26. a three or four decade potentiometer and adjusting the dials); until a null is obtained, and reading the potentiometer setting, the value of r or V, .is obtained.. 7 i The values-of thevarious xs can also be found. By.

'- Lye-re In Figure 5, it is or as explained earlier, some fixed fraction of this amount rl-Q The total voltage across each of the so-called xn potentiometers 29 is arranged to be that same fixed fraction of the voltage across the R resistor 23, which is 1+0 Thus, in the circuit of Figure 5, by using ohm potentiometers 29, the total potentiometer voltage is When the X11 potentiometers 29 are individually switched into the null detector circuit by switch 28, the variable voltage on the potentiometer 29 tap opposes the output voltage of the corresponding Zn resistor 18. By vary ingthe tap of potentiometer 29 (again usually but not necessarily by making eachsuch Xn potentiometer 29 a three or four decade arrangement, and adjusting the dials) until the null detector 24 shows no voltage, the am potentiometer 29 is set at the correct value, given by Equation 16. This value of xn can then be read off the dials of the potentiometer 29.

In one [typical computer designed for 10 constituents, the various resistors had the following values:

Value or Range Type 0.1 to 1,000,000 ohms 7 decades). same.

0. 1 to 100 ohms (4 decades).

same.

100.000 ohms.

10,000 ohms.

The voltage source E was approximately 200 volts, and the null detector was a four stage amplifier and meter with a 10 per cent full scale reading for a D. C. input of about five microvolts. With these components, it is conservatively estimated that the computer gave xn accurate to :0.05% of the total liquid and V accurate to $.05 of the total batch. Three representative problems are given below for which the precision of the answers given by the computer are compared to the calculated values.

211 (Com- 1 (Calcu- Constituent 2.. kn putel.) late 0404 2. 89 0145 0142 8263 1. 90 4306 4400 0533 98 0546 0545 0200 625 0320 0318 0060 458 0137 0138 0110 377 0285 0282 0062 282 0210 0210 0060 260 0221 0220 0062 0352- 0352 .0245 050 .3390 a sass 1 1.. (Com- In C8lCl1- Constituent zn kn puter) lated Ezn=1.0000 EIn=.9990

III

:1: (Com- :r (Calcu- Oonstituent zn kn gut) law Ezn=1.0000 Zen- 1.0000

The time required for the solution of these representative problems was about fiveminutes. About half of this time was taken up in setting the given data into the machine. This time is greatly decreased for the type of problems where a study is made on the behavior of the mixture for various temperatures and pressures. For such .a problem, the zn settings would not be changed and the solution is carriedout for successive settings of kn-values. It is apparent that this is very much less than the present cut-and-try methods, requiring about half an hour to an hour and a half for solution with an experienced computer.

Instead of using decade resistances, adjustable resistances can be employed, in which case, for example, a simple Wheatstone bridge can be set up using the same null detector, if desired, and one multidecade resistor, and set each kn and zn resistor by comparison, from this bridge. If desired, a servomechanism can be used to adjust these values. automatically. The Q values can be given by ganged multiple rotation variables resistors such as those sold-underthe trade name Helipots or the-like, and the Wheatstone bridge can be used for determining the ultimate, correct value'of Q.

It is to beespecially noted that the circuits in the computer are entirely potentiometric or bridge type in operation, and thataccordingly the value of the potential E of the voltage source does not affect the accuracy of the computer,- nor are ordinary variations in this valueof importance. It is also apparent that alternatingcurrent as well as direct current sources could be used, with suitable changes in the null detector, as are well-known in the art. Of course, in the A. C. case, it is necessary that the impedance of all similar elements, such as the S add resistors, must all be alike, so that the currents through each of the-series circuits in Figures 1, 2, and 3 are identical in phase. While this invention has beendescribed with reference to -certain specific embodiments, it will be readily apparent tothose skilledin the art that variations and-modifications may be made without departing from the teaching. given. The invention is best defined bythe scope ofthe appended claims.

wesclaim:

1. A computer'circuit including a .plurality n of adjustable resistors; rr-l-"l ganged variable"resistorysimultaneously variable at equal rates,.n potentiometers each individually adjustable,- each of said adjustable resistors being connected in series with one only of said ganged variable resistors and one only of said potentiometers, the remaining one of said variable resistors being connected in-series with a fixed potentiometer, a voltage source connected in parallel to the 11 series circuits each containing one of said adjustable resistors and also connected across said remaining variable resistance and said fixed potentiometer, n substantially equal fixed resistors each having a value large compared with the maximum values of said n potentiometers, and a voltage detector connected to the tap of said fixed potentiometer and to one end of each of said fixed resistors, the other ends of saidfixed'resistors being individually connected to the taps of each of said n potentiometers.

2. A computer circuit including a source of voltage, a plurality of circuits in parallel across said source, similar components of each of said circuits being substantially equal, said components consisting of an adjustable resistor, ,a variable resistor, and an adjustable potentiometer in series, a number equal to the number of saidcircuits of substantially equal fixed resistors eachindividually connectedto the. tap of one only of saidadjustable potentiometers at one end andconnected together at the other end, a separate circuit consisting of afixed potentiometer con-v nected in series with avariable resistor substantially equal tothe similar component in one. of said circuits, said separate circuit being connectedacross said source of voltage, a voltage detector connected to the common connection to all of saidsubstantially equal fixed resistors and to the tap ofv said fixed potentiometer, and means for simultaneously varying at .equal rates the magnitudes of all said variable resistors.

3. Anelectrical computer circuit for solving the equation where Q is initially unknown while zn and kn are n pairs of known quantities, comprising a source of voltage, a plurality n+1 substantially identical gangedvariable resistors, whereby their magnitudes maybe simultaneously varied at equal rates, a plurality n individually adjustable resistors the maximum:magnitude of which is approximately equalto thatof said variable.resistors,.a plurality n individually adjustable substantially equal potentiometers, each of said adjustable resistors being individually connected in series with one only of said variable resistors and one only of said potentiometers across said'source of voltage, means for adjusting the resistance of each of said adjustable resistors directly proportional to each one of said quantities kn, means for adjusting the setting of said n potentiometers directly proportional to the value zn corresponding in subscript to thevalue kn forwhich the adjustable resistor connected to eachsaid potentiometer was adjusted, a fixed resistor connected in series with the remaining variable. resistor, said fixed resistor having its resistance proportional to the value unity by the same factor as the resistance of the adjustable resistors bears to the values in' series with said fixed resistor andsaid remaining variable resistor across said source of voltage kn, anadditional potentiometer connected in series with said fixed resistor for producinga voltage across said additional potentiometer in a ratio to the total voltage across said fixed resistor as times the ratio of the setting of any of said adjustable potentiometers to the corresponding value zn, a plurality n of substantially identicalfixed resistors large-in magnitude compared with the maximum value of'any'ofsaid n potentiometers, one end of said fixed resistors being individually connected: to. the tap-on one at said n PO? tentiometers, and an electrical null detector Connected in series opposition between the other ends of all said fixed resistors and to the tap of said additional potentiometer, said additional potentiometer, fixed resistor, and one of said identical ganged variable resistors being connected in series across said source of voltage whereby simultaneous variation of said variable resistors until said null detector reads zero produces a resistance in each of said variable resistors directly proportional to the value Q satisfying said equation.

4. Apparatus in accordance with claim 3 including a variable potentiometer and multiple pole switching means for applying across said variable potentiometer a voltage proportional to put of one of said n potentiometers While simultaneously disconnecting said detector from said n fixed resistors and from said resistance means, whereby the voltage output of said one of said n potentiometers can be determined relative to said voltage proportional to 5. Apparatus in accordance with claim 4 including potentiometric means for measuring said voltage proportional to References Cited in the file of this patent

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