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AN INVESTIGATION CF TiE USZ.A§D DE?ELCPBTVT CF AN
ELECTROfiiC CALCULATOR FOR DISTILLATION
CALCULATIGHS CF EULTL~CCKPCRFXT
SYSTEMS

by

HFfiARD JAY COOPER

A THESIS

Submitted to the School of Graduate Studies of Michigan
State College of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of

MASTER OF 5015303

Department of Chemical and wetallurgical Engineering

l9h9

ABSTRACT

In order to economize time and mental effort in mathematical
computations of distillation towers, it is proposed to use an electronic
calculator for this purpose. In general, most calculating machines
do nothing more than solve a series of simultaneous equations. This
is essentially the applicatienwpresented in this work. In industry
it is not inconceivable to enounter a fifty plate column being used
for the separation of ten components. The Solution here would incor-
porate 1,000 equations with 1,000 unknowns. The basic mathematical
processes involved in the solution of these equations are multiplica-
tion, and addition.

With the feed composition, feed plate, number of plates, and
the desired end products known, the composition at the top is assumed.
The calculator is used to make plate to plate calculations going from
the tOp down and from the bottom up until the compositions on the
feed plate are obtained. It is desired that these compositions match,
but should they be different, a new top composition must be assumed
and the calculations done over.

It is further prOposed to make this Operation automatic.

To perform the aforementioned mathematical processes of multi-
plication and addition, a series of d.c. amplifiers are employed. As
used in the calculator, the d.c. amplifier is essentially a three
stage resistance coupled vacuum tube amplifier with negative feedback
passing through a feedback resistor. The output voltage from the
amplifier is equal to the input voltage multiplied by the ratio of

feedback resistance to input resistance.

If a second input voltage is applied, the output voltage of the
amplifier is the algebraic sum of the individual input voltages, ead1
multiplied by the ratio of the feedback resistance to its individual

input resistance.

Kit .
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I

TABLE CF CONTENTS

Title Page .................................. 1
Table of Contents ........................... 2
Acknowledgement ............................. 3
Introduction ................................ h
History ..................................... 9
Theoretical Considerations .................. 13
Method of Procedure ......................... 26
Discussion .................................. 37
Conclusions and Improvements ................ ho
Appendix .................................... 51
Bibliography

Selected ............................... 62

SUpplementlry eeeeeeeeeeeeeeeeeeoeeeeeee 63

P.)

AC Ki: C‘n LE J 3.33533":

The author is deeply indebted to’Frofcssor
C. C. Dehitt and Professor J. E. Donnell for their
Vuidance, advice, eni assistance. ppreciation is
also expressed to the members of the Electrical

Engineering staff for their valuable advice.

INTRODUCTION

Distillation is the separation of the constituents of a liquid-mixture
by partial vaporization of the mixture and separate recovery of vapor and
residue. 'The more volatile constituents of the original mixture are ob—
tained in increased concentration in the vapor; the less volatile in greater
concentration in the liquid residue. The completeness of separation de-
pends upon certain properties Of the components involved and upon the arrange-
ment of the distillation process.

In general distillation is the term applied to vaporization processes
in which the vapor evolved is recovered usually by condensation. Evapor-
ation commonly refers to the removal of water from aqueous solutions of
non—volatile substances by vaporisation. The vapor evolved, i.e., the water,
is discarded.

Rectification, the case used in this work, is a distillation carried
out in such a say that the vapor rising from a still comes in contact with
a condensed portion of vapor previously evolved from the same still. A
transfer of material and an interchange of heat result from this contact,
thereby securing a greater enrichment of the vapor in the more volatile
component than could be secured with a single distillation operation using
the same amount of heat. The condensed vapors, returned to accomplish this
object, are termed reflux. -

multicomponent mixtures are those containing more than two components
in significant amounts. In commercial Operations they are encountered more
generally than are binary mixtures. As with binary mixtures, they can be
treated in batch or continuous Operations, in bubble-plate or packed towers.

It is the bubble-plate tower that is considered here.

It is assumed that the reader is thoroughly acquainted with the
principles and methods used to calculate binary mixtures. It is further
assumed that the reader is familiar with the usual simplifying assumptions
made in most all rectification calculations. Since these are also used in
this work, they will be reviewed briefly here:

1. Sensible-heat changes through the tower are negligible in compar-
ison to the latent heat.

é. The molar latent heats of all components are equal.

3. The heat of mixing of the components is negligible.

h. Heat losses from the tower are negligible.

Fundamentally, the estimation of the number of theoretical plates in-
volved for the continuous separation of a multi-component mixture involves
exactly the same principles as those used for binary mixtures. Thus, the
Operating-line equations for each component in a sulti-component mixture are
identical in form with those for binary mixtures. And the procedure is ex-
actly the same; i.e., starting with the composition of the liquid at any
position in the tower, the vapor in equilibrium with this liquid is calcu-
lated; and then by applying the appropriate operating line for the section
of the tower in question to each component, the liquid composition on the
plate above is determined and the Operation repeated from plate to plate up
or down the column. However, actually the estimation of the number of theo-
retical plates required for the separation of a complex mixture is more
difficult than for a binary mixture. When considering binary mixtures, fix-
ing the total pressure and one component in either the liquid or vapor im-
mediately fixes the temperature and composition of the other phase, i.e.,

at a given total pressure, a unique or definite relation between y and x

 

‘l‘i‘. All!» i

6

allows the construction of the y—x curve. In the case of a multi-component
mixture of u components, in addition to the pressure it is necessary to fix
(u-l) concentrations before the system is completely defined. This means
that for a given component in such aimixture the yen curve is a function not
only of the physical characteristics of the other components but also of
their relative amounts. Therefore, instead of a single y-x curve for a given
component, there are an infinite number of such curves depending on the re-
lative amounts of the other components present. This necessitates a large
amount of equilibrium data for each component in the presence of varying
prOportions of the other; and except in the special cases in which some
generalised rule (such as Raoult’s Law) applies these are not usually avail-
able, and it is very laborious to obtain them. One of the largest uses of
multi-component rectification is in the petroleum industry; for a large
number of the hydrocarbon mixtures encountered in these rectifications, gen-
eralised rules have been deveIOped which give multiccomponent vapor-liquid
equilibriums with precision sufficient for design calculations. Such data
are usually present in the form y equals K‘, where K is a function of the
pressure temperature, and component. K-charts are given in the appendix.

The use of equilibrium data in such a form usually requires a trial-and-error
calculation to estimate the vapor in equilibrium with a given liquid at a
known pressure. This results from the fact that the temperature is not known
so a temperature is assumed and the various equilibrium constants at the
known pressure and assumed temperature are used to estimate the vapor compa-
sition. If the sum of the sol fractions of all the components in the vapor,
so calculated, add up to l, the assumed temperature was correct. If the sum
is not equal to l, a new temperature must be assumed and the calculation re-

peated until the sum is unity. Such a procedure is much more laborious than

that involved in a binary mixture where the composition of the liquid and
the pressure together with equilibrium data immediately gives the vapor
composition without trial and.error.

After calculating a great number of multi-component distillation
problems, it soon becomes apparent hos valuable some kind of calculator
would be. Perhaps the neei for a calculating machine can be seen better
if the problem for which it will be used is presented in a different manner.
Take as an example the three component problem used in this work where the
separation takes place in a five plate column. Basically the results sought
here involve the sclution of thirty equations containing thirty unknowns
(two equations with two unknowns for each component and each plate). In
industry it is not inconceivable to encounter a fifty-plate column being
used for the separation of ten components. The solution here would incor—
porate 1,000 equations with 1,000 unknowns. The first alternative to come
into one‘s mind would be mechanical means. A mechanical differential
equation calculator had been used at Massachusetts Institute of Technology
at one time, and the navy aimed their guns with mechanical calculators until
the recent war. However, these mechanical calculators required new sets
of gears for each problem and to compute the sizes, etc. of these gears meant
practically working the problem itself. During the recent war the army switched
to electronic means for calculating and directing anti-aircraft fire. it
has been learned authoritatively that most large oil companies in the United
States have been working toward deveIOpment of an electronic calculator for
the same purposes as set forth in this work. The big nemesis to the industries
has been the large cost of building an electronic calculator. It is claimed

by them that the plate efficiency in a distillation tower couli be greatly

inproved if the maze of calculations involved could be handled in some
practical manner. It is to this objective that this work has been devoted.
The reader should not get the impression that the calculator as is can
only be applied to distillation. With a few slight modifications the cal-
culator can be utilised for many other unit operations in chemical engineer-
ing. Some examples of other application would be absorption towers and
heat exchangers. This is further brought out by the fact that the calculator
used herein, and in general most calculating machines of this nature, do

nothing more than solve a series of simultaneous equations.

HISTORY

The desire to economize time and mental effort in arithmetical
computation, and to eliminate human liability to error, is probably as
old as the science of arithmetic itself. This desire has led to the
design and construction of a variety of side to computation beginning with
"groups of small objects such as pebbles used first loosely, later as
'counters' on ruled boards, and later still as beads mounted on wires
fixed in a frame, constituting the abacus'. (1,2,h)

The abacus was until the Christian era the only instrument man had
developed for the purposes of calculating; it is still used extensively
in China, Japan, lndia, and Russia. During the time after the invention
of the abacus, gears and pointers were used in the design of clocks.

These machine elements, and more especially a sheel shich at the end of
a complete revolution gave impetus to a seconduwheel, paved the say for
the develOpment of calculating machinery.

In 1617, John Napier, following his invention of logarithms, pub-
lished an account of his numbering rods, known as ”Napier's bones". (3)
Various forms of the bones appeared, some approaching the beginning of,
mechanical computation. Subsequent to the introduction of logarithms,
the slide rule was developed by Oughtred (1630), Evean (1755). Mannheim
(1850) and others. The slide rule is probably the ancestor of all those
calculating devices whose Operation is based upon an analogy between numbers
and physical magnitudes, in'shich the computed results are obtained by
physical measurements. Many such analogy devices have since been constructed.
Examples of these are the planimeter, integraph and finally the differential
analyser. (3) All analogy devices, like the slide rule, are limited to the

accuracy of a physical measurement.

10

The first real calculating cachine enplcying a mechanical principle
did not appear until 16h2, when a simple device consisting of reared num-
boring wheels was invented by Blaise Pascal. (6,?) "The design of Pascal's
machine depended upon rotating wheels and provided for carry by mechanically
turning the wheel of the next higher order one position when file lower
passed from nine to zero". (ll)

Mathematicians hal realized that multiplication is actually a process
of repeated addition, anl a machine to carry out this principle was first
projected in 1671 by Gottfried Wilhelm Leibnits, though not successfully
completed until l69h. (8) In Pascal's machine the wheels were set and
turned individually by hand; in Leibnits's machine all wheels were set
and turned simultaneously by a crank to a previously determined position.

In 1820 Charles Xavier Thomas invented tne first calculating machine
that was sucessfully manufactured on a commercial scale. It could perform
all four elementary arithmetical operations and during the succeeding
several years was extensively'inproved by inventors in EurOpe and this
country.

During the early years cf the nineteenth century several more elabor-
ate calculating machines were proposed. These included the so-called
difference engines of which several were constructed (engines were to
compute and print tables of functions). The most ambitious of all the
proposals, however, was the analytical engine designed by Charles Babbage
(9,10) in 1833 in which several features of his difference engine were to
be embodied. This was a calculator intended for the performance of complete
computations according to given instructions. The numbers in the first
part of the machine, called the "store", were to be Operated upon by the

second part of the machine, called the "mill". A succession of selected

11

Operations were to be executed mechanically at the command of a
''sequence mechanism". (12) The analytical engine was to have been
completely general as regards algebraic Operations.

As in the difference engines, the analytical engine was to print its
own results. Further, a mechanism was to have been added for punching
numerical results on blank cards for future use. In this way, the engine
could compute the tables required and punch its own cards "entirely free
from error”. ‘(13)

The plan, too ambitious for engineering and technical facilities of
that time, was unfinished when Babbage died. Though his principles were
theoretically sound and though he was successful to a limited extent, it
remained for the twentieth century and the evolution Of aivanced mechanical
and electrical engineering to bring his ideas into being.

The familiar keyboard type of calculating machine originated in the
United States at about the middle of the last century and has been develOpsd,
chiefly in this country, for many accounting and commercial computing
purposes.

In 1887, Leon 80110. was successful in producing the first machine
capable Of performing multiplication by a direct method instead of the
method of repeated addition. The principle was further developed in later
machines.

To eXpedits United States Census compilation work, Herman Hollerith,
in 1889, develOped the punched card as a means Of recording numerical infor-
mation for automatic computing. At the same time he devised electrically-
Opcrated mechanisms which performed adding and counting Operations when
actuated by punched cards. This method was perfected through a long pro—

gram of ”research and dschOpment by the International Business Machines

12

Corporation to the point where electro—mechanical machines could perform
a variety of orerations such as roadint, adding, rintinq, sorting, re-
producinv, multiplyinf, collatiny, and summary punching". (1h)

By l93h 1.9.3. had perfected electric punch card machines to such an
extent that they were capable of handling many of the general calculations
of science. in automatic computing laboratory'was established in and
Operated by the Thomas J. watson Astronomical Computing Bureau, a sceper-
ative project of the American Astronomical Society, Columbia University,
and 1.8.M.

The first large-scale peneral~purpose digital calculator'was built
by I.R.M. Known as the I.C.M. Automatic Sequence Controlled Calculator,
it was completed in l9hh. It had the greatest internal storage capacity
and most elaborate sequencing facilities of any machine prior to the
I.B.¥. Selective Sequence Electronic Calculator.

Up to this time the addine wheel was utilized as a basic unit in
practically all calculating»: machines. In 19146 the first large electronic
calculator was dedicated by the University of Pennsylvania and the first
commercial electronic computer was marketed by 1.9.r. The 'Eniac" was built
by the University of Pennsylvania for computing trajectories of shells; it
has storage for about 200 digits including those in the multiplication and
division units, and is controlled by means of pluggable connections.

The newly deveIOped I.B.H. Selective Sequence Electronic Calculator
is the most recent development in the search for a machine more nearly
capable of meeting the size and scope of present-day problems. It has a

memory capacity of over hO0,000 digits.

13

THEORETICAL CONSIDERATIONS

In the present section it is desired to discuss the theory of
amplifiers. Before considering details, certain general remarks con-
cerning the nature of calculating devices should be made. Each such
device will have a number of inputs and an output. A pure calculating
device can be defined as one which has no source of energy between the
input and output. For such a device the outputs must do all the work.

In general it is also true that the results will be accurate only when
the output does no work. Indeed the order of magnitude of the error is
closely associated with the ratio of output work to input work.

It follows therefore that if the mathematical output of such a
device is to be used as an input to a similar device, an energy source
must be provided.

The ratio of the output energies to input energies of available.
amplifiers is very important in considering the physical principles upon
which a device is to be based. Fortunately this ratio is quite large for
, electronic amplifiers and the latter are frequently used as part of other
amplifiers for this reason.

In the discussion which appears in this section, it is supposed that
the reader is familiar with the R.C.A. Receiving Tube lanusl, published
by the 3.0.1. Manufacturing Co. The manual describes the various types
of tubes and their uses in radio receiving sets. Many of these uses are
immediately applicable to calculating devices, others require a certain
amount of reorientation. The manual contains the technical information

'nsoessary for the design of circuits and is a remarkable summation of the

1h
application of vacuum tubes for radio receiving purposes.

Essentially the two uses of a vacuum tube are (l) rectification,
i.e., the process of obtaining a pulsating one directional current from
an alternating voltage, and (2) amplification, the control of power by
less power.

It is assumed that the reader is familiar with the usual discussion
of the action of triodfi and mnlti-electrode vacuum tubes. An excellent
summation of the fundamentals of vacuum tubes is also contained in the
3.6.1. Manual referred to above. It is also desired herein to point
out certain aspects of amplifying ciruits which are important from the
point of view of this work. Amplifiers can be roughly divided into two
kinds. One type is a voltage multiplier and the other is a power multiplier
prOper. Il'he voltage multiplier is the one concerned with here.

For electronic amplifiers in general it is necessary to use high
voltage direct currents. i'nese are obtained by the use of step-up trans-
formers and diode type rectifying tubes as given in the power—pack circuits
in the appendix.

The d.c. amplifier is an electronic device which produces a d.c. out-
put voltage directly prOportional to the input voltage, when the input is
a d.c. voltage. The amplifiers are used to perform any or all of the
following functions:

1. hoduce a d.c. voltage prOpor'tional to the algebraic sum of two
or more d.c. voltages, either with or without weighting of one or more of
the input voltages.

2. Reverse the sign of a d.c. voltage, either without changing its

value or including multiplying the value by a constant factor.

15
3. Isolate lone circuit element from another.
If d.c. voltages from several sources are connected, each through
equal resistance, to a common point from which a resistance is connected

to ground, as shown in figure 1, the voltage across the latter resistance

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is proportional to the algebraic sum of the several voltages. If the
latter resistance is very small compared to the input resistances, the
factor of proportionality will haven nearly the same for any number of
inputs. The voltage measured as in figure 1 would be very small. To
obtain a usable voltage, still proportional to the algebraic sum of the
input voltages, a vacuum tube amplifier is substituted, in the circuits
of the calculator, for the small resistance as indicated in figure 2.
This amplifier is so designed that its apparent resistance (input imped-
ance) is only about 25 ohms. By making the input resistance of the order
of l megohm, the measured voltage is then very nearly proportional to
the algebraic sum of the input voltages. The amplifier amplifies the mea-
sured voltage about 10,000 times. I

If the input resistances are all equal, the voltage across the small

resistance of the amplifier and, therefore, the output voltage of the

16

FEEDBACK
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amplifier will be directly proportional to the algebraic sum of the input
voltages. By suitable arrsnwnt of the circuits, this output voltage
may be made (very nearly).equal to the algebraic sum of the input voltages,
or it may be multiplied by any factor. If one of the input resistances
is made somewhat lower than the others, the input voltage connected through
that resistance will be multiplied by a factor or weighted in the summation.
The d.c. amplifier used has three stages. From the fundamentals of
vacuum tubes the output voltage of such an amplifier is opposite in sign
to the input voltage. the amplifier, therefore, reverses the sign of a
voltage applied to it. From the preceding it is apparent that, in this
case also, the output voltage may be made equal to the input voltage or
to the input voltage multiplied by any factor.
As used in the calculator, the d.c. amplifier is essentially a three
stage resistance-eoi’llpled vacuum tube amplifier with negative feedback.
m. following are some of its mama... '

17
Number Of Stages................................... 3
Tubes Used!
firlt Inga eeeeeeeeeeeeeeeeeeeeeeeeeeeee 6307
Becond .tageeeeeeeeeeeeeeeeeeeeeeeeeeeeee 63017
third stage.............................. 6L6

Supply Voltages.... 350, «350, 300, -l90, 75 d.c.,
and 6.3 a.c.

Net 0sin.......................... 30,000 to ho,ooo

Apparent input impedance............ about 25 ohms

Effective output impedance ......... about 1 ohm

In a d.c. amplifier, the connection from the plate of one stage to
the grid of the next must be a metallic one, containing no capacitor or
transformer which would prevent the transmission of a steady voltage.
The plate of the first-stage tube is usually at a considerable voltage
above ground, whereas the grid of the second-stage tube must be a few
volts negative with respect to its cathode. If this condition were ob-
tained by supplying the cathode with a suitable voltage, the plate supply
of the second tube would have to be the sum of the required plate voltage
and the cathode voltage. With more than two stages this arrangement is
impractical as a very high plate voltage would be required for this last
tube.
Figure 3 shows the plan used in the amplifiers of the calculator.

The plate voltage is opposed by a second equal voltage of opposite polarity,
and the grid of the second tube is connected to a voltage divider to obtain
the prOper bias potential. This plan involves s'loss of part of the amp-
lification as only a part of the voltage change on the plate of the first
tube will be transmitted to the second tube. The ratio of’resistance-ggc‘

to A0 is aboutih to 5, so that about four-fifths of the voltage change is

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trannitted, reducing the gain of the first stage from about SO to to.

The amplifier diagram in the appendix shows that a similar arrange-
ment is used for the connection of the plate of the second stage to the
grid of the third stage. However, if the output voltage of the amplifier
is to be directly proportional to the input voltage, it must be sero when
the input voltage is care. To meet this requirement, the cathode of the
third-stage tube is supplied with a negative potential. Hy applying a
suitable negative bias to the grid, the output of the tube is made to
balance the plate voltage so that the potential at the plate is normally
care. If new the grid is made more negative with respect to the cathode,
the output of the tube will be increased and the potential at the plate
willbepositive. Ifthe gridisaadelessnegstivewith respecttothe
cathode, the output of the tube will be less and the potential at the plate
will become negative. lith no input voltage, therefore, the output voltage
of the amplifier is sore. With a negative input voltage, the output volt-
age is positive, and with a positive input voltage the output voltage is

negative. The amplifier reverses the sign of the input voltage and the

19

value of the output voltage is always directly proportional to the value
of the input voltage.

In this coupling, aboutcne-half of the gain of the first two stages
is lost, but the overall gain of the amplifier is sufficient for the.
purpose for which it is used.

The amplifier diagram in the appendix shows a resistor connected
between the output of the amplifier and the input. Through this feed-
back resistor a portion of the output voltage is returned to the input.
Since the sign of the output voltage is opposite to that of the input
voltage, this is a negative feedback.

The effect of negative feedback is illustrated in figure h where
the amplifier is represented as a single tube. A voltage E, at the input
of an amplifier will produce a voltage e at the grid. This will be an-
plified and appear as a voltage -Ke at the output (K being the gain of
the amplifier). A portion of this voltage'will be returned to the grid
through the feedback resistor RB and, since it is apposite in sign to the
voltage s, will tend to reduce o. This will reduce Ke, allowing e to
increase, until a point of stabilization is reached. This stabilisation
occurs practically instantaneously. Any change in amplification due to
variations in the amplifier itself will change thegvalue of x but, due to
the feedback this will correspondingly change 0 and thus tend to maintain
to at a constant value. Ihe use of negative feedback gives the amplifier.

great inherent stability. ,

If the feedback resistance and the input resistance both have the

same value, R, the current through these resistances will be:
E+Ke

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since the output voltage 30, and the input voltage E are in effect siding.
The potential e at the grid will be the input voltage less the voltage

drop in the input resistsnce or:

e =rl - IR
Substituting the value of I in this equation:
3* K0
. :3 4—1-—
I
or: e = 3%!
KB
Ind: E°= ~Ker-- F!
If: I ' 110,000
then: no- -0.9999SE

Thus, if the Ieedbcck resistance is made equal to the input resistance,
the output voltage of the amplifier will be I negative capy of the input
voltage, exact to about 5 pert. in 100,000. It will be noted thet the
larger the 38111 (K), the greater is the accuracy with which the input vol-
tage is reproduced in the. output.

By the same process, it con be shown that if the feedback resistance

in not equel to the input resistence, then:

R
30 '5 4 B (very nearly)

Ru

 

21
This makes it possible, by using a suitable ratio of feedback to input
resistance to obtain an output voltage from the amplifier'vhich is always
equal to the input voltage multiplied by a constant factor.

In figure 5
31 = 11 R13 Ez‘Izfizs 33" 1333

and: '
I3=Il-*'Iz
therefore: 3 R
n=II 3 Be E .2.

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The output voltage or the amplifier will, therefore, be the algebraic sun

we

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of the individual input voltages, each multiplied by the ratio of the
feedback resistance to its individual input resistance. This makes it
possible, by using suitable values cf input resistances, to give each
voltage a particular weight in the summation or to emphasize the effect
of any one or more voltages. Of course, if the input resistances all have
the same value, the input voltages will all have the same weight and the
output voltage of the amplifier will be the algebraic sum of the input
voltages. '

In an ordinary vacuum-tube amplifier, the input impedance is practically

22
infinite. Negative feedback, however, alters this condition. In figure
h the voltage drOp in resistor BIN is E-e. The same result would be
obtained if the amplifier were replaced by a resistance. But e is very
small compared to E. The resistance which would replace the amplifier
'will then be very small compared to nIN' Actually the equivalent or
apparent resistance of the amplifier with feedback is in the order of 25
ohms. The amplifier with feedback, therefore, satisfies the requirement
of low apparent input impedance which was brought out previously to be
necessary'when the amplifier is used for the addition of several input
voltages.

A generator or source of electric power normally has some internal
resistance. If an external load is connected to such a generate; the two
resistances, HINT and RLoad will form a veltage divider and the output

voltage will be:

 

 

The output voltage 30 will then depend upon the relative values of HINT.
and RLoad' Changing the load resistance will change the output voltage.
If s. internal resistance is high compared to the load resistance, the
output voltage will vary widely as the load is changed. If the internal
resistance is very small, the change in output voltage will be insigni-
ficant. '

In the d.c. amplifier, an increase in the load resistance would tend
to lower the output voltage, but since this change is transmitted through
the feedback resistor, it will also tend to increase the voltage e, there-

by increasing the output voltage -Ke. Due to this compensating action,

23
the output voltage remains practically constant from no load to the full
load which the amplifier can handle. This is the condition that exists
with a generator of very low internal resistance or, as it is usually des-
cribed in connection with vacuum-tube circuits, very low output impedance.
The effective output impedance of the amplifiers used in the calculator
is in the order of 1 ohm.

Since the effective output impedance of the amplifier is so low, the
output voltage is practically uneffected by the load (within the capacity
of the amplifier). The amplifier can therefore, be used to isolate two
circuit elements when the load of one element would react unfavorably on
the other.

Although negative feedback tends to level out variations in the gain
of the amplifier, small changes in gain of the first stage will have an
important effect on the output voltage, because such changes in the first
stage are greatly amplified by the succeeding stages. For example, if
the second stage has a gain of 60 and the third stage a gain of 15, changes
in the first stage will be amplified by 60 x 15 or 900 times. Changes in
the second stage are not so important as they will be amplified only 15 times,
whereas changes in the third stage will not be amplified at all.

The first tube of the amplifier is, therefore, arranged to minimise
changes in gain which may be caused by variations in cathode emission.

A twin-triode tube with common cathode is used, one section being used as
the amplifier and the other section for the stabilisation. The cathode is
connected to ground through three resistors, one of which is variable.

To be a true negative cepy of the input voltage, the output voltage
of the amplifier must be sero when the input voltage is zero. Due to manu-

facturing variations in the vacuum tubes, it is impracticable to make the

amplifiers so that they will altays give zero cutout voltage with zero

input voltage. They are made, tharcforc, so that they always give a small
positive c;tput voltage'vith sure input voltage. To ccrpensatc for this,
each anglifior is provided'witn a snail positive input voltage union may

be adjusted. The Operation of adjusting this voltaye will be called zero-
actting. The vcltage is derived from tnc11;;5:;olt sugply, and the arrange-
ment is shown schematically in the diagram in tho appendix.

By adjusting, the zero-set voltage of each amylifier, the output volt—
ages of all of tnem are brought to zero before the calculator is Operated.
Tuis is essential to accurate computation. tnen zero-setting the amplifiers,
there must, of course, be no input VCltagec other than the zero—set voltage.
There must also be no resistance paths tc ground at the inputs, which
would modify the applied zero-set vol age. Therefore,'when zero-setting
all amplifier inputs must be grounded.

The couplets circuit cf the d.c. amilifier is shown in the appendix.
The second stage tube is a pcntode. he screen grid cf this tube is
augplied with -t7$ volts. The third stage tube is a beam-power tube. Since
the cathode is auyplicd with ~l93 volts, the screen grid is made positiv.
with respect to the cathode by connecting it to ground.

All the tubes have indirectly-heated cathodes, tne heaters using
6.3 volts alternating current. in order to prevent a large pctential dif-
ference between the hcater and the cathode of the third tube, two heater
supyly transformers are used. Cne, at ground potentiob, supplies the
heaters of the first and second tubes, and the other connected to the ~19O
volt supply, supplies the heater of the third tube. These two transformer.

supply all the amplifiers in the calculator.

25
An amplifier witH such high rain is verv readilv set into oscillation
by small dist rbnrccs. To prevent oscillation, the ccntrcl grid of each
take is ccnruntoi to ground thronfih a filter ccmpcsed of a resistor and a
capacitor. These filters introiuce attenvation so that the rain of the
O . af-
afiglifxcr (h0,000) is reduced to unity_o§ about 1,000 cycles per second

uni to a lcss at higher frequencies.

26

EETEICID OF PROCEDURE

While the power unit was being built, it was obvious that an actual
distillation problem would have to be set up and calculated by trial and
error. It was necessary to have a distillation example set up and com-
pletely calculated so as to check and develop the calculator when finished.
Also, it was needed in order to detemine the ratio of feedback resistance I
to input resistance in the amplifier, which is discussed later. For the
purposes here the sat up of the distillation problem and subsequent cal-
culations were varied somewhat hon the procedure with which the reader
is probably most familiar. Two problems, one three-component and one
six-component, were set up and calculated as follows:

A fractionating column with a known amount of plates was specified.
In this case a five and six plate column plus rsboilar. Also specified
was the feed composition, feed plate, reflux ratio, pressure, and certain
requirements of the end product. To proceed from here, the composition
coming from the top or bottom was assumed, and with the top or bottom
composition as assumed, and with the feed composition set, the other
(tOp or bottom) composition is automatically set from material balances
on the entire column. Using the tap and bottom coupositions as assumed,

a plate to plate calculation was mads-working from tbs tap down and from
the bottom up. If the compositions so calculated were identical for the
feed plate, then the compositions assumed were correct. If the food plats
compositions do not match, a new composition at the top and bottom must

be assumed and the calculations repeated until the {sad plate compositions
match. It was found to be extrsmly difficult to match these compositions

100 per cent. in alternative is to calculate down from the top and determine

27
he vapor compositicn from tic fuel plate, and calculate up from tue

bottom an! dctemino the liquid composition from the fee-J plate. Using
these values of y and x calculate K for the feed plate. ultn these values
of K, the corresgonling values of temperature are obtained from the K-
cherts, and these temperatures must be identical.

In each of the two problem following, several trials were found
necessary by the author. Only the final calculation is given.
Problem _I_: Three-component water.

A mixture of 30 mol per cent prepane, LS mol per cent butane, and
30 mol per cent pentane is to be fractionated in a five plate column. The
feed to the column will enter in such a condition that no net vaporization
or condensation will occur on the feed plate (Vn= V.), and the column
Operates at 10C) pcunds per square inch absolute. Reflux ratio of 0/0.}.

D270 71:33.

 

Assume: 1d
(3h 0.53/3

Using as a basis 100 mole of feed: 23

1 Since O/D ‘3, in the top
'{ part of the tower

 

 

 

 

 

 

 

:2. )n'aD =210
4’ cfoAtR
Cr“ 3 CS’ 30.037 Om=0n+F 2 310.
e :30
‘ L giving Zm= 280
. is.
QB‘OM .09":
H 8:995: 0350

cg‘QA’3 Mil}?
For the part of the column above the feed plate, the

operating lines are
for propane:

yn =(O/V)nxn+l +(D/V)nxd =- (210/280)xm_1+ (70/280)xD

7
for butane:

u’

yn“ 0e75xog+l + Gel-3?
for pentune:

Yn = 0.75xn*l+-0.012
For the part of the column below the feed plate, the

operating lines are
for propane:

ym-(O/V)mxm+1 - (EV/me‘, =(ilO/280)xm+1 - (BO/280%,

zl’lqul+1 " OeOO)
for butane:

.06?
ym = 1.1qécmfl- 0.,011
for pentane: ‘

. ,C (J
ym =i.1g§:m1- 0.096
Beginning with the composition of the vapor at the top
and the liquid in the still, a temperature is assumed and the

values of K found from.the charts. Using these values of K

2}
and composition, the composition of vapor or liquid in equilibrium is
calculated. If the sum of these moi fractions add up to one, the assumed

temperature was correct.

36

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Como— Tl °F K.

”E“ $222. f. 3‘5" “WK "’ 2%: 434
Cs \3‘L' 1‘ 09715 on: o no, 0.7.32
C4 0-3 0.5% 0.670 O 930 0.644—
Cg 0.26 0.037 0447, 0.144- 0M7

63/10: 0423 57‘; =01“
L N/K )‘4' 443
(L5 KG 3.} 0.73? 0.017 0.071 0.1“,
Car \.\ 0.644 0.5%: 0.517 0-§8I
L; 0.37 0.117 0.3“. 0.323 0.25,
__ éz/(L = 0472 in: 0.3;“
.33— M fig /:
C3 at 3.1 out 0.04: 0,04;
C4 l3 058! 0-447 0-453
c,‘ 050 am 04:22: @*
A 29414: 0.444,, ixjr- 1.000
-' BOTTOM 0P —

CoM90— T3 0‘: #4

”arr Ars— \<~ Xv, XK ‘olm={;; X‘

63 nor 5.1 mono; 0.0074: coolsmom;
(‘1. l.\ 0033 0414, 04’], 04(93me

0; om 0.610 0.949 __ 0.374 0.34?
in“: hm? flask-om
1, mg 31‘ x1
C3 ‘U’L 4.8 bpou‘ 0.0\\ 0.0” 0.0“
0., L61 0,163 0-3\D 03\\ 0.7110
c; on? 0,343 0.9%” a £11 01101
ZXK : am 29:: 0 m
XL m. iv
Ca Mb 43 0.0” 0.04]; q 0.04 o.
C“, V] 0. Mo 0.4% o. 4‘17. @
C; 0.06 0.707 0%, 0 4% 0513
21(ch Moot £¥wl000

Iran the reed plate composition as calculated

 

 

 

Oompo- Tempo
cent 3: :2 .K erature
03 0.166 0.01.1. 3.7 170°?
0‘ 0.581 O.h5h 1.28 176
65 0.251 0e51, 0eh91 176

The maximum operating conditions obtainable with the
specified bubbleaplate column and under the condition:
designated are then

 

 

reed Distillate Residue
ucl Eel
component M01- .Ibll traction lblc rection

 

Propu0eeeeeeeeee 30 30.0. 0.1028 0.000% 0.0005
Butane........... “0 37051 0e535 20kg 00083
POnm.¢eeeeeeeee 3° 2.59 00037 270,4'L 00913

100 70.00 1.000 29.89 0.9965

 

 

 

 

 

 

Problem.II: Six-component system. 32
A natural gasoline of composition given below is to

be separated in a six plate column. The column is to oper-

ate at 100 pounds per square inch absolute pressure with a

reflux ratio, 0/0, of 3, and the feed is to enter in such a

condition that no net vaporization of condensation occurs

 

on the feed plate (Vh==Vh). Feed composition:
assume: xD propane 15 mol %
iso-butane 15
-butane _25
prOpane 0.271 n .
iso-butane 0.205 lac-pentane 10
n-pentane 15
n-butane 0.h22 heavier 20
iso-pentane 0.031
n-pentane 0.013
heavier 0.001]. D 7150.9 E‘J‘L5.l

/ , oral; I

Using as a basis 100 mole of feed:

I Since O/D is 3, in the
, X,3 top part or tower

5—-

 

 

 

 

 

 

 

 

: €3.33: 011 " 3D ‘15“
c-»{ »- ‘Oo
“1:62: 9 “£50.06 and Om‘On*F =26h.h,
'- 3 --‘0.0°\‘
”c5 \‘0, "L ct giving Vm .2393
MC * s
{
c ~32“ .
6 \ 122 “0 egg 0- ‘3‘
. C3=o.oeo\ IKCS“ 0.3L?
M&’o.oog C ...-. o. 443
MCA’O.040 0

For the part of the column above the feed plate, the

operating lines are
for prOpane:

yn = (O/V)nxn+l+(D/V)nx9 = (Maw/219.2)zn,‘3‘.151+.9/219.2)XD

=—0.75xn~_11-0.0o85
for butane (iso):

yngoo75xn4 +0.0662

for n-butane: 33

Y = 0.751! 4- 0,101+
for iso-pentane: 4M’\

for n-pentane:

y '- oe75I + 0.001..
for hexanes: “ M*\

For the part of the column below the feed plate, the

Operating lines are
for prepane:

X“ = (O/VL‘IM

~‘o (xv/mg”:(264.0/219.2)xw - (tea/219.2)!”

for lee-butane: ““4

y 9-1-0211 ¢ 0.002
for n-butane: ”“ “H

y 31021: - 0.008
for iso-pentanezm “*‘

y“: 1.21xM\ - 0,037

for n-pentane:

LL 1.211 ‘- 0.063
for hexanes: Mn-

yk‘ 1..le ‘. 00089

3h

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

" T °F : ., 376‘
m Jag K K 30 ML 6" 2717'- 1g...
0, \30 1.0 0-7!" 0.104 0.104. M03
mc‘ H 0.7.0; 04’1“ 0-24! 0.751
mg, an oA'LL 0.95 051$ 04%
#506," 0.33 093‘ 0.0%! 0.086 0.068!
mL{ 0.2% 0.0“; 0-0413 0.0473 o.03q{
Cr 0.I4 000“ 0.0019: 0.007K0.00M
2B/acr- M18 £19. = 0.332
L 34(— A; L.
C; ‘58 3| 443 0.003 0X0 0408
mCo, I35 :25! (948B 0M€ 0.246
mg. H 0.410 0.445/ 0,45{ 049.
10005 0.0 0.063 0- BBC 0.140 0-HZ
«05’ 032 0.03: 0404 0401 0086’
C‘» 0.1% 40.00L1___0.1233:)_ 0.0;“.0024:
L (#00453 23:12.11}
ALIA X45
(‘1 We 3? Wag 0.0247. 0.0307.
10.64 H. we 013$ 0.!40
ma (-3 00.9. 0.341 0.3!»!
14°C; a.“ 0M1. . M13 0m
mtg 0.9) 0. cu 0411 0473
C’b’“ mu ID.0M_.S/__0._I2L_ 04012...
2 lg r0167 2%.; 20.494,
a -— Bottom 0 P — ,
C323” 30; K Xv) XL #400 5% X.
as 7/44 5.9 0.000! 0000“ 0.00000 .0009?
“C4 1% 0003 ' 0.07,; aO’Bg .016
“CG ‘ 7/40 0-040 0.016 0- 0‘18 .0‘10
me; m mm 0.254 mm .230
MW MB 0-97 0359 0.366 .357
9;“ 0.4.0 0-443 0.24.1 07:30 .301
{x 1; = 0&7} 23.303614

“.

 

35

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- ? XK
€323; .4530. ‘4 ’9 MC 3 Ex ‘9
C3 no (.0 0.00044! 0007.“ o 0019] 0.007,!0’
”at 714’ 0.034 0.05% 0.0914 HQOM‘L
AC4 1.0 £0010 0‘30 0H0 0407
mg H 0.150 0.08 0.167 0-754-
m 6; Mo 0. 357 0.327. 0. 340 0.3%
C.-- (9.46 0.501 0432 - 0. We 0.116
fine“? 21; =1. 00.0 _
L X214 524 X;
C} M 4.; 0.001.; 0.00103 (low 0.00%;
hoCo, H 0.0472. 0.0% 0. [07. 0.0344
AC4 L4 0107 0.3” 0.317 0.180
A006; 0.10 o 154—4 0.7/74 0. 256 O. ’ZLY
AC( 0717, 0.33{ 0.1M 0.144 0. 7400
Cg'” 0%? 0w, 0.0?“ 0 01L 0. {3“
(XL-10370 2 32: 3.00] ,
J; >94 5,; Xq._
C; . . m, 0,0 0.0083 0.0331. 0. 030.2. Ham/24'
1mg L3 0.0944 045’3 am? 0.84,
Mg m P23" 0.420 0.437, 0.367
new 0-1; cm 0-H»? am, 04%
MC! 0.63 0.200 04:: 0. IS"; 0481
C’b’" 0.30 0433 0.0447 0.0%} 0, m
. éxlé': 0. M=QQQ§ .

 

 

From.the feed plate composition as calculated

 

 

 

36

 

Compo- Temp-
nent yh 3h K erature
03 0.108 0.0280 3.80 17690

n0“ O.h52 0.367 1023 172
13005 0.112 0.175 0.00 170
n65 0.0858 0.182 0.07 172
06" 0.0265 0.111 0.24 172

The maximum Operating conditions obtainable with the
specified bubble-plate column and under the conditions

designated are then

 

 

 

 

 

 

 

Feed Distillate Residue

M01 M01
Component M013 M018 fraction. "913 fraction
Propane.......... 15 10.9 0.271 0.00 0.0001

130 Entaneoooooooo .15 1&055 O. 65 0.36 0.008
n Entaneoooocooooo 25 23.2 00 2;, \0g0 0.0h0
13° Pentan60uuu 10 107 0. 03‘ 2.3 0.1814
n Pentanocouoo0ooo 15 0..” O-°\3 ‘4-3 00317
HGIBDBS. o o o o o o o 0 a 20 O. 0% 0. 00‘ woo (3.th
100 55.0 \.003 ##08 0.992

 

 

 

37

DISCUSSION

upon completion of the poser unit and several amplifiers (wiring
diagrams shown in appendix) they were tested to make sure each was
Operating properly. The general scheme was to have one amplifier unit
for each component in the system to be calculated. It should be noted
that two amplifier units are mounted on each base. is see pointed out
in the section on theory, it is the ratio of the feedback resistance to
input resistance that determines the multiplication factor. Therefore
the first problem to be overcome was setting up these resistances so
as to get, exactly, the various multiplication factors needed. It was
decided to keep the feedback resistance constant and vary the input re-
sistance to give the multiplication factors. Because of practical limi-
tation neither resistor should be less than 200,000 ohms. An IRC sire-
eound precision resistor of 200,000 ohms was selected for the constant
feedback resistance, since the accuracy obtainable depends largely on
the accuracy of the feedback and input resistors. The next step was to
prepare a variable inputlresistance that would provide the accuracy
needed. Using the sample calculations given previously as a basis, it
is noted that the first step in the calculations is multiplying by I or
l/K. The ratio of feedback resistance to input resistance (multipli-
cation factor) is therefore used to correspond to K or l/K. thus, tsc
sets of resistors are needed for each component; one for the upper part
of the column share multiplication is by l/K, and one set for the loser
part of the column where the nultiplication is by K.

The "K” charts given in the appendix shoe that x is definitely not

a straight line function of temperature, and also that the range of K

38

values is greatly different for each hydrocarbon. This fact complicates
the operation of the calculator. me ideal method of arranging the cal-
culator would be where a series of resistors are ganged on one central
shaft, each resistor corresponding to the K curve of a particular hydro-
carbon. In that way, setting the shaft to a certain temperature on a
calibrated dial automatically sets each resistor to its particular value
of K. Actually a value of resistance is set which when divided arith-
setically into the resistance value of the fixed feedback resistance gives
the particular numerical value of K. In this way the first step of nul-
tiplication in the calculation series is accomplished.

Due to factors of time and economy, special variable resistors
of this kind could not be ordered from a manufacturer. Thus the main
task of this project was undertaken by the author. The first proposal
was to wind wire on a thin card of insulating material which can be bent
into a circle to save space and better facilitate its use. a brush is
arranged to run around one edge of this card making contact with succes-
sive turns of the wire. By suitably shaping the width of the card, the
resistance of the card at the brush can be made proportional to almost ‘
any desired function of the angle of brush displacement. For the problee
in this investigation, the card would have to be shaped by computation
and trial until a shape is found which gives the desired resistances at
every point. Obviously, the shape would approximate the shapecf the
teasperaturs-K curve for each component.-

Ln investigation was conducted to determine the possibilities of
making potentiometers as pr0posed above, and it was found that the best

resistance wire obtainable was one ohm per foot. The highest resistance

)?
‘needed'was calculated to be about three million ohms. Because of this,
the preposal was considered neither practical nor economical and had to
be abandoned.

Another preposal offered was to impregnate a liquid plastic (hardened
upon heating) with finely divided carbon. If the right preportion of
carbon could be found, sheets of this plastic could be made and then cut
into the desired shapes. This proposal was investigated quite extensively
and found to be unobtainable. Since the plastic was fairly compressible,
any change in pressure due to the saving brush caused a large change in
the resistance at the point of contact. This effect was due to the mov-
ing of the carbon particles closer together.

Finally, the present set-up had to be adopted. Regular IRC carbon
volume control potentiometers are used as the variable input resistors.
Two resistors are used with each component, one for calculating the top
part of the column and one for calculating the bottom part of the column.
For the three-component problem worked out by the author, it can be seen
in the pictures of the calculator that there are two panels with three
calibrated.aetal dials on each. One panel for'each section of the column,
and one dial for each component.

The methods of obtaining a suitable variable input resistance have
been discussed in sufficient detail to warrant a discussion of calibration
procedure.

Assuming that the feedback resistor is exactly its rated value of
200,000 ohms, it can be seen that an extremely accurate ohm meter is
needed to measure the resistance of the variable input resistor for various

portions of the contact slide. harking these positions accuratelwaould

ho

also be quite difficult. Since an accurate numerical ratio of feedback
to input resistance is needed, this procedure introduces too many sources
of error. To eliminate almost all possible sources Of error and also
simplify the task of calibration, each amplifier should be calibrated for
a particular component, and used only for calculations involving this
particular component. By doing the calibration this way it is unnecessary
to use an expensive wire-wound precision resistor for the input resistance.
Instead, a carbon resistor of approximately the value needed for the con-
stant feedback resistance can be used. The variable input resistor is
adjusted until the ratio of feedback to input resistance is such that the
output voltage is exactly K times the input voltage (or 1/1 times input
voltage for tOp part Of the column). This position is then marked and
labeled with the temperature corresponding to this value Of K. This is
continued until the possible range of temperature is marked.

Using the tOp panel as an example, a temperature is assumed and
each pointer set at that temperature. The output voltage of each ampli—
fier, which is :1, expressed in volts multiplied by 1/x, is fed into one
amplifier that does nothing but add. If the output voltage Of that
amplifier is equivalent to one, then the assumed temperature was correct.
If the output voltage of the uplifier is not equivalent to one, the
pointers must be reset to another temperature value until an output vol-
tage equivalent to one is obtained. Thus the first step in the calculation
has been completed. All that remains is to apply the proper Operating
line equation and repeat the sequence for the next plate. An inspection
- of the Operating line equations shows that to use them involves only mul-

tiplying the result of the first Operation (ID multiplied or divided by

111

the prOper value of K) by a constant value and then adding a constant value.
This Operation can be accomplished in the amplifier by merely applying
a constant voltage in accordance with the theory presented earlier. '

In order to move from plate to plate in the calculations it would
seem that a use set of amplifiers is needed for each plate.e If this
were the case, a tremendous number of amplifiers would have to be built
and tested. The cost of these additional amplifiers would not*warrant '
their use. Instead, Just one set Of amplifiers is used for the calculations
on all plates as follows. Using a galvanometer es the measuring instru-
ment, a balance is struck between the output voltage of the amplifier and
the output voltage Of a second variable d.c. supply voltage. The two
voltages are applied on Opposite sides of the galvanometer, so when the
galvanometer needle shows no deflection, the voltages balance. The
present input supply and the galvanometer are then disconnected, and the
voltage that balanced the output voltage is applied as input voltage for

the next step.

 

:The output chtage of each amplifier is really the answer to the mathe-
matical operation performed by that particular amplifier. In otherweords,
if an amplifier is des'ii‘ed to multiply by 3 and the input voltage is 50,
the output voltage will be 150. If an amplifier is designed to multiply
by 2.5 and then add to, for an input’mltage of 20 volts, the output volt-
age would be 90 volts. Therefore, in a continuous calculation the out-
put voltage of one amplifier becomes the input voltage of the next one.

[2

In summary, the three component problem given in the section on pro-
cedure will be specifically applied to the calculator. Included in the
poser unit is a 100-105 volt supply which is used for the starting input.
The scale to be used is 100 volts equals 1.0 on a mol fraction basis.
Starting at the tap of the column of ID are assumed as given. For prepane
‘D is 0.h28, so the input, voltage to the amplifier for prOpane is h2.8
volts. Similarly, the input voltage for the other amplifiers is 53.5 volts
for butane, and 3.7 volts tor pentane. Using the panel for the top section,
the three pointers are set at the mark on the calibrated dial corresponding
to a temperature of 132 deg. F. The outputs of the three amplifiers are
then channeled into the amplifier that does nothing but add. I: the output
or this amplifier is 100 volts, then the assumed temperature is correct.

In this case the pointer settings must be corrected slightly since the out-
put from the addition amplifier“will be 98.3 volts. Adjusting the pointers
to some position between 132 and 136 deg. F. will give an output voltage of
99.8 volts. It should be stressed that no pointer can be moved to a new
position unless all the others are moved to the same reading. This is assu-
med to be close enough, so the calculation proceeds to the second step. In
the second step the output voltages are separated and each connected to a
galvanometer. On the other side of each galvanometer is a variable d.c.
voltage supply. This voltage is adjusted until it balances the output
voltage of the amplifier as shown by the galvanometer. The present input
line and the galvanoeeter are disconnected and the balancing voltage from
the variable supply is connected as the input to the same amplifier for

the third step. This procedure is followed for each of the three amplifiers.

The third step consists of calculating the vapor composition from the plate

1:3

below by using the preper Operating line equation. Applying the operating
line equation involves multiplying the input by a constant and then adding
a constant. For the top part of the column the multiplication constant is
0.75 and is the same for all components. The addition constant is 0.106 for
prepane, 0.132for butane, and 0.012 for pentane. These constants are the
same for any plate in the upper part of the column. For the bottom part

of the column the multiplication constant is 0.91 and is the same for all
the components. The addition constant is 0.000 for propane, 0.011 for
butane, and 0.096 for pentane. These constants are the same for any plate
in the lower part of the column. The correlation between this and applying

the calculator can be seen more clearly in the following diagram.

2‘} 200, 000 .n.

A“

IHG
Emma)

 

 

 

 

 

 

 

 

tiuiolwcxt
OUTPUT

f A.

‘3 o—Jiiv
ii‘; F3 AiAPLlFHEi9~

4’ \ . conewaux uoCTAee.

e Magi—1‘59: 9.3. 209,000... «we seen 25qu “LED
5 f .000.» (,3 10.6 J. 0.00s}.
7} batons Fees: Pmcmc. 1 \ ‘
-v 7,749,000 A. Essex-op C‘ ‘3' . o

3 CS L1. “V50

5 E,= Ki K,

The feedback resistance, 3., is a part of the amplifier and is always
200,000 ohms. The adding resistor, R3, is always 200,000 ohms also. 31
and 33 are mounted on panels, and together with the constant voltage shown,
are connected to the amplifier when needed.

The output voltage, 23.8 for propane, is the composition of the vapor
from the plate below and is recorded as such. The procedure is now repeated

for the next plate, using a starting input voltage of 23.8 for propane, 6h.h

5—"

for butane, and 11.? volts for pentane.

The calculations are continued in this manner from the top down and
from the bottom up until the compositions on the feed plate are obtained.
It is desired that these compositions match, but should they be different,
a new tOp composition must be assumed and the calculations done over. This

is continued until the compositions match at the feed plate.

 

 

Fig. 6a. Front View of calculator
showing oower unit, control panels,
and amplifiers connected.

 

Fig. ob. dear View of “ower unit and
a~plifier chassis.

2:5

 

 

hfl

COlC.JSiC¥S AND lEPROVEHKHTS

As was stated earlier in the discussion, the power unit and the
amplifiers were tested upon their completion and they were found to be
operating quite satisfactorily, multiplication and addition proceeding
exactly as expected. However,-shon the calibration was attempted sevenfl.
difficulties were enoounteredyshich proved to be the most troublesome of
the entire project. As has been pointed out already, the most important
physical measurement connected with the calibration is the output voltage.
During calibration the output voltage was observed to oscillate in such
a manner so as to make an accurate calibration impossible. An analysis
of the situation was attempted and the fellowing conclusions arrived at
as to the possible causes of this oscillation.

The a.c. line voltage supplying the power unit was tested and found
to vary about one or two volts. This may not seem like much of a vari-
ation, but it should be remembered that this slight variation is amplified
in the amplifier unit'with a resulting variation oflnuch larger magnitude.
A voltage regulator was put on the line current, but the output oscillan
tion still persisted. Other reasons advanced concerned the possibilities
of variation in the carbon resistors due to heating, and the possible
effect of heat radiation from the black tubes on the filament temperature
of adjoining tubes. Extensive trial and error eXperinents'were tried
following this line of thought in an effort to determine the cause of the
output oscillation, but nothing concrete was found. Time tests were run
on an amplifier in an attempt to learn something of the nature of the

output oscillation. The results of the time tests showed the oscillations

1:7

to be greatest at first with a leveling-off period occuring after several
hours. Cne might infer from this that a "saturation" point is reached
wherein the carbon resistor undergoes no further change due to heating.

Two amplifiers built with carbon resistors were selected for further
time tests as regards this point of “saturation". One of the amplifiers
had been used quite extensively for other miscellaneous tests and therefone
was in effect, run for a considerable length of time. This one shall be
designated as amplifier No. l. The other one had been used hardly at all.
This one shall be designated as amplifier No. 2. A log of the observations
made is as follows:

10:00 A.E. : Power unit and amplifiers started. Oscillation
for sore setting tested (zero input voltage).

Re. 1 was more not at 20 volts and stayed con-
stant. No. 2 oscillated from beginning and was
not set at any value.

1:30 P.M. s No. l amplifier was at 2 volts, but showed no
signs of oscillating. No. 2 was still oscillat-
ing as before.

Eth P.M. x No.-l was constant at 2 volts, but was reset to
20 velts. No. 2 was still oscillating as before.

103h5 A.H. : No. 2 was giving a negative voltage. No. l was
constant at 52 volts.

Zahs P.B. : No. 2 was still giving a negative voltage. No. 1
was constant at 52 volts.

h320 P.¥. 8 No. l constant at 52 Volts. No. 2 gave positive

voltage, but was oscillating. Test terminatei.

3.3

The results of this run tend to bear out this "saturation"
theory a little more.

The first improvement that should be attempted would involve the
variable input resistors. Efforts should be directed toward gauging the
resistors on a central shaft. Perhaps the investigator will be pleasantly
surprised at the cost of having resistors made to order by'a manufacturer.
In any case, it is felt that this improvement can be made in due time. If
this suggestion can be accomplished, a second improvement of great importance
could be introduced; namely, the use of a servo motor at the point where
the input resistances are adjusted until the output voltages of the amplifiers
total one. A servo system serves merely to transform eleptrical data (a
voltage) into mechanical data (angular position of a shaft).

As an example, consider the addition, using a.d.c. amplifier, of
tie voltages having Opposite signs. if the positive voltage is the greater,
the output of the amplifier will be a positive voltage. The output voltage
of the amplifier will be zero when the values of the two input voltages are
equal.

If one of the input voltages is furnished by a potentiometer‘whose
brush is positioned by a reversible motor controlled by the output of the
amplifier, the output voltage of the amplifier can be automatically main-
tained at zero, if the connections to the motor are properly made. If the
positive input voltage is greater than the negative input voltage, there
will be a negative output from the amplifier which will cause the motor to
turn the brush in a direction.which increases the negative input voltage.
When, by this means, the two input voltages are made equal, there will be
zero voltage output from the amplifier and the motor will stop. This is a

typical servo system.

It is not entirely inconceivable that the calculator could be made
fully automatic in its application to the problem. To do this a servo motor
would he used at the point where the input resistances are adjusted until
the output voltages of the amplifiers total one. A storage or memory cap—
acity, consisting of a revolving bank of potentiometers, would also be used,
and in conjunction with this could go a servo system for balancing with the
galvanometer. This balanced voltage would be stored, and a relay might then
switch the amplifier for applying the Operating line equation into the sys-
tem and withdraw the balanced voltage from the memory unit for use as the
input to this amplifier. This output is then stored until used as input
for the first step in repeating the calculations over the next plate.
Another servo system would be utilised at the feed plate where the composi-
tions as calculated down from the top are supposed to match those obtained
calculating up from the bottom. In this way the amplifiers would first be
set-up to meet the conditions of the problem (reflux ratio, simplifying
assumptions, constants in Operating line equations, etc). Then the assumed
composition of vapor Off the top and liquid composition off the bottom are
introduced. The machine would be started and the calculations would proceed
simultaneously from the top down and from the'bottom up. If the composition
at the feed plate does not match, the servo system would throw the unit back
to the beginning, and repeat the process with different assumed and conditions.
Thus the calculations would go up and down the column until the correct end
conditions are assumed, at which time the servo motor at the feed plate would
stop the calculator.

Throughout this work the calculator has been applied to problems where-

in the usual simplifying assumptions could be made without introducing

So

appreciable errors. However, in many petroleum problems these assumptions
Of equal molar latent heats and negligible heat capacity changes cannot be
made. it is felt that the calculator could be applied equally well to
these problems for here the sectional heat balance equations are used in
conjunction with material balance equations on a trial and error basis.

A liquid composition on a plate is always a starting point in plate calcu-
lations. In this case, the variable input resistances would be correlated
with heat contents and molecular weights together with Kocharts.

As pointed cut previously, there are many applications of the calculator
to chemical engineering protlems besides distillation. An example cf another
application of the calculator to a chemical engineering problem would be
calculating flow of fluids (pressure drOp) in a pipe still. Due to vapor-
ization of the Oil, the viscosity changes through the equipment, and this
has the effect Of changing the value of Reynolds number. To avoid this in
the analytical calculations the pipe still is divided into sections over
which the change in Reynolds number is not great. In this case the resis-
tors would be correlated with f, friction factor, and flash vaporization
curves instead Of K-charts. The desired pressure drop at the end is known,
so a large pressure is assumed at the other end. Then the pressure drOp is
calculated over the several sections of the pipe still and if the end pressure
is that desired, the assumed large pressure value was correct. If not, the
assumed pressure value is altered and the calculations repeated until the
desired pressure is Obtained at the other end. Again the calculator could
be made automatic so as to repeat the calculations over and over until the

correct pressure is assumed.

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SELECTED RV". {Mali-T"?!
Baxandall, D., Catlogus‘gg the Collectioning the Science Euseum,

South Kensington. Mathematics lrfislculating Wuchincs
and Instruments (1926), p. 7. Cited from (11).

 

Knott, C. 0., “The Calculating Machine of the East: The Abacus“, in
Eggggg instruments and Methods gg Calculation
3.x. Horsburgh, ed., London, 3. Ball and Sons, Ltd.,
(191k). Pp. 136.1Sh.

 

Gibson, G. 1., ”Nepier and the Invention of Logarithms", in Modern
Instruments 223 Methods of Calculation, E.fl. Horsburgh,
ed. London, 0. Bell and gone, Ltd., (l9lh), pp. 1-16.

 

Cajori, F., Historz g; Eatnematics (1919), p. 7. Cited from (11).

Horsburgh, E. H., sd., Modern Instruments and yethcds cf Calculation
London, 0. Bell and Sons, Ltd., (iiiuyt pp. 181-22 .

 

 

Chapman, Se. P‘Icfil, Be. Nature, 150. 508-509 (17h2)s Cited from (11).
Turck, J. A. V., Origin 2; Modern Calculating Machines (1921), pp. 11-13.
Jacob, L.,'E=_Calcul Hecaniqug,_(1911), p. 3. Cited from (11).

Babbage, 8., "0f the Analytical Engine", Passe as from the Life 2!
2_Philospher, (lébh), Chap. V , pp. llZ-Ifil.

 

 

10. Ludgate, P. 8., “Automatic Calculating Machines", in Vodern Instru-

 

ments and Methods of Calculation, E. H. horsburgh,
03., London, 0. Raff and Sons, Etd., (l9lh), pp.
12h-127.

11. A Manual of ngrstion for the Automatic Sgagence Controlled Calculator,

CambridgeT-harvard Un1?3F§I£§ Press, (I9 , Vo . I.

12. Babbage, Cs. Ops Cite, pp. 116-1170

13. Ibid, p. 1220

lbs 108s I. Litfir‘tur.3

”Frinciples oi Operations of too Alphabetical Accounting Machine,
typo h05-, AM 17-(3).

"Card Operated Sorting hachinss‘, A! lh-l.

"Collator - Type 077‘, AH 25-5.

"Multiplying Punches“, AH 21.

1.]! I I‘ll I'll 1' ll ii 1". i‘lllll .I' ['1' I lllllll [- |.ll|ll. I Eli! I'll

 

1.

3.

h.

.S.

9.
10.

11.
12.

63

9' v ‘. v" p 0-. V. y..- r), 7(- #010,; "".Y
SL1 ‘a-o-I-L- do- *ou‘o a. ore-IJo-lsv-‘o-ce‘.‘ .L

Babbage, 0., "Difference Engine", Passagesm from the Life of a Philoapher,
(13J“)’ Cduye ‘J, pp. 41" J.

Wendell, 1.3., Catalcuo Li tic .rlmcu‘ws .-.n +"__.___c Scier cc ’umun,
§outh isnsington. Katie atics ”I Calculating Machines
and instrumeztc (1926), pp. BO-Bu.

 

Grant, 3. 8., ”On a New Difiercnce 3igine", American chrnal cf

Sciences and Arts (3) 23 113 ~117, (18

Robinson and Gilliland, Elements of Fractional Distillation, New IOrk,
Hoflraa-lEiII Cook Cc: fipany, (19EI).

 

Murray, F. J., Tile Tnec§z_ f flatJC3aticuli whines, hes krk: (13":
Crown Press, _(19h8).

Eckert, W. J., Punched Card Methods in Scientific Computation, Her Iorkc
Tzcmaa J. 3:3tscn Act ronc micaI Coaputing Bureau, Columbia
University, (19h0).

Morgan and Crawford, Petroleum Refiner, Vol. 23, (l9hh): 9- 3h}. CA
“5?” sub '
J t C

Elaindlhoicr, K. anJ Larsen, 3. M., American Institute of Yinin
Retallurgical Encineers, Tech. Pub. nd"1793, (1953)
p. -9.
“Giant New Calculator", Science, NL hbzlll, Ag. 12, 'hh.
R.C.A. Rec.iving Tube lanuAl.

Myers, 3. 1., Journal Scientific instrsments, Vol. 16, (193 ). Pp. 209-22.
Fry, Recon, "Designing Computing ficchanisms", Enchine Desi ., Vol. 17,

No. 8 (19L5). PP. 103-083 No. 9, pp. 113415; So. 10,

pp. 123-23; ho. 11, pp. lul% ¢3 No. 12, pp. 123-126; Vol.

18, (191.6). pp. 115-118,180.
Regener, Reviee 2; Scientific Instruments, Vol. 17, (19h6), pp. 180-89.

Bode, H. i., Network Analzsis and Feedback Amplifier Desi.gn, New York:
5.9a1 Nostraud,'rf§}l

EacCcll, L. i., Servo Rechanisme, New Ycrk: D. Van Fostrani 00., (19h5).

L! .1

 

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