OPTWEUM FEED PLATE LOCATiON IN
MULTECGMPONfiNT DESTiLLAfiON

Thain forhboguooéMJ.
MICHQGAN STATE UNEVERSITY!

Russell Howard Fey
1959i

THESIS

 

Rm??? ESE will“
5% H 21011

 

OPTIMUM FEED PLATE LOCATION

IN MULTICOHPONEHT DISTILLATION

by

RUSSELL HOWARD POY

A THESIS

Submitted to the College of Engineering
Michigan State University of Agriculture end
Applied Science in partial fulfillment of
the requirement: for the degree of

MASTER 0" SCIENCE

Department of Chemical Engineering

1959

70 I1 v11

their patiencq

DEDICATION

TO‘IU'VIIO, Janet, and daughter, Beth, for

their patience and understanding.

OPTIMUM FEED PLATE LOCATION

IN HULTICOMPONENT DISTILLATION

by

RUSSELL HOWARD POY

AN ABSTRACT

Sub-itted to the College of Engineering
Michigan State Univereity of Agriculture and
Applied Science in partial fulfillment of
the require-ante for the degree of

MASTER OI' SCIIIC'B

Department of Chemical Engineering

1959

V f

-1-

ABSTRACT

In a multiple component distillation design. it is
evident that there exists an optimt- £eed plate location
somewhere bemen the inaperative conditions of top or
bottom plate, except in the ease of an abbreviated colts-n
such as a stripper.

The two most comly used -thods for locating the
optin- teed plate are those of Gilliland and hontrose-
Scheibei.

Gilliland's method consists of choosing the feed plate
so that the ratio of the key components on the feed plate
is equal to the ratio of the key components in the feed.
the method has been checked by far too few problems because
of the long and tedious: plate to plate calculations required.
Several problems involving eleven plates have been checked by
Gilliland's method and an» fairly can with the correlation
developed in this investigation.

The method of Uontrose and Scheibel is based on an
impirical equation which involves the use of the ratio of
the key components on the feed plate at total and minimu-
refln. The equation appears to be based on only semi-
rigorous calculations since the simplifying «eruptions of

constant relative volatility and latent heats were made to

“I. I I»... n ...- {a

. ‘4.|.

355: :...S wilting:

-2.

reduce the labor of calculation. This empirical equation
also makes use of the less than rigorous terms of minimu-
reflun and ninimm cider of plates. no attempt was made
to check if the method agreed with the results of this
investigation, as the Montrose and schema: assmptions are
too general.

It was the purpose of this work to obtain an npirical
multicomponent opti-n teed plate location relation based
upon a considerable order of truly rigorous plate to plate
calculations. A rigorous plate to plate calculation is one
vhich takes into consideration both the variation of equili-
brit- oonstaat with temperature and an snthalpy or heat
balance about each plate. ' To perform these rigorous cal-
culations, a method of solution suited for a high speed
computer was developed and programsd. The electronic
digital computer used was the Michigan State University ao
cathode ray tube, single address machine.

The computer was used to solve several hundred problems
rigorously. The results of these problems were than used
to study the effect of certain variables such as reflux
ratio. teed composition, and umber of plates upon the rela-
tive optht- teed plate location. It was found that reflux

nth, umber
littls affect
Hutton of
various iced c
Mud no rain:
faction was I
Although
tin, so claim
M mun
1'01:th vol“
lWins as fa
e.u'eial up;
a“ M non.
N ’1'“ 10¢
“lieu: km.

.3-

ratio, nimber of plates, and feed temperature had very
little effect on the location of the optimum feed plate.

 

a function of In!“ I XL! was found to fit the data of
la: " xu

various feed compositions very well, and a correlation

based on relative optinum feed plate location versus this

faction was made.

Although many problems were solved in this investiga-
tion, no claim is made that all possible combinations of
feed composition, as well as types of components, i.e..
relative volatilities. will have the optimum feed plate
location as fond using this correlation. However, most
co-ercial applications will be covered. It is probable
that when non-adjacent key components are used the optima
feed plate location is more sensitive than when employing
adjacent keys. lince this investigation did not cover
sen-adjacent keys, care should be exercised when attenting

to use the correlation for such systems.

TABLE OF CONTENTS

Acknowledgement
Introduction

Statement of the Problem
lead for High Speed Computer
Derivation of Equations
Computer Used

Detailed Coding Procedure
Beta and Discussion of Results
Conclusions

Appendix

Nomenclature

Bibliography

22
25
29
67
so
90
99

100

123

125

acmowmcmrr

The author wishes to take this opportunity to
thank Professor .1. H. Donnell for his helpful guidance
and advice .. the many problems which arose during
this investigation.

Thanks are also extended to the Computer Labora-
tory staff of Hichigan State University for their
cooperation in making the HISTlC and the auxiliary
equipment available for use in this investigation.

INTRODUCTION

-6-

INTRODUCTION

The unit operation of distillation is an old one,
dating back to the early days of the alcohol stills.

Through the years, the use of distillation as a means of
separating a mixture of liquids into desired products has

been growing steadily. The patrolm- industry, perhaps,

has been the largest contributor in the expansion of dis-
tillation techniques and applications. It has been estimated
that two‘thirds of the total investment in petroleu refineries
is in distillation equipment.

The solution of binary distillation problems was first
analysed and organised into a systematic approach by Sorel (15)
in 1893. His solution consisted of making energy and mate-
rial balances around each plate and naming that equilibriu
is attained on each plate.

Practically all distillation calculations today use the
theoretical plate concept; that is, the “eruption that equi-
libriu is attained on each calculated plate. Then one applies
the theoretical calculations to actual design by using an
efficiency factor to obtain the nfler of physical plates
to use. For example, if 'a plate of certain design is
been to give fifty per cut efficiency on the liquid-vapor

\

mt. is que
Mutual 0!
mm.
tbs! plate a
Soul's 1
ad of the din
(“tilted by 4
‘0 calculate 4
db other and
'1 the liquid
WMIM a
th "Pot an:
“leuhtud b}
tray 1‘ Mat.

““1“ . C4
hull lad t

-7.

system in question, then two plates mat be used for each
theoretical one. Henceforth then, subsequent distillation
discussions in this paper will be confined to the theore-
tical plate approach.

forel’s rigorous method involves starting at either
and of the distillation tower and using and products
(obtained by a material balance and product specification)
te calculate downward (or upward) plate by plate until
the other end of the tower is reached. The composition
of the liquid on a tray is obtained from vapor-liquid _
equilibrii- data. Then the amount and composition of
the vapor entering this tray from the tray below is
calculated by a material and heat balance around the
tray in question. This last calculation is made by
seeming a certain vapor rate and checking from known
latent and specific heat data for each component to
see if this but data will allow the ancient of vapor
assumed to enter the plate in question. This, then,
issaentoinvolveatrialanderrorprocedure-a
tedious process.

Ponchon (14) however, developed a graphical method
which can be used to execute the Coral plate to plate

 

ulcuhtioa to
is s relative}.
tin as sathal
emit fractio
Istustsd vspo
€011th re
Tb ntbod tak
vapor rates fr
Itbod ICCOnpl

ltCsbe an

calculation for binary syst-a in a rigorous fashion
in a relatively short time. The nethod involves plot-
ting an enthalpy versus cognition (mole fraction or
weight fraction) diagram for both saturated liquid and
saturated vapor. This diagram is than used to satisfy
equilibriu relationships and to make material balances.
The method takes into account the change in liquid and
vapor rates from plate to plate, which is what the Coral
method accomplishes.
llcCabe and Thiele's (13) graphical nethod has be-
come the nest popular method of solution for binary mix-
tures; in fact, it has become a classic. This method,
as many others before and after it, makes certain
simplifying assmptions to handle problems more easily.
The primary assumptions one must make when applying a
solution such as this are:
l. legligibla sensible heat effects of liquids
and vapors as compared to latent heats.
2. Latent heats of vaporiaation per mole of
both components are equal and do not vary
with temperature.
3. legligible heat losses to surroundings.

1». lo heats of mixing.

.9-

The latter two assmptions are two which are
standard assinptions to nearly all methods of solu-
tion; and well they night be, for both effects are
very small in comparison to the large amounts of heat
being considered in a column. The first assimption
is usually a good one to make. However, the second
asst-ption is the one that could be greatly in error,
and thus cause incorrect results. For nest mixtures
of two components which are members of the cane
homologous series, the assmption of equal nolal heats
of vaporisation is a reasonable one, and the McCabe-
Thiele method provides a very quick and accurate nethod
of solution. The McCabe-Thiole method can also be
Iodified to handle cases where the heats of vaporiaa-
tion are man. In this case, the nethod is slower
but still gives good results.

The mechaniu of the McCaba-Thiele method consist
of plotting the equilibriu diagram for the components
in question on a vapor-liquid composition graph.
Plotted on the sen graph are the operating lines, i.e. ,
the upper operating line starts with the top product

-10.

couposition and has a slope equal to the ratio of
liquid to vapor rates in the top of the tower, while
the bottom operating line starts with the coepoaie

tion of the bottom product and has a slope equal to the
ratio of liquid to vapor rates below the feed plate.
The lines represent material balance equations and
relate the composition of'the‘vapor leaving a plate to
the composition of the liquid leaving the plate above
it. The W of plates required can be determined by
alternately'moving fren.the operating line horizontally
to the equilibritaa line, and from the equilibrim line
vertically downward to the operating line, and.so on
Autil the button composition is reached. The procedure
may be reversed and, starting with the bottom product,
take vertical and horisontal steps until the top pro~
duct composition is reached. lither way, each pair of
harisontal andnverticsl steps represent a plate. If
constant heats of vaporiaation are assumed, the operating
lines referred to above are straight lines. If the heats
of veporisetiou are not assumed to be equal, than the
operating lines*will not be straight, but curved. One
method of plotting the curved operating lines would be

.11-

to make use of a Ponchon diagram in conjunction with
the McCabe-Thiele diagran. But rather than do that,
one might Just as well use a Ponchon diagram by itself,
which accomplishes the same purpose in a simpler
fashion.

The solution of multicomponent distillation pro-
blena is closely related to the solution of binary
distillation prdblems, in that they are both based
on theoretical plates, material balances, and heat
balances. The procedure for the solution of a multi-
component problem is different, however, because the
boiling points of the liquids are no longer a function
of one component composition as was the ease in binary
mixtures. In nulticomponent nixtures (three or more
cmonents) the liquid on a given plate nay have an
infinite number of boiling points corresponding to a
certain conposition for one component, depending upon
the composition of the other components in the mixture.

In the previous discussion of binary distillation,
the lIcCabe-Thiele graphical method was referred to as
a classic because it gives rigorous (if curved operating

lines are used) yet rapid and clear solutions to most

 

.12-

binary distillation problems. There is no similar
method which is simple enough for multicomponent cal-
culations. Plate to plate calculations are therefore
widely recognised as the standard method for multi0
component systems. The other methods of solution may
be roughly broken down into the categories of

l) graphical solutions, 2) overall equations, and

3) eqirical solutions. Several examples of each
category will now be outlined briefly.

The two most common plate to plate methods used
are the lewis-hatheson (12) which makes the major
assuption of constant liquid and vapor rates, and
the Thiele-Geddes (16) which uses heat balances as
a major calculating tool.

The Lewis-Hatheson method consists of starting
with the desired and products and calculating the
oder of theoretical plates required. Plate to plate
calculations from both extremes of the colin to the
feed plate are carried out by using material balances
and equilibriu relationships and by making successive
approximations as to the temperature on each plate.

The reflux ratio mist also be found by trial and error.

-13-

The calculations in detail are carried out as follows.
The reflux ratio is first approximated and the com-
position of the vapor leaving the top tray is calculated.
Tor a total condenser this step would not be necessary,
since the composition of the vapor would.be the same as
that of the top product. By using some sort of equili-
brium relationship such as Raoult's law, relative
volatility, or K values (where y 3 K x and equilibrium
is attained when X y = l, K 3 f(T,P) ) the liquid com-
position and the temperature on the tap plate are found
by asst-ing values for the temperature until the sun
of the mole fractions, as calculated from the equili-
brim relationship, is unity. Similarly, the temperature
of the still and the composition of the vapors rising
from it are calculated. Reflux is seemed not to change
from.one end of the column to the other, except at the
feed plate where the reflux is increased by the amount
of liquid in the feed. By use of a material balance and
the dew point equation, the temperatures and compositions
on each plate are calculated plate by plate.

By studying the composition determdned.by working
up ft” the bottom, a suitable feed plate is chosen.

-14.

The composition of the light key (highest boiling comp
ponent‘which.does not come out in bottomxproduot) on
the toad plate is calculated. The computation is
continued until the hoevy key (lowest boiling component
which does not appear in appreciable amounts in the over-
head product) is of negligible concentration. If the
compositions thus determined correspond substantially
with those determined by calculating down the coin,
the problem is solved. If not, the composition on the
feed plate must be re-estimated and the last series of
calculations repeated.

The‘most important contribution of Lewis andfllhtheson
was to demonstrate that multicomponent systemm could.be
solved.by using a plate to plate calculation similar to
that used for binary mixtures.

because the method starts with the distillate and
bottoms maition, the method is not readily applicable
to*miatures that have two or three components which appear
. in both product streams. It will be pointed out later
that there are not enough degrees of freedemnto specify
the elect product composition together with the ads: of
plates. This is the most serious disadvantage of the

-15.

method. The Lewisduatheson method can be madeamore
rigorous by taking into consideration the changing
liquid and'vapor rates by applying the principles used
by Sorel, i.e., heat balances.

The method introduced by Thiele and Geddee in 1933
is a rigorous plate to plate calculation in which it is
not necessary to know or assume the products. It is,
however, necessary to start with the nunber of equili-
brit- plates and the reflux ratio. These constitute
the primary assumptions. The secondary assumptions are
the temperatures on each plate. The method makes use
of mole fraction ratios; that is, the ratio of the mole
fraction of a component in either the liquid or vapor
phase to the mole fraction of the same component in the
end product stream» Above the feed the ratios are with
respect to the distillate, below the feed*with respect
to the bottom product.

Calculations are performed from both extremes of
the tower toward the feed platen making use of the
previously mentioned mole fraction ratios. When the feed
plate is reached, these ratios are meshed to find the
composition of the products. After the feed plate mesh

.15.

is accomplished, one must go back and calculate the
compositions on each plate, which in turn are used

to calculate the corresponding temperatures. If the
calculated temperatures do not agree with those assuned,
the process is repeated using the new assumptions,
until the temperatures for all the plates agree on

two successive trials. ‘It should be stressed that

all temperatures must agree, since an incorrect tem-
perature at any point will invalidate all of the
calculations.

The Thiele~ceddes method is a very good method for
mlticomponent systems. Its main advantage over the
Lewiséuhthoson method is the manner in which the unequal
molal overflow is taken into account, as well as not
‘having to start with the composition of the products.

In 1935, Gilliland (7) published a shortcut method
for solution of mlticomponent problems by using relative
volatility, as well as a new function of relative
operability. Equilibrit- relationships are written for
the two key components in terms of relative volatility.
by writing component. material balances around a plate
for each key component, and by dividing one component
balance by the other, Gilliland uses the resulting

 

 

‘\‘_

.17.

equation to define relative operability. as then
codines the relative operability with relative
volatility to give the relative changes in composition
for one complete equilibrit- stage, i.e., from liquid
on one plate to liquid on the neat. By expanding the
above relationship for total plates in each section,
he obtains relative composition changes across both the
enriching and stripping sections. The method is a rapid
approximation that can be used with a fair degree of
accuracy for sharp separations. however, using this
method, it is necessary to know the composition on the
feed plate.

The limitations of the method are that there are
too many simplifying asst-ptions. for instance, if
the relative volatility or operebility varies from one
end of the calm to the other, as aritbetic average
is used. it is, nevertheless, a good method for giving
quick approximations, which could be used as a first .
estimate in a more rigorous method.

Some investigators, such as Lewis and tops (11) and
Jenny (10), develOped graphical solutions conerable to
the McCabe-Thiele method.

.13.

The Lewis and Cope method consists of constructing
a separate plot of y vs. 1 for each component. Assuming
an equilibriu relationship of y : Ix, with K dependent
on temperature only, equilibrit- lines are plotted for
several temperatures, and the correct temperature deter-
mined by trial and error. This process is repeated for
each plate. The method is very cuebersome and also
requires a knowledge of the composition of the products.

Jenny proposed a graphical'method.utilising a 3
vs. y diagram similar to the McCabe-Thiele diagram,
which involves constructing a modified equilibrima
. line, which is supposed to allow for the nonvvolatile
lighter than hay and heavier than key components. The
mums. line is 916cm by making a few plate to
plate calculations. Separate diagrams are used for
both the stripping and enriching sections, using the
light key for the enriching section and the heavy key
for the stripping section. The operating lines are
seemed to be straight. This method requires knowing
the composition on the feed plate.

a method based on overall equations for both sections
of the tower‘was proposed by ldmister (5). The equations
are based on the use of absorption and stripping factors

will: to those

\

method at th‘

In, so-cal
pond, based on

“We After

haul of these

It 1939. 31':
in: chum.“ a“
f" ‘ 31M scpm

“WM isba

similar to those used by Kremser in absorption calcu-
lations. After evaluation of these equations, the results
are meshed at the feed plate.

Kaey so-called empirical solutions have been pro-
posed, based on various correlations of past calculations.
Several of these correlations will nov be discussed.

In 1939, brown and Martin (1) proposed a method
for obtaining the number of equilibriu plates required
for a given separation at a specified reflux ratio.
the method is based upon an eqirical correlation and
the variables plotted are actual reflux divided by
minin- reflun versus the actual plates divided by the
mini- plates. Key components and pinch-point concepts
are used. The correlation was developed from the results
of rigorous calculations for a umber of separations.
lost of the systems were binary, with some mlticomponent
systems.

About the same time that brown and Hartin published
their method, Oilliland (0 proposed a method very si-ilar.
although developed independently. this correlation plotted
the actual minus the linin- plates divided by one plus

the actual pie
reflux dividec
variables are

Gillilan:
rigorous calm
The correlatic
Went cyst
Ilittle 31'.an

In 1950,
Mon which 1
Plates to mm
ratio of “m
{ions of Fans]
"1““ for the
h of th‘ ho:
hum the :1.
“link! re;
”‘1"- com
"flu, Thus
M “my.

-20.

the actual plates versus the actual minus the minimum
reflux divided by one plus the actual reflux. The
variables are plotted on log-log scales.

Gilliland's correlation was also the result of
rigorous calculations for a umber of binary mixtures.
The correlation was also checked for a few multi-
ement systems. The correlation of Gilliland is
a little simpler to use than that of Brown and Martin.

In 1950, Donnell and Cooper (4) proposed a corre-
lation which involved plotting the ratio of actual
plates to ninimus plates versus the logarithm of the
ratio of actual boil up to ninim boil up. The equa-
tions of Females (6) and Underwood (1?) are used to obtain
values for the mini-um plates and minimum vapor load.
One of the scat important advantages of this correlation
is that the curve approaches a straight line in the region
of liaison reflms. This is of inortance since nost
optimal conditions lie in this range near the ninian-
retlur. Thus. it is desirable to be able to read the
graph easily, or even interpolate if necessary.

Several other investigators made correlations

sinilar to those already discussed. Included is the group

fl correlati-.-l
Fuhert (9)-

In, 1915}.
detenzining tie
nth-:5. consists
ratio of tin no
the feed is be:
the plate above
Silliland's net.
feed is partial

Elcntmss a
I” Optimum rec
0” an enzirica‘.
M10 01' the 1.2
“i Eizliuurl ref
3&1: 86:21-p1.~;~.

”MEtions of
ieea:a new We} )0
‘ 4cm

i.
“‘3 aIthaca

as 21..

are correlations presented by Colburn (3) and by
Herbert (9).

In, lQhO, Gilliland (8) published a.method for
determining the optimum food plate location. This
method consists of placing the feed plate so that the
ratio of the mole fractions of the key components in
the feed is between the ratio of the key components en
the plate above and below the feed plate. According to
Gilliland's method, there is a slight variation if the
food is partially vaporized or all vapor.

Hontrose and Scheibol in 19h6 (8a) offer a.mcthod
for optimumgfood.plato location. This method is based
on an.empirical equation which involves the use of the
ratio of the key components on the feed plate at total
and minimum reflux. The equation appears to be based on
only semi-rigorous calculations since the simplifying
assumptions of constant relative volatility and latent—
heats‘uero made to reduce the labor of calculation.
This empirical equation also makes use of the less than .
rigorous terms of minimum reflux and minimum number of
plates. No attempt was made to check if the method
agreed with the results of this investigation, as the

honorees and Scheibel assumptions are too general.

sum 05' THE P3031311

.22.

SIAM“? 0! m PROBLIH

Tbs ossd o! s rigorous solution to uultioo-ponsut
distillation problus is not s sow idss. It on ststod
sols yssrs book by Gathers (2) thst shot ths sugisssris;
protsssios ussds is ultioo-possot calculations is
"sithsr so sssot solution. soon though it is difficult.
or‘ss optimists solution. it it is sssy.” With tbs
sdosst of‘high spssd.oosputors. tbs ohsllssgs to sss who
could dsvsloprsu.sssot solution first‘hss gross consi-
dsrsbly. This invsstisstios was unsortsksn.to: l) dsvslop’
so mot solution using s high spssd ooqutsr as s tool to
potion tho osloulstious, sad 2) uss tbs usct solution
to study tho offset of (sod troy loostiou on tho dsxros
of sopsrstioo is sultico-poosut nixturss.

Whoa s distillstios oolusn is assignsd sud built.
it is dssirsd thst for s givsu snubs: of pistss. rsflus
rstis. out food oospositios. ths1sssilus sspsrstios.bs
obtsinsd. It is dssirsbls. thou. to loosts ths food
pists so thst tbs options sspsrstiou is obtsissd.

1's illustrsts tho uscsssity to: tho opti-n flood
pasts loostiou, ooasidsr tbs following bissry’problss.

-23-

 

 

 

 

 

 

 

 

 

 

Figure 1

If the feed plate were not located on the fourth
plate from the bottom, but higher up, it would require
more plates to do the same Job of separation, or a worse
separation would be obtained, if the same number of plates
were used.

The red line in Figure 1 illustrates the case where
the feed plate is not the fourth but the sixth plate from
the bottom. In this case, it would take two more plates to
do the same Job of separation. Simdlarily, if the feed plate
were located lower than the fourth plate from the bottom,

the same situation would arise.

-24-

miticonponsnt systems are not so easy to illustrate
as the foregoing binary one. but tbs sans type of relation-
ship exists. That is, there exists an optinun feed plate
location, or series of locations, so. that a sari-\-
ssparstion is obtainable.

In attempting to study the affect of feed tray
location, it boconss necessary to work out nsny problans
to ass how the option- vsriss vitb umber of plates.
reflux ratio. and toad composition. In a study snob as
this . a rigorous solution should be used in order to get
a sore accurate picture of the variables involved. Thus.
this investigation utilised a high spssd conutsr to
solve my problsns in a rigorous fashion (that is, taking
into account changing vapor and liquid rates and perfect
latching at the {sod plats.)

unto FOR HIGH SPEED COMPUTER

NEED FOR HIGH SPEED CW

The importance of greater and greater accuracy has
been brought out as one reason why more rigorous methods
of solution must be employed. The more rigorous a pro-
blem, the more trial and error calculations are required,
until finally it is conceivable that an engineer working
a rigorous multicomponent distillation problem might
take weeks to solve the problem. Most of that time
would be spent doing the rather routine trial and error
calculations to make sure that all compositions, amounts,
and temperatures were consistent with the material
balances, heat balances, and equilibrium data. The
answer to the engineer’s dream is.- a high speed electronic
computer. Of course. the engineer would still be
required to set the problem up, but the computer would
do all the calculations in a very short period of time.

The same problem that might take an engineer a
task to solve could be solved using a computer in a few
hours or less.

The great Speed at which computers operate is also
inportant from an economic standpoint. Once a program
has bsen written for a problem, it can be used over and

over for the solution of nsny sinilar problems. Although

~26.

the cost of buying or renting a computer is quite high
(rentals run on the order of $200 per hour) the cost

is still substantially lower than paying the salary of

an engineer for the time necessary to work out the proble-
by hand.

As was pointed out previously. the study of the
effect of feed tray location on the separation obtained
is one which requires many problems to be solved. This
lends itself to computer application very nicely. since
the computer can perform a rigorous solution in a short
period of time.

Rot only does the computer provide a means of
studying the effect of feed tray location, but also it
affords a detailed study of other variables which enter
into the problem. One of the variables now being
studied is the effect of condition of feed, i.e.. pre-
heated or cold, on the tower performance. Another _
inportant study is being made on the relationship
between umber of plates and reflux ratio to obtain a
desired separation.

Another important advantage of the use of conputers

is their reliability. Although some night argue this to

-27.

be a trivial point, it is nevertheless an important

one. The reliability of computers is certainly better
than an engineer running a slide rule or desk calculator.
It must be admitted that computers do occasionally make

a mistake. However, when a mistaae is made, it is almost
always so obvious that it is immediately noticed. On the
other hand, an engineer could easily carry a mistake on
and on without it being noticed.

In the discussion of previous methods used in
solving multicomponent distillation problems, it was
mentioned that some methods use the ratio of the so-
called key components as a criterion for convergence
of the feed plate meSh. This, of course, is only an
approximation and serves to shorten the calculations.
Once again, the compute- can perform these calculations
exactly and thus eliminate the need for the assumption.
It may be argued that this advantage of the computer ii
merely due to the Speed at which the machine operates.
However, there is more to a computer than speed and
accuracy. It enables one to solve lengthy and complex
problems that could not be worked without the use

of such a computer. ‘Many of these seemingly

{possible so

11¢er by con;

 

There are
Men of applyi
problems. The
one of tin welt
presented by 01
alternative cow
[Mrticularly 31
litter altema
Iona 0f the ex
‘0 “Mastic cl
ital: or b eta

'hich til. math
to uh

~28-

impossible solutions are now being handled very
nicely by computers.

There are two alternative approaches to the pro~
blen of applying computers to solve distillation
problems. The first alternative would be to adapt
one of the well-known and accepted calculation methods
presented by other authors to a computer. The second
alternative would be to develop a calculation method
particularly suited to automatic calculation. The
latter alternative was chosen since it is felt that
none of the existing calculation methods are suitable
to automatic computation, either because of the method
itself or because of certain simplifying assmnptions
which the method required, which were felt unnecessary

to snake.

DERIVATIOI or BQUA‘I'IOIS

flu wlutio,
is on of trial

the Iiiplifying .

m not side. 1'!

 

obtain a solution
2) arterial bald:

At this poi:
“VII feed, the l
lifferent in a In

“mm. In a b:
M *7 'PEley;

-29-
DERIVATIOI 0F EQUATIONS

The solution of a multicomponent distillation problem
is one of trial and error. This is even.more pronounced if
the simplifying assumptions of constant liquid and vapor rates
are not made. The three tools with which we are armed to
obtain a solution are: l) Vapor-liquid equilibriumnconditions,
2) material'balances, and 3) energy balances.

At this point, it is well to point out that from any
given feed, the problem.of product specification is quite
different in a multicomponent mixture than it is in a binary
mixture. In a binary mixture, the product desired may be
fixed by specifying the composition of one component, since
the composition of the other component will then also be
fixed. however, in a mlticomponent mixture the product
cannot be specified for all the components. Instead, only
the composition with respect to one component may be specified.

The situation of not being able to specify the products
and the fact that computers are limdted as to the number of
simultaneous equations they can solve, leads directly to a
trial and error solution. The solution becomes, then, an
iterative process of assuming the composition of the products,

working through the problem, and correcting the product com-

positions until the asst-ptions prove correct.

.30-

The primary'variables which rust be known.before
starting the solution of a problem are: 1) feed composi-
tioe and condition of the feed, 2) Reflux ratio, LID,

3) number of plates above and below the feed plate, and
‘) tower pressure. The latter is necessary for equili-
briun.and.emthelpy data.

There are two types of problems whdchLmey'arise. The
first would be the problem of designing a new calm with
the proper number of plates to give a desired separation.

The desired separation, of course, must be in accordance
with the foregoing discussion on product specification.

The second type of problem would be the utilisation
of an existing calm and the desire to determine the products
obtainable'with.a given feed. Actually, both types of pro~
blems would be solved utilising the same method of solution.
The problem of determining the eI-ber of plates necessary
to obtain a desired product requires an estimate of the lumber
of plates, working through the problem» and checking the
results*with the desired products. If the results agree,
than the number of plates assumed*will be sufficient. If the
results do not agree. then a new estimate of the number of
plates must be‘made, and the problem reworked until the

.31.

products obtained are acceptable. The problem with the
nfler of plates already known and the products unknown
is solved using the same method of solution as for the
above type prob]... except that the nfler of plates

need not be assumed since it is already known. Therefore, 5‘1
the solution of both types of problems will be handled as ]
one,andthem-berofplatesinthecolmwillbetaken 5
as a known variable. f;

 

The general solution of the problem will be to asst-e —“
one of the product conceitions and quantities (the top
product in this solution) and calculate from both extremities
of the tower toward the middle util the feed plate is reached
from both directions. At this point a mesh, or comparison,
of the compositions obtained from both directions is made.

If the compositions are equal, to a specified degree of
accuracy, then the products asst-ed are correct and the solu-
tion is complete. If the compositions do not nesh, then the
ensued product is nodified in proportion to the variation of
the mesh, and the calculations are carried out again until the
feed plate mesh is satisfactory.

In the development of the method, frequent reference to
previous equations already developed will occur, and so are

-32-

numbered to help identify them. A diagram is provided to

help picture the problem and also to refer to as to nomenclature.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

rj i - (L
*L J ‘r
v, F 1"
£ i T; LO
jVM‘Z J The.
TV "’
”’ m 7'"
F'
3K:
1
‘th Tn
IwflvoLnJ'
T -I
t Ln-o‘
Ti

 

 

1..
Figure 2

For simplification purposes, a basis of one mole of
feed is chosen. This allows the composition of the feed,
expressed in mole fractions, to be the moles of each conr
ponent in the food. It also provides an easy, quick estimate
of the amount and composition of the top product by estimating

-33.-

the nfler of moles of each component which will be
produced overhead. The first estimate of top product,
as well as estimates of the top temperature, bottom
temperature, and snout of vapor in the bottom section,
are read into the computer as data. In the section on
the actual computer progra-ing, the entire list of data
necessary to work a problem will be outlined.
The statement and derivation of the algebraic pro-
cedure used in the problem follows:
1) Calculate the amount of overhead product.
9 3:59 a: bi
for the first iteration this step is necessary,
since the top product has been asst-ed. however, in
later iterations the top product will be altered, making
it necessary to perforn this calculation.
2) Calculate the amount of botton product.
W O I - D 0 1 - D
3) Calculate the bottom composition.
1“ e "71 w l“Di
4) Using the assumed moles (sum) of each component
and the B from step 1, calculate the overhad

composition. X” II 22%

-34.

5) Calculate V, and 1..o from given reflux ratio and D

calculated in l.
v, = D(R+l)

L0 = RD
6) Determine the t-perature on the top and bottom
plate, using the bubble point and dew point

calculations as shown below.

r, of 7‘0p WA... g. 7:1" = /

Tsaf boHom when g KL Xw; =/

 

The values of K1 are obtained from a third degree

polynonial in temperature. The R values are seemed to

be dependent on temperature and pressure only. When the

correct temperatures are found, then K12“. '3 T“ and each

Tu is saved for later calculations.

7) Determine the dew point of the overhead product

as follows:

To when Z K; Km; = /
d.
8) Calculate heat flux in top of coin by sub-

tracting enthalpy of reflux from enthalpy of

top vapor, thusly:_
h, = L, 2;. A“ X0; a." 7”c
H, = V' Z '57:: xoi 4+ T,

4:

On: HI“ A0.

his hat
Itwuld have ti-
mm condens I
” Amanda
Q: from
of the
the tan
enthal;
produm
Meat
calcul
temper
Hake a

‘ hilt ba]
”Nam, 81?!

T09 se

-35-

Note that this solution is for a total condenser.
It would have to be nodified slightly for the use of a
partial condenser.
9) Meaning no heat losses to surroundings, calculate
Q: from enthalpy of the feed and (2.. The enthalpy
of the feed is read in as data and is calculated in
the same manner as all other enthalpies, i.e., the
enthalpy of a mixture is the ‘l- of the individual
products of mole fraction and enthalpy of pure com-
ponent. The enthalpy of each pure component is
calculated fron a third degree polynomial in
temperature.

flake a heat balance around the entire colmn?’
hr"“s"“c“‘n“‘w
153(thrns)f(hcfho)
(bs’hw)'<hc’bn”"s
A heat balance around the top end botta section
separately gives:
Topsection H-hpfhclh
or H-h'hnlhc'QA
Botton section B } h" I h I h,
or n-h-hs-hv-Qr
Thus Qr=Q‘-h'

21m to

has the conden

flats to plate calculations are now ready to be nade

from the condenser down to the feed plate.
_ TV». lLo-m
Tm IZT'W m'fh p/oj'c
TVn-l le
Flgure 3
The general case of plate n will be illustrated. By

 

 

looking at the second plate from the top in figure 1, it is
easy to see just what is known and what is unknown. The
same will apply to the m'th plate as one works downward.
The composition and temperature of L...” are known, while Vm
gut) Tm , Low”, and 1...; are all unknown. Actually,
Vm-,,T,,,., , and w“); are unknown also, but come into
consideration on the next plate. If there are i com-
ponents present, then there are 2i+3 unknowns to solve for.
The equations available for their solution are: 1) total
Interial balance above m'th plate and around top of tower,
2) i component material balances around same portion of
tower, 3) heat balance around above mentioned section of
the tower, d) dew point equation, and 5) i equilibrit-
equations. It is well to point out that if a set of
simultaneous equations were set up for the whole tower, it
would involve equations which would an»: (2i+3) :1... the
o‘er of plates in the column. It is conceivable to have

-37-

a colm with fifty plates and ten conponents, which would
require the solution of 1150 equations and 1150 unknowns.
Very few, it any, conputers even approach a capacity large
enomh to handle such a problem except by an iterative
process. Even if a coeputer were large enough to handle
the 1150 equations, it is doubtful if a solution could be
obtained, since it is unlikely that all the equations would
have constant coefficients.

The procedure used here to solve the (2.3-3) equations,
one plate at a tine, is a trial and error nethod based on
seeming values tor-Land Lmfl and using lewton's nethod to
arrive at better values for the asst-ed variables. This is
done until the correction factor for rm and L...“ becomes
arbitrarily close to earn.

10) Choose a temperature T," and a liquid rate L...“ .

A good first estinate is to use the values obtained
as answers to the previous plate. After the first
iteration through the solm this step will be altered
by using the te-perature and liquid rate for the
previous iteration as the first guess, since they
will be a better approxination than the te-perature
and liquid rate for the preceeding plate.

-33-

ll) Calculate Vm from b and the asauned 1...", by an
overall material balance around top of tower.
l/m = Lmi, 1* D
12) Calculate 51...; from a component material balance

around top of tower.

gm; 3 Lou: xnm-di * Dorm;
V».
13) Calculate ¢ using seamed T... This also gives
the values of X”; .
¢ = l- 2' HM /Krn
Note that ¢ wil1 approach nero as the correct
tenpera ture is found.
14) Using assumed Tm, gm; , and 7f,“ as calculated in
12 and 13, find Hm.
H'" = Z ’7’” 5/»,

15) Calculate hm, tron tenperature of plate above, T»,w .

Ami-l : Z Am.” va-l

16) Making a neat balance around top of coin,
nu 05'.
¢’-‘- / - VMHM'LM*I I‘m“
99..

I
¢ nust also tend to earn as the proper T,,, and Ln,“

are obtained.

 

Th: flwton
taxation! cons ‘
hrimim of
{or III M vari
which an: be au
utiantu to in;
th hrivatives

17) M
M

id
5L

bt

\

O/IQ/

-39-

The Newton technique for quick convergence of

iterations consists of substituting the elapse, or

derivatives of the fmction at the point in question,

for the new variables. A correction factor is calculated

which met be subtracted fro. the previous Tm and L"...

esti-etes to inprove their accuracy. The equations for

the derivatives are:

17) r) 49
ET...

axle;

_ a m
P: '- 57: (z '5 /Km)
2 .12.. (b. +2cKTm + anti)

6T...

Q1
9:

 

0/

P
3
:2

Km

P. = 73-5“ (2 E""/A<,,,)
Z

xmel " gm
Km

Vm

KnHm “Lam howl)

Q‘

P3” T’T("

=-—5—':Z’Cb. *ZchTm *3dhrmz)3m

 

(I... We Hm "’ Ln"! bowl)
I

M 9| 0‘

p.= at.

‘-_Q’: [5: I?“ X0314»: - ZZMH Kin-u]

 

A1

19) The new
by “1121

Previo

Thu. new
“PI 11 . 19 a

“at step
N '1'“ is c
M the col-
‘tu ‘50 feed 1
“W Ming 1
"M for thfi f4

Th. “Icula
that 1. “Ch th

.40-

18) The correction equations are:
p. AT... + P: AL»... = ¢
P3 ATm "’ P-I ALM-H = ¢’
rewriting and solving for ATmand Aim“: '

AT... = (Pm-AQ’

Pa] Pa '72 P3

ALM+I = Q -/OI!ATM

P4
19) The new esti-stes forT... and L...“ are obtained

 

by subtracting the correction factor free the

previous esti-ates:
Tm(ncw) = Tm (old) " A Tm

Lmu (“U”) = [nu-H (0/0!) - A Law”

These new values for Tmand L"... are used to go through
steps ll - 19 again until they satisfy all the equations.

After steps 11 - 19 are solved, the solution for the
n'th plate is conplete, at least for the first iteration
through the cola. Steps 10 ~ 19 are repeated I! tines
util the feed plate is reached. The conposition of the
liquid leaving the feed plate as calculated above is then
saved for the feed plate nssh later.

The calculations are now perforned on the button of the

tower in nuch the sane nanner as for the top of the tower.

.41-

_ IV" LLnel
Tn [;%* r, e

Ive-a 1L"
Ftsure "l

‘A

n ‘1'}! plQT’E

 

 

by looking at the reboiler of Figure 2 and considering
it a theoretical plate, one can see that the known quantities
for the solution of the n'th plate will be the conposition
and teeperature of the vapor entering the plate fro- below,
i.e., plate n-l. The mknown quantities are 'n-l' in, x“.
T“, and Y(n-l)i° Once again, there are actually nore unknown5
in Lhfl)’ T01“), and Hall-)1 but they will be solved for
on the (ninth plate. The sale equations as used for the
section above the feed plate are used in this section below
the feed plate, except that the bubble point equation is
substituted for the dew point equation. The lewton nethod is

used here also, with the alteration that ‘1"I and V” are the

1
two variables which are estinated.
20) Choose a first estinete of the tenperature, Tu,
and the vapor rate, 'n-l‘ Use as a first estinste
the tenperature and vapor rate fron the solution of
the previous plate. After the first iteration through
the tower, this step will be altered the sans as was

step 10 in the other section of the coin.

-42-

For the first plate above the reboiler, the
original estimate cannot be obtained from the
plate calculated below it, and so must be a good,
qualified approximation. The vapor rate can be
approximated quite well by considering the reflux
ratio and the condition of the feed, i.e., liquid
or vapor, superheated or supercooled.

21) Find K,"- using assumed Tn :
K”; = a,“- + b,“ Tn "' Cm: Tn: * din: Ta,

22) Calculate the liquid rate from a material balance:
Ln = V -, + W

23) Calculate the composition of liquid on the n'th

plate using a component material balance:

X,”- .-.- WXV; 4- V..., Vow):
Ln
For the first plate 3‘“) g was calculated in
step 6 when E Kn xwal , For succeeding plates
Sim-m: will be calculated in step 24 of the
previous plate.

24) Calculate 9 (bubble point equation.)

a = I - Z Kn x.
23) fro- the asst-ed Tn , and the tenperature of the

plate below, calculate H..-, and h... -

H a szv-I .f/n-I
h. = :7», x"

26) Calculate 5’ (heat balance.)

9’ 3 I "' Ln kn " MD-l Hfi-L
Q.-

27)Thelewtonnethodisusedinthesanenanner
here as for section above the feed plate and
the equations for the slopes will not be derived.
Find 3" 3-!
3, - $3.03., 1» 2a,, 7;, + 34,, 7.3)
agar-,5. Z K. (3..-, - X»)
3, = -L,, /Q.-f(6/,"fzca73 *30'1. 7:22))“.

3" -_QL,. [f [70,,‘g,_, - El“! 5"]
20) Deter-ins the correction factors A 7'» and A V,,-, .

41,, = Gav-226’

 

 

2034’ iii:
AV"_’= fil-‘gisdrn
4/

29) Detenine the new values of 77, and V,,-, to put
back into step 21. steps 21 . 29 are repeated
util the correction factors becone arbitrarily

close to earn.

V
Step. 20 -

so ant be rep“

 

bl coapositions
u ulcuhted fr.
m mm to
The feed p1
“volition of c
t“ “3 condena
th “boiler Up.

44-

Tn (new) ' Tn (old) - ATn
Vn-l(new) 8 Vn-1(old) -Avn.1

Steps 20 - 29 represent the solution of one plate, and
so neat be repeated I tines. When the feed plate is reached,
the co-positions of the liquid strean leaving the feed plate,
as calculated free the condenser down and the reboiler up,
are conpared to see if convergence has been attained.

The feed plate nesh consists of taking the ratio of the
co-position of the liquid leaving the feed plate as calculated
fro. the condenser down to the conposition calculated fro-
the reboiler up. This is done for all conponents.

X (down)

:11

I“ (up)

This ratio r1 should, of cones, approach unity. The

r1

convenient property of r is that it not only tells whether
or not one has convergence but also gives an indication of
the sine and direction the correction on the use-ed products
should be nsde. If r is greater than mity, then the anount
of that conponent coning out overhead has baa assumed too
great. Conversely, if r is less than one, the quantity of
that ccnponent in the overhead has been asst-ed too small.

-45-

The nagnitude of r also indicates the magnitude of the error
in the assumed products.

The important thing is that the ratios be used to
correct the products in such a manner so as to conforn with
the overall naterial balance. In order to be able to apply
the ratios to all components, it is very important that sons
quantity of each component be assumed going out in each
product. This can be illustrated by taking the case where one
co-ponent was alliflBd to cone out in only one product, i.e.,
top or button product. If this were so, then when the asst-ed
product for that particular component was nultiplied (or
divided) by the feed neah ratio, the anount of product would
still be sero, and thus unchanged. It should be pointed out
that the components will always be corrected in the product
strean where their composition is the smaller. The product
strean containing the larger conposition of the conponent is
then corrected using an overall eaterial balance.

For the conponents which tend to leave in the overhead,

the following equations are used for correcting the canned

products:
me. (rewsed) " T; ' wa‘. (prewous)

D X“ (rewsea’) = Fxfl "' waa (rewsed)

-45-

For components which tend to leave in the bottom

product the following correction equation is used:

onafrewsed) = 7-,;- ong (prewous)

The fact that the revised wa; is not calculated here
for the conponents which tend to leave in the buttons is
explained by pointing out that when re-iterating through
the entire problen, one nust go all the way back to step 1.
It can be seen that in steps 2 and 3 the null and Km:
are calculated, and thus need not be calculated here.

If the feed plate lash ratio is arbitrarily close to
one for all coemonents, the solution is cosplete, at least
for the nil-bar of plates used. However, if the problem is of
the type where one wants to deternine the amber of plates
necessary to obtain a desired separation, then the solution
may not be complete. That is if the products do not nest
the desired specifications, than a new cider of plates must
be chosen, and the problemnworked through again.

This is the advantage of using a computer, since it
can calculate the new conditions very quickly, while without
such a machine one Inst be satisfied with trying to set
approximate specifications.

CWUSID

.47-
comma uses

Throughout this investigation, the conputer owned
by hichigan State University was used exclusively. The
conuter is named "The Kichigan State Integral Conputer,"
better known as HISTTC. The conputer operates in the binary
amber ante. and lakes use of punch tape input and output.
II! card input and output are also available but were not
used in this investigation.

Tb storage or nsmory consists of forty cathode ray
tubes and the associated circuitry. At the present time,
the capacity of the computer is rather linited, with only
1024 storage locations. However, this will soon be altered
to well over 16,000 locations, when the new magnetic core
nary is installed.

ensue is a single address nachine, i.e., each instruction
carries only one address. Orders for the mac contain two
sydols free the deci-sl digits 0, l, 2, 3, 4, 5, 6, 7, 8, 9,
and the letters K, 0, I, J, I, L, and one decimal nuer
between 0 and 1023. The two sy-bols form the operation code,
while the amber is an identification number (address) for
one of the 1024 electrostatic nanory locations. In essence,

the operation code tells the computer what to do and the

 

up «he» tell
to: muses, th
duty locati
M orders
nerds: pair.
Mn is each we
hit to right.
lines the H

Itch order sue t

-43.

the address tells it what to do it with or where to go.
for instance, the order '5 133 says, "Bring in the contents
of “I" location 133 to the acctmulator and add one to it."

Two orders constitute one word and are referred to as
an order pair. There is a lefthand order and a righthand
order in each word. The orders are obeyed in sequence
left to right.

since the 141an is a binary machine, the address in
each order nest be in binary for. before entering the machine.
This would require a tremendous amount of work by the pro-
grausr; a'nd,‘.tfortunately, there is an input program avail-
able to convert the decimal addresses to senadecimsl
automatically. This progrsn is known as the Decimal Order
Input (DOT) and is used in all problems.

When using the 901, each order nust contain a two digit
operation code, an address batsmen 0 and 1023, and a tarni-
nstion synbol. The termination synbols are R, 8, I, J, I,
and 1..

because of the complexity of the nethod of solution of
the distillation problem, it was decided to use the floating
point subroutine even though the subroutine actually causes

the conputer to perforn the calculations at a such slower

-49-

spssd. However, by using the floating point routine,
hereafter referred to as A,, the tedious task of scaling
the nudbers was bypassed, since this subroutine keeps
track.of'the decinal point autonaticslly. To use ordinary
HEBTIC orders would require that all numbers be scaled
so that they are between plus one and minus one. This
scaling lust also consider all numbers which'will be cal-
culated, snaking sure that they, too, would lie in the
proper range.

Almost the entire distillation progran is written in
A,, with a few orders being in ordinary MISTIC language.
For any questions that arise concerning the few MISTIC
orders, reference should be ads to the 111an Progra-ing
Manual. In the appendix of this thesis is an outline of
the orders encountered in using the A., subroutine. This
nay prove helpful as a reference when reading through the

progran.

DETAILED CODING PROCEDURE

-50-

DETAILED CODING PROCEDURE

This section will be devoted to outlining the
problems of progra-ing s problen for use on a high speed
coeputer, as well as the detailed coding of the main
progran used. It is intended that such a detailed coding
of the program night aid the reader in visualising the
lethod of calculation used.

Liquid vapor equilibrium data used throughout this
investigation was of the type y ' Ix. It was assumed that
K depended only on temperature and pressure. In order to
quickly calculate a desired K value at a given temperature,
third degree polynomials of the fore K I ak } ka [ csz I ak'r3
were used to describe the variation of waith temperature.
The four constants were evaluated for various coeponents,
using the nethod of least squares on the data of Cooper and
Donnell, and Harwell. These polynomials were prepared at
various pressures within the range of operation for a
distillation calm. .

Inthalpy of liquids and vapors of each component were
also represented by third order polyno-ials in tseperature.
The data used was from Maxwell. The enthalpy of a mixture
was seamed to be the sun of the individual products of eole

fraction and enthalpy of pure product.

-51-

Before one reads through the detailed coding of any
progran, it is well to point out that in many cases,
calculations are set up in a far different manner and order
for a coeputar than would be done if a person were to do
the sees calculations by hand or with a desk calculator.

It should also be pointed out that in programming such a
proble- for a conputer, there are quite often several
choices of orders one could use. Thus, a person reading
this progra- night well find places where orders could be
changed or possibly even left out. This is especially toes
in the progran illustrated here. Due to the conplexity of
the problem, there were many changes to be made after the
program was put together. In order to conserve tine, the
progra- was altered in sort of a piece-eel affair. However,
dhis in no way affects the principles involved, nor the
calculations which are being carried out.

Iafore getting into the main program, it should be
pointed.out that the enthalpy polynoeial subroutine (BER)
and the equilibrit- constant subroutine (KS!) will not be
outlined. They'sinmly involve the calculation of the K
values and the enthalpy values for a given compound free
a third degree polynomial. The factored fore.of the

-52-

polynoeial is used to decrease the number of orders
required. For instance, K = [Y dKT +cx)T r 5x] T + 4g .
This way, the constants for the polynomials must be

input in reverse order; that is, in the order d, c, b,
and a for each component. The constants must be changed
for each different tower pressure as well as for when
different components are in the feed.

Whenever control is transferred to HSR or KSR from.the
main program, the K values or enthalpy values are calculated,
than control is transferred automatically back to the next
order in the main program. In other words, both HSR and
KSR are closed subroutines.

The outline of the program shall be broken down into
three sections: 1) Specification of Parameters, 2) Outline

of Data, and 3) Main Program.

specification of Parameters

This involves specifying various para-stars before the
problem can be worked. These parameters are essential to
the solution of the problsn. The parameters are used in
conjunctioe*with the 8 termination symbol to specify certain
addresses'within the programs The parameters which must be
specified and stored in locations 3 - ll are:

-53.

3) Specifies floating register for floating point
subroutine
4) lumber of components
5) Plates above feed plate
' 6) Plates below feed plate
7) Imber of components a: lo
8) lumber of components a 8
9) Total number of plates less feed plate
10) Number of components expected in overhead product
in appreciable snount
ll) Huber of components expected in bottom product
in appreciable amount
For this program, location 3 is always the same and
specifies location 28 as the floating register. All the
other parameters may vary with the particular problem
being‘eorked. Perhaps the parameters specified in locations
10 and ll should.be made a little clearer. An example'vill
be given to illustrate their use. In a given problem, there
are eight components in the feed, and it is to be split in
two products, the top product containing essentially the
three most volatile components and the bottom product con-

taining essentially the other five components. It is evident

-54-

that some of the light components will appear in the bottom
product and some of the heavy components will appear in the
top product, but in small amounts. In this case, location
10 will specify three components in overhead product and
location 11 will specify five components in bottom product.
The sum of locations 10 and 11 must always be equal to the
total number of components in the feed. In the case of a
component which will appear in both products in appreciable
amounts, it won't matter where it is seemed to be in the
greater amount.

The parameters are used primarily for the reading in
of the program to the computer; and many of them are
destroyed by storing other results in the same locations,

once the program has been read in.

Outline of Data

There are certain bits of data that are necessary
to work a problem, such as feed composition, feed condition,
as well as initial estimates of certain variables which are
to be determined by trial and error. Following is a list of

essential data and the locations in which it is stored.

647-654

655
656
657

658
659
660
661-663

664

665-672
673
675
675

-55..

Assumed moles of each component leaving in
overhead product

Initial estimate of still temperature
Integer one

Constant for bubble point and dew point
convergence tests

Constant for temperature convergence
Reflux ratio (LID)

Initial estimate of top temperature

Any other constants which are necessary when
program alterntions are made

Initial estimate of vapor rate in stripping
section

‘Mble fraction of each.component in feed
Enthalpy of feed (BTU per mole)

Constant for ratio r convergence

Same as 661-663

The maxim- number of components this program will handle

is eight. If more memory space were available, the program

could easily be altered to handle as.nmny components as

‘..1r.de

The constants Which.mmst be specified to: various

convergence tests will depend on just how accurate an

.56-

answer is desired. For example, in finding the temperature
on a certain plate, the temperature is changed until the
st- of the mole fractions is unity. However, to actually
obtain unity might require very much time when a value of

l t .001 would serve just as well. In this case, then, the
constant in location 657 would be .001.

‘When a feed is used which contains less than eight
components, the remaining memory locations must be filled
‘eith.some arbitrary constants. The reason being that the
computer, in reading in the data, stores it consecutively.
Thus, if the blank locations are not filled, the data following
‘vill be stored in a different location than specified. For
the same reason, all data locations must be filled. It is
also essential that in the feed composition, seemed on ,
and in the KSR and HSR the components are always in the same

order.

loin Program
Outline of Storage Space
0, l, 2 Temporary storage
3-ll* Parameter specification
10 Temperature storage for equilibriumland enthalpy

subroutines

11-18
20-27
28-29
30-300
300-356
357-398
399-478
679-646
647-673
676-686
687-706
707-719
720-1023

Storage of K and E values
Storage of 11 values

Floating accumlator (Specified by 3)
Program

Answer storage

Equilibrium constant subroutine
lnthalpy subroutine

floating point subroutine

Data

Space for program alterations
Program

Space for program alterations

Answer storage

*l'he parameters specified in locations 10 and ll are destroyed

after program is read in.

Outline of Answer Storage
D
W
(2 "°/x)-/ , (z wa)-/
Qa
Qr
W", ATM) -a, ATn
th,,Lm, 37¢!) Aim“ : ivh-IHn-l) 6’) AV-I

307
308
309
310
311
312
313
314

315
316

317-324
323-332
333-340
341-348
349-356
720-808
813-903
906-998
999-1007
1008-1013
1016-1023

-53-

Tenperature storage in calculating P, —P,/ J m .. 9.,

2H” xmw , 2 HOW-I Uri-I

ZAMHXMH .9 2,7,, 5n

PI , r C].
”P: , "‘ 3.,
-P3 , " 93
P4 ; 74

Constant for testing iterations through top
of colu-n

Used over and over for various ans
Constant for testing iterations through botto-
of column

xoi

X»:

X; as calculated from condenser downward
56w”.

7(m:

Temperature on various plates

Vapor rates iron each plate

Liquid rates from each plate

K values, r values

Hm: ) Um:

xfmu) i I 1m:

0030K

0)

1)

2)

3)

4)

S)

6)

7)

8)

9)

10)

41 314!
30 L

26 479'
11.29!
88 I

13 647!
13 2L
83 660!
83 720'
83 653!

88 72183

83 664?

83 81383

3K.’
8!.’

88 316'
0! $3
I! 84
8K.’

14 647?
12 9L

88 3001

Put a zero in location 314

Standard entry to subroutine

Enter floating point subroutine

Set box 1 counter at 29

Read in floating point fraction

Store fraction in location 647

Loop to left side of location 2L

Bring in T,

Store I. in location 720

Bring in T;

Store I, in location 72183

Bring in V,

Store V, in location 81385

Waste order (change for program alteration)
Put zero in accumulator

Store zero in location 316

Sat box 0 for number of plates above feed
Sat box 1 for number of components

Put acre in accumulator

Add Dru,- to accuumlator

Loop to right side 9L

Place Z Data in location 300

 

11)

12)

13)

14)

15)

16)

17)

18)

19)

20)

21)

87
85

88
85
80
88

15
10
86
13
13

15
86

13
85
83
IX
SJ

6593
906?
300?
813?
656’
300?
301?
$4
665!
647?
301?
325?
15?
84
647!
300?
317?
18L
720?
10!
$4
22L

~60-

Multiply l by R

Place DR : Lo in location 906

Add D to DR

Place D(R + l) 2 V, in location 813
Bring in integer l
Subtract D

Store l-D :‘W in location 301
Set box 1 counter at 84

Bring in ‘X;
Subtract on
Divide by‘w
Store W= xx, in 1ocation 325
Loop to left side of location 15L
Set box 1 at 84

Bring in 0 x0

Divide by D

Store Ora/D = x., in location 317
Loop to left side of location 18L
Bring in T.

Place I, in location 10 for KSR
Set box 1 at 84

Leave A, go to left side of location 22L

22)

23)

24)

25)

26)

27)

28)

29)

30)

31)

41
50
26

16

88
12

85
81!
83

85
83

85
80
88
82

315?
221.
357?
317!
11'

1016!

315!
315?
231.

656!
302!
657?
302!
34L

302‘!
321.

720?
658?
720?
20L

-51-

Put zero in location 315

Standard entry to [SR

Transfer control to KSR

Bring in x. (equals 9.)

Divide by K

Store Hull I X. in location 1016

Add content. of location 315

Store eun back in location 315

Loop to right aide of location 231.
Subtract 1 fro- : X.

Store I 71,-! in location 302

Bring in convergence teat constant
Subtract absolute value of (£X,- I)

If poeitive (convergence) go to left aide
of 341.; if ninua, go on

Bring in (In-l)

If poaitivn (temperature too low) go to left
aide 321.

(Temperature too high) bring in '1'.
Subtract te-perature convergence constant
Store new T. in location 720

I. alwaye positive, to transfer to right side

201.

32)

33)

34)

35)

36)

37)

38)

39)

40)

41)

42)

85

88
82
85

ll

41
50
26

17
18

88
12
80
88
85

720?
658?
720!
20L

72185

10!
S4
36L
315?
36L
357!
325!
11!
341!
315!
315!
37L
656?
302'
657?
302!

83_48L

~62-

Bring in T. (temperature too low)
Add temperature convergence conatant
Store new T. in location 720
Tranafer control to right aide 20L

Bring in T5

Place in location 10 for KSR

Set box 1 counter at 54

Leave A.‘,tranafer to left aide location 36L
Place aero in location 315

Standard entry to [SR

Tranafer control to ISR

Bring in X“,

Multiply by K

Place xw- K 3 Y5 in location 341
Add contenta of location 315

Store an. in location 315

Loop to right aide location 37L
Subtract l fro. 2' 95

Store-(1 -i3s) in location 302
Bring in convergence teat conatant

Subtract abaolute of-(l - i 35)

1f poaitive (convergence) go to left aide 48L

43)

an)

45)

46)

47)

as)

49)

50)

51)

52)

53)

85
83

85

88
82
85
80
88
82
85
88

83
41
5O
26

17

12

302!
46L

72185
658!
72185
34L
72185
658’
72185
34L
660?
10?
S4
50L
315!
50L
357?
11!
317'
315'
315!

51L

-63-

Bring in-(l - Z 3;)

If plua (temperature too high) go to
left aide 48L

Bring in T5

Add temperature convergence constant
Store new T. in location 72185
Transfer to right side of 34L

Bring in Ta

Subtract temperature convergence constant
Store new T; in location 72185
Transfer to right side 34L

Bring in initial estimate of T.
Place in location 10 for [SR

Set box 1 counter at 84

Leave A.‘,and go to left side of 50L
Store sero in location 315

Standard entry to KSR

Transfer control to XSR

Bring in l;_

Multiply by x 0.;

Add contents of location 315

Place aun.in location 315

Loop to right side of 51L

54)

55)

56)

57)

58)

59)

60)

61)

62)

63)

85
8!
82

85
82

85
84
88
82
85
80

82

85

41
50

656'
302!
6577
302?
61L

302!
59L

660!
658?
660!
48L
660!
658!
660’
48L
660!
10?
63L
315?
63L

~64-

Subtract 1 from i K x0

Store -(1 - i K x... ) in location 302
Bring in convergence test constant
Subtract absolute of-(l - i K x, )

If plus (convergence) transfer to right
side 61L

Bring in-(l - 2'. t x...)

If plua (temperature too high) go to
right side 59L

Bring in T:

Add temperature convergence constant
Store neu’Tc in location 660
Transfer to right side of 48L

Sting in Tc,

Subtract te-perature convergence constant
Store neU'Te in 660
Transfer to right side of 48L

Bring in Tc

Store in location 10 for SSR

Leave A.‘.transfer to right side 63L
Place aero in location 315

Standard entry to BSR

64)

65)

66)

67)

68)

69)

70)

71)

72)

73)

74)

26 399!
11.84
15 20?
17 317?
84 315!
88 315?
13 65L
87 906?
88 3153'
8K 2!
83 687!
8K‘P

05 721!
88 10!

BJ 72L
41 315?
50 72L
26 357!
15 ll?
18 999!
12 73L

-65-

Transfer control to HSR

Set box 1 at 84

Bring in 7.

Multiply by :0 -

Add contents of location 315
Place sun in location 315

Loop to left side location 65L
Multiply hc by Lo

Store h..Lo in location 315
Place interger 2 in accumulator
Transfer control to left side 687
Waste order

Bring in ‘1'...

Place in location 10 for KSR
Set box 1 counter at 84

Leave A. ,transfer to left side 72L
Place zero in location 315
Standard entry to KSR

Transfer control to KSR

Bring in K;

Store K; in location 999

Loop to right side of location 73L

75)

76)

77)

78)

79)

80)

81)

82)

83)

84)

85)

05
84
08
1K
05
17
14
06

13

88
12
80

05
88
8.7

90 7?
300?
814?
S4

9077

1016?

64 7?
814?

1008?

77L

1008!I

999?
349!
315'
315?
801.

656!
305!
720?
10?

86L

-66-

Bring in La“.
Add D

Store 1...... + D '-' V... in location 814
Set box 1 counter at 84

Bring in L.......

Multiply by X....,,

Add x.

Divide by Vm

Store Y... in location 1008
Loop to left side location 77L
Set box 1 counter at S4

Bring in Y...

Divide by K

Hm/ K m =

Add contents of location 315

Store at... in location 349
Store .1. in location 315
Loop to right side of location 80L
Subtract 1 fro. Z X,"

Store-l + i X... 8‘¢ in location 305
Bring in '1' m“

Place T m... in location 10 for HSR

Leave A. ,transfer to left side of 86L

86)

87)

88)

89)

90)

91)

92)

93)

9:.)

95)

96)

41 309?
50 86L
26 3998
4K 84
45 20F
47 1016?
84 309E
as 369.-
43 88L
O7 907?
88 3061
05 721?
88 10F
83 93L
41 315!
50 93L
26 3991
42,84
8K.!

88 308?
45 11!
47 1016!

-57-

Place zero in location 309
Standard entry to HSK

Transfer control to HSR

Set box 4 counter at 84

Bring in 1:

Multiply by X...“

Add contents of location 309
Store sum in location 309

Loop to left side of location 88L
Multiply by 1......

Store L.n,, ° h,n,, in location 306
Bring in T...

Place T”. in location 10 fer HSR
Leave A. Jtransfer to left side of 93L
Place zero in location 315
Standard entry to HSR

Transfer control to HSR

Set box 4 counter at 84

Bring in xero

Store aero in location 308

Bring in F7...

Multiply by X mi,

 

. 97)
9s)
‘99)
100)
101)
102)
103)
104)
10:)
100)

107)

84

45
47

308?
308?
11?

1008?

315?
315?
96L

814?
306F
303!
656!
306?

-53-

Add contents of location 308
Place sum in location 308

Being in T51,“

Multiply by Y...

Add contents of location 315
Place sum in location 315

Loop to left side of location 96L
Multiply by V...
Subtract L....,.. 11......

Divide by Q0.

Subtract integer l
Store'¢’in location 306
Set box 1 counter at 4
Place zero in accumulator
Place zero in location 310
Loop to left side of 104L
Set box 1 counter at zero
Set box 2 counter at 84
Bring in integer 3
Multiply by (1..

Multiply by TI

Store 3dkTm in location 307

108)

109)

110)

111)

112)

113)

114)

115)

116)

117)

118)

8K
17
84
O7
14
27
84

IL
23
1K
15
10

84
88
12
06
88

8K

2?

368!
307?
721!
369?
349?
310?
310F
4P

106L

S4

1016?
1008!
' 999?

311?
311!
113L
814!
311!

S4

-69-

Bring in integer 2

Multiply by c“

Add 3dKTn

Multiply by T111

Add b.‘

Multiply by X”.

Add contents of location 310
Store sum in location 310
Increase increment of box 1 by 4
Loop to left side of location 106L
Set box 1 counter at 84
Bring in X...“

Subtract Y".

Divide by X...

Add contents of location 311
Store sum in location 311
Loop to right side of 113L
Divide by V...

Store -pz, in location 311
Set box 1 counter at zero
Set box 2 counter at 84

Bring in integer 3

119)

120)

121)

122)

123)

124)

125)

126)

127)

128)

129)

17 416?

07
88

721!
307'?

Bit 2!
17 417?

84
07

307'
721!

14 418!

27
84
88

1008?

312?
312!

1L4?

22
07
86
88
85
80
86
88
83
87

1181.
814!
303?
312!
309?
308!
303?
313?
311?
312!

-70-

Multiply by dh

Multiply by Tm

Store in location 307

Bring in integer 2

Hultiply by c).

Add .38). 1'...

Multiply by 1‘...

Add b1.

Hultiply by Y...

Add content: of location 312

Store sun in location 312

Increase increment of box 1 by 4
1.00;) to right side of location 1181.
Kultiply by V... ’

Divide by Q...

Store -pa in location 312
Bring in iT'Inu-l XrM-l
Subtract f n... In.”
Divide by Q“

Store p, in location 313

Bring in -p.,

mltiply by “P3

130)

131)

132)

133)

134)

135)

136)

137)

138)

139)

140)

IS
85
87
80
88
85
87
88
81
87
80
86
88
85
87

86

05
80
08
05

308?
313!
3101'
308!
308?
311?
306?
3097
3058‘
313?
309?
3081"
3053‘
312?
305?
306!I
313!
306!
721!
305'
721!
907?

-71-

Store pz p3 in location 308
Bring in p,
Multiply by p,
Subtract p,’ p 3

Store p, p, in location 308

Bring in «pa
”ultiply by - ¢’
in location 309

.sz3

Store 1),, ¢’
Bring in ¢
Hultiply by 11.,
Subtract {11¢ ’
Divide by p" p. - 111 p,
Store A '1'... in location 305
Bring in «1:3
Multiply by AT...

Subtract - ¢’

Divide by 1),.

Store A L...“ in location 306
Bring in old ‘1'...

Subtract A '1'...

Store new Tm in location 721

Bring on old 1......H

141)

142)

143)

144)

145)

146)

147)

148)

149)

150)

80
OS
85

BR

82

85

SN

82

15
18
12
02
1!

18
13

83

83

306?

907?

305F

658F

69L

306F

657E

69L

349?

1016!

145L
695!
S4

349!
333?
148L

181?

181!

-72-

Subtract A 1......”

Store new L...“ in location 907
Bring in A I‘m
Subtract absolute of temperature

conVergence constant

If plus not convergence, transfer to right
Bide 69L

Bring in A L...“

Subtract absolute of temperature convergence
constant

If plus not convergence, go to right side 69L
Set box 1 counter at $4

Bring in X...

Store x... in 1016 (now becomes 11...,” )

Loop to right side l45L

Next plate, loop to right side 695

Set box 1 counter at $4

Bring in x... (feed plate conpoeition)

Store in location 333
Loop to left side 148L
Bring in integer 2

Transfer to left side location 181

Waste order

00181!
0) 0!
81
1) L5
L0
2) 36
F5
3) 40
50
4) 26
05
5) 08
05
6) 08
82
7) 22
05
8) 84
08
9) ll
15
10) 07
18

36
1L
31st
er

71 _
316!
316?
31
479!
72135
72235
01355
3145:
7L
704:
81484
3011
90755
34
3411

81485
1016!

Set box 0 counter at $6

Leave A. ,tranefer to left side 1L
Bring in loop counter constant
Subtract number of plates below feed
If plua, go to left side 7L

Bring in loop conetant and add 1 to it
Store new loop constant at 316
Standard entry to A.

Transfer control to A,

Bring in T;

Store I, in location 72285
Bring in qu
Store‘Vnd no 81485
Transfer control to right side TL
(HISTIC) transfer to right eide 704
Bring in Vfi_,

Add.“

Store V..-,+ U I L in location 90785
Set box 1 counter at 84

Bring in Y...

Multiply by Vn -I
Store in 1016

11)

12)

13)

14)

15)

16)

17)

18)

19)

20)

21)

85
17
14
06

12
05

1K
8J
41
50
26
15
18
17
18

88
12
80
88

301?
325?
1016?
90785
1016F
9L
72285
10F

16L
315?
16L
357E
11F
999?
1016?
1008?
315?
315?
17L
656!
305!

-74-

Bring in.W

Multiply by Kw

Add Vn-I ya-)

Divide by 1...

Store X"; in location 1016
Loop to right side of 9L

Bring in Tn

- Place In in location 10 for KSR

Set box 1 counter at 84

Leave A..,go to right side of 16L
Place zero in 315

Standard entry to KSR

Transfer control to KSR

Bring in K

Store K at location 999

Multiply by Xn

Store Y.. in location 1008
Add contents of location 315
Place sum in location 315
Leap to right side of 17L

Subtract 1

Store (iyh - 1) 3'9 in location 305

22)

23)

24)

25)

26)

27)

28)

29)

30)

31)

32)

05 72185
88 10?
1K.S4

SJ 24L
41 308!
50 24L
26 399?
15 11!
17 341!
84 308!
88 308!
12 25L
07 81485
88 306B
05 72285
88 10?
11 S4

8J 31L
413B”
50 31L
26 399?
8K4?

-75..

Bring in Tn-)

Store 2.“. in location 10 for HSR
Set box 1 counter at 84

Leave A. , go to left side 24L
Place zero in location 308
Standard entry to HSR

Transfer control to HSR

Bring in.§

Multiply by Hn-l

Add contents of location 308

Store sum in location 308

Loop to right side of location 25L
Multiply by V.._.

Store I! n... ° ‘5... in location 306
Bring in In

Store In in location 10 for HSR
Set box 1 counter at 84

Leave A. ,transfer to left side 31L
Store zero in location 315
Standard entry to HSR

Transfer control to HSR

Put zero in accumulator

33)

34)

35)

36)

37)

38)

39)

40)

41)

42)

43)

88

17

88

17

88

12

87

80

86

309?
20!
1008!
309!
309?
20!
1016?
315?
315!
33L
90785
306!
304!
656?
306'

11.4?

8K.’

18

310!

12 41L

1K.?
21.84
8K 3'

-75-

Store sero in location 309
Bring in 3

Multiply by an

Add contents of location 309
Store sum in location 309
Bring in.b

Multiply by X...

Add contents of location 315
Store sum in location 315
Loop to right side of location 33L
Multiply by L n

Subtract V..-) Hn-I

Divide by 0':

Add integer 1

Store 6' in location 306

Set box 1 counter at 4
Bring in zero

Store sero in location 310
Loop to right side location 41L
Set box 1 counter at sero
Set box 2 counter at 84

Bring in integer 3

44)

45)

4e)

47)

48)

49)

50)

51)

52)

53)

54)

17
07
88
8X
17

07
14
27

88
1L
22

10
17

88
13
06
88

367?
72285
307!

368!
307'
72285
369!
10087
3101
310?
4?
43L
84
341!
1016!
999?
3118'
311!
51L
90785
311!

-77-

Multiply by d..

Multiply by ‘1'..

Store 34.3.. in location 307
Bring in integer 2

Multiply by 13..

Add 34.1..

Multiply by In

Add bx

Multiply by Y!)

Add contents of location 310
Store sum in location 310 (-q. )
Increase box 1 counter by 4

Loop to right side of location 43L
Set box 1 counter at 84

Bring in I..-)

Subtract x n

Multiply by in

Add contents of location 311
Store sun in location 311

Loop to left side of location 51L
Divide by L.

Store ~11, in location 311

9. er

55)

56)

57)

58)

59)

60)

61)

62)

63)

64)

65)

1K!

2K
8K
17
07
88

17

07
14
27

88
1L
23
86
07
88
85
80
86

S4

416!
72285
307?

417V
307?
72285
418?
1016?
3121'
312?
4"
56L
304!
90 785
312’
309?
308?
304!

-73-

Set box 1 counter at zero
Set box 2 counter at 84
Bring in integer 3

Multiply by d ..

Multiply by Tn

Store 301.1%. in location 307
Bring in integer 2

Multiply by c).

Add 36.3..

Multiply by 'l' r.

Add b h

Multiply by 1..

Add contents of location 312
Store 111- in location 312
Increase box 1 counter by 4
Loop to left side of location 56L
Divide by Q,-

Multiply by L...

Store -q, in location 312
Bring in 11.. Y...

Subtract '13.... 1..-.

Divide by Q .-

66)

67)

68)

69)

70)

71)

72)

73)

74)

75)

76)

77)

88
85
87
88
81
87

88
81
87
88
85
87

86

85
87

86
88

05'

80

08

313!
311!
312'
307!
310!
313!
307!
307?
305?
313!
305?
311!
306?
305?
307!
305!
312!
305'
306?
313!
306!

72285

305!

72285

-79-

Store q. in location 313

Bring in - qz
‘Multiply by - :13

Store q in location 307

2q3
Bring in q.
Multiply by q“
Subtract qzq3

Store in location 307
Bring in 19

Multiply by q,

Store 9 41., in location 305
Bring in - qz
Multiply by e ’
Add Eiqq
Divide by q.qq qzlq3
Store AI... in location 305 ’
Bring in - q3

Multiply by AL.

Add 9'

Divide by qq

in location 306

Store A V.,_,

Bring in '1'... (old)
Subtract A'l‘..

Store new T.. in location 72285

78)

79)

80)

81)

82)

' 83)

84)

85)

86)

05
80
08
85

82

85

8M
82

16

18

1008?

341!

83L

181!

3331'

1016!

999?

-80 .-

Bring in old V.._.

Subtract AV...

Store new V..-. in location 81485
Bring in A 'l'..
Subtract temperature convergence constant
If plus (not convergence) loop-to right side
7L

Bring in AV..-.

Subtract convergence test constant

If plus (not convergence) loop to right side
7L

Convergence, so set box 1 counter at 84
Bring in yn

Store ya in location 341 (now becomes Yn-l)
Loop to left side of location 83L

Mext plate. loop to right side location 181
Set box 1 counter at 8!

Bring in x. as calculated fro- condenser
downward

Divide by X; as calculated from reboiler
upward

Store 1‘ in location 999

87)

88)

89)

90)

91)

92)

93)

94)

95)

96)

97)

87
17
88
81
14
18
12

16
18
13

301!
325?
302?
302!
665!
647!
85L
SS
3338K
1016SK
9998!
6478!
9998!
6478K

91L

1! 84

15
80

83
82

13

999!
656!
674!
98L

95L

8‘2!

-31-

Multiply by W

Multiply by X.”

Store r wa in location 302

Bring in - Y‘wa

Add x. (also equals 1’ x, )

Store revised D x.) in location 647

Loop to right side of location 85L

Set box 1 counter at 88

Bring in x. as calculated from tap down
Divide by X; as calculated from bottom up
Store r in location 9998!

Bring in previous D 71.,

Divide by r

Store on revised in location 6478!

Loop to left side of location 91L

Set box 1 counter at 84

Bring in r

Subtract integer one

Subtract absolute of convergence constant
If plus must beiterate. transfer to right
side 98L

If above minus component converged. test next

component

Bring in integer 2 to make plus

98)

99)

100)

101)

10 2)

103)

104)

105)

106)

107)

82 99L
8! 28
83 38?
8K.F

88 314!

8X.l

1! 185
15 720!
8 96?

12 101L
1K 86

15 72089

89 6?
IL 1022!

12 103L
1! 185
15 906!
89 6?
13 106L
lI.S6

-32-

Transfer control to right side location 99L
Make plus for next order to be obeyed
Reiterate through entire tower

Bring in sero

Store sero in location 314 (for additional
reflux ratios)

Waste order

Set box 1 counter at 185

Bring in temperatures above feed plate
Output temperature

Loop to right side of location 101L
Set box 1 counter at 86

Bring in temperatures below feed (in
reverse order)

Output temperature

Used to output temperatures in forward
order

Loop to right side of location 103L
Set box 1 counter at 185

Bring in liquid rates above feed plate
Output liquid rates

LoOp to left side of location 106L

Set box 1 counter at 86

108)

109)

110)

111)

112)

113)

114)

115)

116)

15

89
1L

13

15

89
IL

12

89

13
85

90689

6?

1022!

108L
135
813?
6?
110L
86

81339

6!

1022!

112L
16?
317!
6?
115:.
300!

-33-

Bring in liquid rates below feed
(reverse order)

Output liquid rate

Used to output liquid rates in forward
order

Loop to left side of location 108L
Set box 1 counter at 185

Bring in vapor rates above feed
Output vapor rate

Loop to right side of location llOL
Set box 1 counter at 56

Bring in vapor rates below feed
(reverse order)

Output vapor rates

Used to output vapor rates in forward
order

Loop to right side of location 112L
Set box 1 counter st 16

Bring in :0 and 1N

Output X0 and xv

Loop to left side of location 115L

Bring in D

117) 89 6F
81 118L
118) 0! f
0! F
00 687K
0) 85 720!
88 10!
1) 1K 84
81 2L
2) 41 303?
50 2L
3) 26 399
15 11?
4) 17 317!
84 303!
5) 8S 3031
12 3L
6) 87 813?
80 315!
7) 88 303!
80 673?
8) 88 304’
8J 9L

-84-

Output D
Leave A, , transfer to location 118L
Shuts machine of!

Waste order

Bring in T,

Store T, in location 10 for HSR
Set box 1 counter at 54

Leave A, , transfer to left side 2L
Store zero in location 303
Standard entry to HSR

Transfer control to HSR

Bring in ii,

Multiply by x0

Add contents of location 303
Store sum in location 303

Loop to right side of location 3L
Multiply by L.

Subtract 110

Store Q., in location 303

Subtract'fi;

Store Q.. in location 304

Leave A, , transfer to 9L

10)

ll)

12)

13)

14)

15)

16)

17)

18)

19)

32
F5
40
50
26
05

05
OS
BK
82
50
26
8X
83
50
26
8X
82
82

314B
5F
15L
314'
314!
11L
479!
900?
907?
720?
721?

16L
15L
479?

100?
17L
479!

188!
188?

(MISIIC)

Subtract

-35-

Bring in loop counter

contents of location 5

If plus go to right side of 15L

Bring in
Store in
Standard
Enter A.
Bring in
Store in
Bring in
Store in
Bring in
Transfer
Standard
Transfer
Bring in
Transfer
Standard
Enter A,
Bring in

Transfer

contents of 314 and add one
location 314

entry to A,

Va
location 907
Tn

location 721

integer 2

to right side 16L

entry to A,

control to A,

integer 2 (makes plus)

to left side location 100

entry to A,

integer 2

to location 188

Waste order

-86-

There are many ways in which the foregoing program may
be altered to perform a desired calculation. Several of the
possible desirable alterations which have been.made shall now
be discussed.

In an investigation such as this where many problems
met be solved, the program as it stands would only allow
one problem to be worked, then the computer would shut off.
If more problems were desired to be run, the new problem
would then have to be read into the computer. It is desir-
able, then, to be able to put five, ten, or even twenty
problems on one tape, and let the computer solve the-.all
one after the other. The only major change which least be
made is to remove the order which instructs the machine to
shut off and to replace it by a transfer of control order
to some location where the program alterations are to be
stored.

If one desires a given problen to be worked for various
values of reflux ratio, holding everything else constant,
this my be accomplished very simply by changing the right
hand order in location 36 to be Sl(n)l, where (n) is the
number of various reflux ratios to be run. Then it would

only require a few new orders which would change the reflm:

ratio as desired and start the problem over using the new
reflux ratio. This could be accomplished by either instruc-
ting the computer to read in more tape (on which the new
reflux ratio would be) or by changing R in a stepwise
manner, such as by increasing it by five each time.

As mentioned in the section on the HISTIC computer it-
self, it is necessary to use 001 when reading in more tape.
Because of the lieited storage space in the computer, the
001 has been overwritten and thus destroyed. Before any-
thing can be read in again, 00! lust be read once again and
stored in its proper locatiOns. Thus, whenever the stain
program is altered to read in sore date instead of shutting
off, the 901 must be the first thing on the tape. The
computer may be instructed to read the 301 by writing a
bootstrap start in the progra- alteration. Even though the
801, when read in again, will destroy some of the stored
answers, nothing is hurt since the solution was already
completed and the new problem will simply store its answers
overtop the new DO! inst read in.

Other variables which can be changed by slight program
alterations are: l) ntfler of plates in the column, or

simly the location of the feed plate, and 2) the feed

-88..

composition. If any changes are desired in the date to the
program, such as feed composition or reflux ratio, the entire
set of dete must be msde up, even though many of the things
remsin the same.

If it is desired to change the number of plates or the
feed plete location, then only the orders which use the 8
terminstion syebol comma by e s. 5. or 9 must be repeated. .
This is because they ere the only orders which will be changed
in this case. Because this change in number of plates was s
canon occurrence in this investigation, a special tape con-
taining only the orders which would change (35, 86, and 89
orders) was made up and used frequently.

Another progre- slterstion which was used mainly at
first to see if the program wee working was to instruct the
computer to punch out the composition of liquid on each
plate for each iteration. By doing this, one can see how
feet the problem is converging end also see how many- iterations
are required.

Throufi the cooperation of the computer laboratory staff,
problems for this investigation were many times run off at
night. in these instances, the foregoing progran alterations
were mede use of to prepare problems which would run all
night end require no watching. tinny times, tapes were prepared

-39-

which contained several combinations of feed composition,
reflux ratio, nunber of plates, and feed plate location.
One inprovenent which could be made in this program,
if snore storage space were available, would be to include
various tests and checks to make sure certain physical
laws are not broken, such as negative equilibrium constants.
The computer could be instructed to shut off it such a
thing occurred, or could go on to the next problem, it a.

program alteration were used to run a series of problems.

-90-

DATA AND DISCUSSION OF RESULIS

At first glance at the data, the reaction one might
'have is that it does not natter‘nuch.where the feed plate
is located. This, in a majority of cases, results in
overdesign if the optimum feed location is not used and
the coluln still carries out the desired separation.

Of course, only in special cases such as stripping columns,
'will the optimum location be near either extreme of the
ooluna.

The variables which were studied to see if optima
location changed were: 1) feed composition, 2) reflux
ratio, 3) number of plates, 4) condition of feed, and
5) tower pressure.

It was generally found that for most feed.conpositions,
the optimal: location for the feed plate varied from ”-731.
of the way from the botton of the colunn upward. If either
entrees of mostly all light key or heavy key in the feed
were approached, the optima would be near the top of the
cola for high heavy key concentrations and near the bottom
for high light key concentrations.

The method of deter-hing the degree of separation in
a multicomponent problem nay take on different for-s depending

.91.

upon what is being attempted in the coltm. The criterion
for separation used in this investigation was concerned
with: l) the highest purity of light key in the overhead
product (with particular attention paid to the amount of
heavy key there also) and 2) the maxim- recovery of light
key in the overhead and the heavy key in the residue. The
maximi- recovery was taken as the maxim:- of the sus of
the recovery of light key out the overhead and.the recovery
of heavy key out in the residue. This criterion was found
to agree very well with the criterion of purity of products.
The various variables involved'will now be discussed
individually.

eggpgsiohnnggizggg

This was without a doubt the meet studied variable of
those involved. Many different feed compositions were tested
to see how the optima. feed plate location might change with
cowposition.

Key coeponents are those cowponents between which the
actual separation is made, and not the components which may
be specified in atteapting to obtain a desired product. The
key conponents depend.upon pressure, condenser duty, and top
and bottom temperatures. Upon fixing these variables, the
key components are fired and one has no choice but to take

what separation is obtained for a given ntaaber of plates.
The key components in all the calculations made were butane
and isopentane.

Table I

Feed Co osition xnx‘ ‘. ‘11
r... a, rim—Fem —‘§'Lxu an
Feed A 126 .20 .25 .15 .20 .20 .72
Peed I 126 .10 .30 .30 .20 .10 .65
Feed 0 125 .10 .50 .20 .10 .10 .06
feed 0 117 .10 .60 .10 .10 .10 .94
feed I 109 .05 .70 .10 .10 .05 .96
PM P 137 .30 .30 .15 .15 .10 .77
feed a 113 .10 .20 .40 .20 .10 .10
700‘ H 123 .10 .15 .50 .15 .10 .35
Feed 1 100 .30 .30 .15 .15 .10 .77
Food 3* 137 .30 .30 .15 .15 .10 .77
Weed J at 150 psi, all others at 100 psi.
it has been previously mentioned that for the extreme

cases of nearly all light key or heavy key in the feed, the
optin- location of feed plate would approach the bottom

or the top of the calm. To take advantage of this,

the function LHKXLK 6 XL! was used as the uses of

Xux " XL!
defining the composition of the feed in terns of the key

DATA AND DISCUSSION 01' RESULTS

-93-

 

00.

q

vslx +14x
3
X... x. x

Oh. 00. on. 0*. 0». ON.

.1 q q q a a 1

20:400.. ugh...“ 0mm“. EDI—baa
m>

zo_._._m0n_zoo ommu

n UHDMHH

0..

 

_I—._i°
O
'0’

i
O
n

“NWD'IOO JO "01.1.08 "08$ 1"

6
0
NOliVOO‘l 3iV'ld oaaa wneuao

3 2

/
O
a

 

'igurmé

AVERAGE % KEY COMPONENTS RECOVERED

-94-

 

j

 

07

e4?-

02!-

 

Ll

 

87

    

FEED PLATE LOCATION
V8

KEY COMPONENTS RECOVERED

mm“ \A

 

 

«...... _ /\

GASES l-b

 

 

_ FEED PLATE LOCATION
-%FROM BOTTOM OF COLUMN-

-95-

coqonents. Figure 5 shows the results of plotting this
faction versus optima feed plate location expressed in
percentages from the bottom of the calm. The data does
not cover the entire range of feed composition; but does,
however, cover most cases which will normally be met (see
Table l). The ends of the curve are dotted since they are
strictly qirical. By enanining the abscissa of Figure 5,
itcanheseenthetwhenthefeedisall lightkey (In-0)
then the faction goes to l and the optiu- location of
feed plate should approach the bottom of the col“. When
thefeedisallheavykeyamI-O) thamthafmctiongoes
to ears and the Optl-I feed plate location approaches the
top of the cola.

figure 3 was determined using the data of Table I!
(see Appendix). The maria. separation, and thus the
opti— location of feed plate, was determined by plotting
the average of the per cent light hey recovered out the
overhead and the percent heavy hey recovered out the
bottom, versus feed pm. mam. mm: plots .2. shown
in figure 6. The optima feed plate location was then plotted
versus the function describing the feed composition in Figure
5. The band was drawn in to include the points scattered, due

to changes in reflux ratio, feed condition, and calm
pressure, as well as to include the "band" of optimum
locations observed for several calms.

It is felt that the most important variable not inves-
tigated was that of variation of relative volatility between
the key components. Although some problems were solved
using a six-component feed, nearly all the problems solved
in this investigation had a feed composed of the one five
hydrocarbons. Any future work in this field should include
this variable, as well as including components other than
aliphatic hydrocarbons.
£21.12. nae.

by examining Table I: for canes 141 and cases ”-155,
which illustrate variation of reflux ratio, it can be seen
that the degree of separation increases with reflux ratio.
Thisistrueuptoahighvalueofreflunrstio,andthenthe
products obtained remain the same with increasing reflux
ratio. From plots of the type shown in figure 6, it was feud
that the optimtm feed plate location remained nearly the same
for various reflux ratios. There is only a slight shift of the
optima feed plate location upward in the calm with increased

reflux ratio .

Lee 2!. 1.1.19:

Once again, the amber of plates in a column has very
little effect on the relative optim\- feed plate location,
that is, the feed plate location expressed as a percentage,
such as used in figure 5. In towers with a small nueber of
plates (11) the optima location sometimes resulted in a
specific location, rather than a band of feed plate locations,
which occurred in many columns with more plates. This band
occurred due to the flat shape of the separation versus
feed plate location curve (Figure 6.)

The colt-e with 21 and 31 plates which were calculated
often had pinch points where the composition and temperatures
did ndt change from one plate to the next. One set of pro-
blems was solved using 41 plates and the same relative optima
feed plate location was obtained as for calms with 21 and
31 plates. However, because of the increased umber of plates
in the pinch region, the aptim- location band was slightly
widened.

Condition 9; g_e_e_d_

To determine if the optimum feed plate location changed with
the condition of feed, that is, hot or cold feed, the same
feed composition was used at two different temperatures. feed

I was at 137°? and Feed 1 at 100°P. Cases 211-222 and 254-268

-93.

are the solutions applicable here. In this case, the
optimum location was not affected by the change of feed
condition. It seems safe to generalina that, at least
for all liquid feed, the condition of the feed will not affect
the relative optimum feed plate location. However, caution
should be used in .....a... this generalisation to include
vepor feeds.
3395 Pressure

Since the tower pressure is not an independent variable
in commercial design but‘muet be conpetible*with condenser
temperature and product specifications, it is difficult to
determine the effect of pressure on the optim feed plate
location.

The only check was the comparison of feed I with reed J
(cases 211-222 and 269-262.) Feed J was used in.a column
at 150 psi pressure while the colunn for feed.! and all other
cases were at 100 psi.

Although slightly different products were obtained, no
appreciable change in optinun.feed plate location'wes found.

C ONCLUSIORS

l.

2.

3.

A.

.99.

CONCLD810HS
A rigorous method for the solution of multicomponent
distillation problems has been developed and progra-ed
for a high speed digital computer.
Several hundred problems have been solved rigorously
to use in making a correlation of optimi- feed plate
location.
From these onerous solutions, a correlation between
the optima feed plate location and the feed composition
hasbeenmede. The function wu’xH. was

X31 ’ X“
fond to give a good correlation of feed composition.

 

The effects of other variables such as reflux ratio,

tower pressure, feed condition, and number of plates,
upon relative opti-m feed plate location, have also

been studied and found to be very small.

APPENDIX

 

~100-

 

 

E g3 SE3 Table II
g <3 I):
ma. mo.

” n E 3% gag - Hole traction of Distillate

3 E 2:,- Mb. T134 ‘34 1 5 C5 Ce D

1 A 2 3 7 .4525 .5095 .0263 .0111 .0007 .4261
2 A 2 4 6 .4397 .5194 .0307 .0099 .0003 .4441
3 A 2 5 5 .4257 .5130 .0476 .0136 .0002 .4604
4 A 2 6 4 .4065 .4935 .0763 .0236 .0002 .4812
5 A 2 7 3 .3813 .4639 .1106 .0440 .0002 .5100
6 A 6 3 7 .4532 .5345 .0095 .0027 .0001 .4359
7 A 6 4 6 .4418 .5394 .0157 .0031 .0000 .4499
8 A 6 5 5 .4297 .5327 .0319 .0056 .0000 .4642
9 A 6 6 4 .4094 .5075 .0680 .0151 .0000 .4861
10 A 6 7 3 .3805 .4719 .1130 .0345 .0001 .5220
11 A 10 3 7 .4534 .5385 .0065' .0016. .0001 .4370
12 A 10 4 6 .4422 .5424 .0131 .0023 .0000 .4504
13 A 10 5 5 .4297 .5327 .0319 .0056 .0000 .4642
14 A 10 6 4 .4098 .5095 .0067 .0140 .0000 .4867
15 A 10 7 3 .3803 .4731 .1137 .0328 .0001 .5239
16 A 14 3 7 .4534 .5401 .0053 .0011 .0000 .4374
17 A 14 4 6 .4424 .5437 .0120 .0019 .0000 .4506
18 A 14 5 5 .4299 .5336 .0312 .0053 .0000 .4643
19 A 14 6 4 .4100 .5103 .0662 .0136 .0000 .4869

 

20
21
22
23'
24-
25
26
27
28
29
30
31
32
33

35
36
37
38

39
40
41

> >3» > b b bib > >>

>

5' h» h- h» h» h- b- >- :>

ta rd #0 1d r4 r-
a: a» 4» 1» c» J>

O‘O‘NNNNNN

0‘

10
10
10
10
10

wouJ-‘wu

”03“

10

.12

14

10
12

10
12

wbuoxuw

16
14
12

10

16
14
12
10

16
14
12
10

.3801
.4535
.4425
.4300
.4100
.3800
.5337
.4438
.4375
.4178
.3842
.3661
.5230
.4450
.4421
.4267
.3829
.5225
.4450
.4425
.4274
.3821

-101.

.4735
.5409
.5443
.5341
.5106
.4736
.4592
.5464
.5453
.5209
.4790
.4554
.4750
.5541
.5525
.5332
.4784
.4763
.5545
.5531
.5342
.4775

.1141
.0047
.0115
.0309
.0660
.1143
.0054
.0082
.0156
.0156
.1158
.1403
.0016
.0009
.0051
.0383
.1279
.0009
.0004
.0043
.0369
.1308

.0323
.0009
.0017
.0051
.0134
.0321
.0017
.0015
.0016

.0057*

.0210
.0383
.0004
.0001
.0003
.0019
.0108
.0002
.0000
.0002
.0015
.0097

.0000
.0000
.0000
.0000
.0000
.0000
.0001
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000

.5247
.4376
.4506
.4644
.4871
.5253
.3672
.4501
.4569
.4785
.5201
.5450
.3790
.4494
.4524
.4687
.5223
.3801
.4494
.4520
.4679
.5235

42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
.59
160
(51
(52
‘53

>>>> >>>>>>>> >>>>>> >>>>

rd 9* rd rd 6* r- rd hi hi rd
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O‘O‘OO‘O‘NNNNNNN

10
12

10
12

12
15
18

12
15

16
14
12
10

16
14
12
10

25
24
23
21
18

12

24

21
18

-102-

.4764
.5546
.5532
.5343
.4767
.4766
.5547
.5533
.5342
.4760
.5225
.5412
.5493
.5537
.5503
.5200
.4690
.5437
.5524
.5555
.5544
.5339

.0007
.0003
.0040
.0369
.1326
.0005
.0002
.0039
.0371
.1343
.0104
.0074
.0051
.0026
.0091
.0614
.1367
.0013
.0007
.0001
.0020
.0384

.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000

.3802
.4493
.4519
.4679
.5243
.3804
.4493
.4518
.4680
.5252
.4300
.4442
.4496
.4510
.4542
.4807
.5329
.4397
.4475
.4500
.4509
.4682

64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
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80
81

82 '

83

'85

UUUU>>>>>>>>>>>>>>>>>>

10
10
10
10
10
14
14
14
14
14
18
18
18
18
18

NNNNNNN

12
15

12
16

“#UN

25
24
21
18
15
25
24
21
18

25
24
21
18
15
32
28
24

UO‘NN

.4541
.4467

.4437
.4282
.4539
.4467
.4445
.4437
.4282
.4538
.4467

.4437
.4281
.4451

.4421
.2202
.2204
.2137
.2030

~103-

.5451
.5529
.5555
.5546
.5352
.5456
.5531
.5555
.5546
.5353
.5458
.5532
.5555
.5546
.5351
.5510
.5551
.5526
.6386
.6406
.6245
.5951

.0006
.0003
.0000
.0017
.0362
.0004
.0002
.0000
.0017
.0362
.0003
.0001
.0000
.0017
.0365
.0035
.0007
.0052
.1092
.1125
.1340
.1682

.0001
.0000
.0000
.0000
.0004
.0001
.0000
.0000
.0000
.0003
.0001
.0000
.0000
.0000
.0003
.0004
.0000
.0001
.0302
.0259
.0273
.0335

.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0018
.0008
.0004
.0003

.4404
.4477

'.4500

.4508
.4671
.4405
.4477
.4500
.4508
.4671
.4406
.4477
.4500
.4508
.4672
.4493
.4503.
.4524
.4498
.4486
.4624
.4861

86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108

GOOO‘O‘O‘N

10
10
10
10
10
14
14
14

14
18
18
18
18
18

OU§WNOU§UNO

#NO‘UrFUNINUl-F-‘UN

mb

UbUGNUWUO‘NU5‘UGNUDUO‘N

pa
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.883

.2353
.2318
.2230
.2095
.1915
.1723
.2345
.2248
.2108
.1921
.1721
.2356
.2255
.2113
.1924
.1718
.2363
.2259
.2115
.1924
.1717
.2382

-104-

.5532
.6917
.6859
.6626
.6237
.5706
.5135
.6960
.6700
.6294
.5740
.5142
.7004
.6729
.6314
.5752
.5139
.7029
.6743
.6323
.5758
.5140
.7028

.2122
.0608
.0716
.1014
.1479
.2073
.2628
.0619
.0947
.1433
.2060
.2658
.0577
.0922
.1419
.2058
.2680
.0552
.0910
.1414
.2057
.2687
.0497

.0460
.0117
.0105
.0130
.0189
.0305
.0514
.0075
.0105
.0164
.0278

.0479

.0062
.0094
.0154
.0266
.0462
.0055
.0088
.0148
.0261
.0455
.0091

.0002
.0005
.0002
.0001
.0001
.0001
.0001
.0001
.0001
.0000
.0000
.0000
.0001
.0000
.0000
.0000
.0000
.0001
.0000
.0000
.0000
.0000
.0002

.5225
.4231
.4298
.4471
.4757
.5200
.5770
.4255

.4734
.5192
.5792
.4236
.4428
.4726
.5190
.5807
.4225
.4422
.4724
.5190
.5812
.4193

109
110
111
112
113
114
115
116
117
118
119
120
121
122
123

125
126
127
128
129
130

O‘C‘O‘O‘O‘NNNNN

94 r4 r9 r9 e9 r9 r! r9 r9 r9 r9
as ca 9- a- e- c~ S: c» c: c: c: c:

10
12
14

10
12

10
12

10
12

14
12
10

16
14
12
10

16
14
12
10

16
14
12
10

16
14

.2356
.2224
.2023
.1791
.1634
.2484
.2468
.2362
.2111
.1761
.2495
.2480
.2379
.2122
.1750

.2499

.2484
.2383
.2124
.1742
.2500
.2486

~105-

.7031
.6653
.6054
.5359
.4884
.7420
.7399
.7084
.6330
.5280
.7459
.7437
.7135
.6365
.5249
.7471
.7449
.7148
.6371
.5224
.7477
.7455

.0550
.1024
.1740
.2492
.2867
.0084
.0126
.0532
.1500
.2788
.0041
.0081
.0472
.1468
.2858
.0027
.0065
.0458
.1466
.2903
.0020
.0057

.0064
.0098
.0182
.0358
.0615
.0011
.0007
.0021
.0060
.0172
.0005
.0003
.0015
.0045
.0143
.0003
.0002
.0012
.0039
.0013
.0002
.0002

.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000

.4243
.4494
.4949
.5580
.6112
.4024
.4052
.4233
.4738
.5679
.4007
.4033
.4204
.4713
.5714
.4002
.4026 .
.4197
.4708
.5741
.3999
.4023

 

131
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133
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135
136
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139
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141
142
143
144
14.5
146
147
14.8
149

waUUUUUCUUUUtflU’uUUUUUUU

r4 #9 ea
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O‘O‘O‘O‘O‘NNNNN

1d rd rt rt 1- hi r0 1d rd rd
Oma'fiJ-‘J-‘OOOO

10

12

12

18

12

15
18

12
15

12
15

12
10

24
21
18

12
24
21
18
15
12
24
21
18
15
24
21

15
24
21

.2384
.2123
.1737
.2425
.2421
.2292
.2067
.1774
.2496
.2494
.2435
.2170
.1665
.2499
.2497

.2448

.2189
.2499
.2498
.2450
.2192
.2500
.2498

~106-

.7151
.6370
.5210
.7226
.7259
.6875
.6120
.5320
.7481
.7482
.7306
.6510
.4994
.7491
.7491
.7344
.6568
.7494
.7493
.7351
.6576
.7496
.7495

.0454
.1471
.2928
.0314
.0304
.0799
.1641
.2614
.0022
.0024
.0255
.1303
.3253
.0009
.0012
.0206
.1232
.0006
.0009
.0197
.1223
.0004
.0007

.0011
.0036
.0125
.0035
.0016
.0034
.0095
.0292
.0002
.0001
.0044
.0017
.0088
.0001
.0000
.0002
.0011
.0000
.0000
.0002
.0009
.0000
.0000

.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000

.4195
.4709
.5757
.4124
.4130
.4362
.4839
.5637
.4007
.4010
.4106
.4608
.6007
.4002
.4005
.4085
.4568
.4000
.4003
.4081
.4562
.4000
.4003

 

155
156
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GU8‘UO‘NU3‘UONG

.2451
.2192
.1689
.1681
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.1703
.1686

.1661

.1622
.1555
.1689
.1673
.1664
.1631
.1588
.1667
.1666
.1664
.1669
.1474
.1467

-107-

.7353
.6575
.7972
.8010
.7974
.7823
.7512
.8176
.8192
.8159
.8021
.7711
.8293
.8317
.8315
.8153
.7940
.8332
.8332
.8318
.8331
.8381
.8413

.0194
.1225
.0293
.0278
.0340
.0525
.0871
.0110
.0114
.0171
.0339
.0690
.0017
.0010
.0021
.0213
.0465
.0001
.0002
.0019
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.0101

.0001
.0008
.0043
.0031
.0030
.0041
.0077
.0011
.0008
.0009

.0018-

.0044
.0001
.0001

.0003
.0007
.0000
.0000
.0000
.0000
.0032
.0020

.0000
.0000
.0003
.0001
.0000
.0000
.0000
.0001
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0002
.0001

.4080
.4563
.5822
.5846
.5932
.6092
.6346
.5826
.5890
.5987
.6134
.6388
.5917
.5977
.6011
.6131
.6297
.6001
.6001
.6011
.5991
.6690
.6731

 

177
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183
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185
186
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191
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193
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195
196
197
198

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.1447
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.1388
.1456
.1438
.1429
.1422
.1375
.1429
.1429
.1428
.1425
.0708
.0704
.0698
.0690
.0681
.0708
.0700
.0692
.0682
.0673

~108-

.8414

.8277
.8536
.8557
.8567
.8533
.8251
.8571
.8571
.8571
.8548
.9166
.9201
.9217
.9214
.9176
.9252
.9271
.9281
.9281
.9258

.0121
.0121
.0300
.0007
.0004
.0004

.0366
.0000
.0000
.0001
.0027
.0097
.0079
.0074
.0086
.0130
.0032
.0025
.0025
.0034
.0064

.0018
.0011
.0035
.0001
.0000
.0000
.0001
.0008
.0000
.0000
.0000
.0000
.0028
.0017
.0011
.0010
.0013
.0007

.0002
.0003
.0005

.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000

.0001
.0000

.0000
.0000
.0000
.0000
.0000
.0000
.0000

.6821
.7006
.7174
.6865
.6951
.6998
.7031
.7271
.7000
.7000
.7000
.7019
.6915
.6952
.7003
.7066
.7141
.6977
.7059
.7151
.7258
.7368

199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217

218~

219
220

”N‘N‘N'IN'Q‘NNMHNNNNNIIHN

O‘O‘O‘O‘OkO‘O‘O‘O‘O‘O‘O‘O‘O‘O‘O‘O‘O‘

O1

O‘O‘O‘

10
12
14
10
11
13

17
19

10

12

11
13

15
14

10

20
19
17

13
11

14
12
10

23
21
19
17

-109-

.0739
.0705
.0673
.0667
.0664
.0639
.0669
.0667
.0667
.0667
.0666
.0656
.5022
.4934
.5008
.4990
.4889
.4489
.5092
.5039
.5000
.4994

.9252
.9290
.9326
.9330
.9294
.8942
.9331
.9333
.9333
.9333
.9322
.9184

.4732 .

.4876
.4986
.4989
.4888
.4488
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.4961
.5000
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.0007
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0002

.0042
.0410
.0000
.0000
.0000
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.0012
.0160
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.0218
.0980
.0002
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.0001
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.0001
.0000
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.0000
.0000
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.0000
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.0000
.0000
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.0054
.0022
.0001
.0001
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.4043
.0000
.0000
.0000
.0000

.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0002
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000

.6743
.7074
.7431
.7495
.7530
.7823
.7474
.7493
.7499
.7500
.7509
.7622
.5875
.6063

.5989.

.6011
.6136
.6682
.5890
.5953
.6000
.6007

 

221
222
223
224
225
226
227
228
229
230
231
232
233

235
236
237
238
239
240
241
242

lflflflflflflflflflfiflfififlflfifififi‘fl

O‘GO‘O‘@GOOGO‘

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16
14
12
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24
22
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20
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.4937
.4608

.3022
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.2936
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.3275
.3269
.3240
.3199
.3143
.3318
.3323
.3322
.3320
.2962
.3681
.3643
.3591
.3531
.3470

-110-

.4937
.4608

.5876

.5881
.5828
.5738
.5632
.6520
.6528
.6470
.6380
.6254
.6634
.6644
.6643
.6639
.5923
.5103
.5173
.5153
.5086
.4989

.0125
.0078
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.1091
.1094
.1092
.1178
.1310
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.0001
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.0148
.0122
.0111
.0107
.0110
.0018
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.0009
.0009
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.0003
.0001
.0001
.0001
.0025
.0115
.0088
.0077
.0072
.0071

.0000
.0000
.0007
.0003
.0001

.0003
.0001
.0001
.0000

.6077
.6510
.3258
.3258
.3325
.3370
.3405
.3053
.3058
.3086
.3125
.3177
.3014
.3010
.3011
.3012
.3377
.2663
.2702
.2741
.2777
.2803

243

245
246
247
248
249
250
251
252
253

255
256
257
258
259
260
261
262
263
264

HHHHHHHHHHHIHMIEMHHIUMH

O‘O‘O‘O‘GGO‘O‘O‘O‘O‘O‘OO‘O‘G‘GO‘OO‘OO‘

10
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rt 94
94 c: 19

GOUNOU§U

#9 r9
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~111-

.3895

“.3876

.3825
.3754
.3662
.3957
.3959
.3956
.3942
.3942
.3426
.5056
.5041
.5024
.5010
.5001
.5044

.4992
.4897
.5012
.5000

.5781
.5793
.5718
.5601
.5443
.5933
.5938
.5933
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.5911
.5138
.4860
.4883
.4893
.4894
.4887
.4946
.4986
.4990
.4896
.4986
.5000

.0304
.0319

.0634
.0884
.0107
.0100
.0109
.0145
.0145
.1413
.0068
.0067
.0075
.0088
.0104
.0008
.0005
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.0019
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.0002
.0002
.0023
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.0009
.0008
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.0000
.0000
.0005
.0000
.0000

.2566
.2579
.2613
.2661
.2723
.2527
.2526
.2528
.2537
.2537
.2919
.5885
.5909
.5928
.5937
.5926
.5944
.5988
.6010
.6127
.5986
.6000

265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282

NHHHHHHHHHHHHHHHHH

U‘O‘O‘O‘O‘O‘O‘O‘O‘O‘O‘OO‘OGO‘O‘O‘

13

17
19

CONGU‘U

10
12
11
13

17
19

17
15
13
11

U§UON

14
12
10

19
17

13
11

.4999
.4999
.4999
.4998
.4920
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.4893
.4878
.4863
.5012
.4996
.4950
.4981
.5001
.5001
.5000
.5000
.5000

-112-

.4999
.4999
.4999
.4998
.4872
.4864
.4851
.4834
.4811
.4984
.4994
.4949
.4977
.4999
.4999
.5000
.5000
.5000

.0001
.0002
.0003
.0004
.0154
.0174
.0196
.0223
.0253
.0003
.0009
.0089
.0038
.0000
.0000
.0000
.0000
.0000

.0000
.0000
.0000
.0000
.0053
.0055
.0059
.0066
.0073
.0001
.0001
.0011
.0004
.0000
.0000
.0000
.0000
.0000

.0000
.0000
.0000
.0000
.0001
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000
.0000

.6001
.6001
.6002
.6002
.6079
.6094
.6107
.6115
.6109
.5984
.6004
.6060
.6022
.5998
.5999
.6000
.6000
.5999

~113~

CW LABORATORY
1.1an 110mm; A 1 - 6;!

run Floetin; Deoi-ei Aritbetic Routine
'1'!!! Interpretive routine vith 18 interpretive

ordere, entered ee e cioeed routine. left

by en 8.! interpretive order.
m 0! wows 168
MP0.“ Thie routine Hamlet“ nubere in the
tinting deci-el fore. thet ie, nubere Ihich ere represented
ee A x 10’. It ie of the interpretive type. thie neene thet
it eeleote perenetere celled inmguive 9.59.3.9. which ere
written by the our one at e tine end perform e «1th
correepondin; to eech interpretive order. Interpretive
ordere any out nor-e1 eritbetio operation each ee eddi-
tioe end mitipiicetion end lone red tepe operetione each u
oomtin; end eddreee obenxiu.

In general. one will nee thie routine to
do ooqetetione which do not require the toll epeed of the
counter but which ere too tile-mean; to be done by bend.
1t ie eepeoieuy effective for problem with ecelin; diffi-
on1tiee. 111 e eenee, one my think of the floating deoi-el
routine ee converting the 1118210 to e uediu epeed floetine

~114-

deck-a1 coeputer having a very convenient order code.
ACCURACY About 9 decimale
mama! STORAGE o, 1, z
PRESET’PARAMETERS 83 ie used to epecify two locatione of
non-temporary etorage, 83 and 183, which are need for the
floating decien1.accueulator.
METHOD 0! USE The floating decfleel routine ie entered
at a etendard eubroutine. Following the entry, i.e., after
the tranefer of control to the subroutine, one begine‘writing
interpretive ordere. Theee ordere each occupy one-half word
and coneiet of a pair of function digite followed by a
eingle addreu. They, therefore. have the ease for- ae
etendard nechine ordere and my be read by the Decinal Order
Input with full uee of the conventional tereineting eynbole.
The first of the two function digite of an interpretive
order deecribee the group characterietice of the order and
eey take valuee 0, l. ..., 8. loneal aritheetic interpretive
ordere have thie digit equal to 8. The eecond of the two
function digite deecribee the type of interpretive order.
IMPRET‘IV! ORDER LIST WITH FIRST MO! 0101‘! b t 8
let I be the floating deck-cl nueher in the floating
acculetor and let 1(a) be the floating decimal mnber in

location n.

 

80!
81h
82h

83h

8411

85:1

8611

87h
880

89h

8.1.1.6. 1r by I/I(n).

Replace I by I - I(n).

Replace I by -I(n).

Tranefer control to the right hand interpretive order
in n if I >.0.

Tranefer control to the left hand interpretive order
1e 11 if ”,0.

Replace I by I + I(n).

Replace I by I(n).

 

Replace I by I x I(n).

Replace I by one ntnber read from the input tape
punched ee eign, any umber of decinel digite, eigu,
and two decinal digite to represent the exponent.

Ior era-ple. .8971 x 10 4°

would be punched ae

+ 8971 + 10.

Punch or print I ae a eign, n decinel digite. eign,
two decinel digite to repreeent the exponent and

two epacee. Thie print out nay be reread by thie
routine. After I ha been punched or printed, it

my not rain in the floating acct-alator modified.
n can tahe veluee 2 to 9.

Replacerynifos n<200.

~116-

88 n Replace I(n) by I.

8! e Replace I by III - lI(n)|.

8.) n Tranafer control to the ordinary llliac order on
thelefthandeideofn. Thieueedtoeecapefrol
the floating deoinal aubroutine.

8I 11 Give a carriage return and line feed and etart a
new block of printing having e colt-1a. Thie order
in only obeyed mg for a particular block of printing.
At thie tile, a counter ie net up which will cauee
a carriage return and line feed to occur auto-eti-
cally fro- then on after every eat of nubere that
ia printed.

W.

If the firet faction digit of an interpretive order
ia 0. l, .... 7. it will refer to one of a eat of control
regietere or b- regietere in the floating decinal routine
which are ainilerly Met-ed. Theee regietera are need for
counting the ember of paaaagee through loopa or cyclea and
for advancing addreeaee on aucceeeive paaaagee. Ior thie
purpoae. a particular b- regieter which nay he need in a
particular cycle containa two counting indicea g. and ob.
Theaearebothintergeraintherangeo to1023. Theindex

 

-117-

ch ie need for counting purpoeee to deternine the nueber
of paeaagea through a loop. The index gb ia need for
advancing the addreeaea of interpretive aritl-etic ordere.
Although the interpretive order with first function digit
b ia not actually altered in the I-ory, it ie obeyed an
if 'b ia inoreaaed by one upon each paaeage through the
cycle. The multiplicity of b- regietera allowa one to progran
nany loopa within loope.

ORDIR LIST WIT)! n f 8

b0 :1 Replace I by I - I(n+gb).

bl :1 Replace I by -I(n+gb).

 

‘2‘ Repl‘c. ‘b’cbbyab'. 1. cb'. 1e
Then tranafer control to the right hand (if b2 u) or
left hand interpretive (if b3 11) order in n if °b"' l

 

b_3__n__+ in negative. Thia tranafer ie need at the end of a loop.

b4 11 Replace I by I + I(n + g5).

b5 u Replace I by Na 4» gb).

b6 u Replace I by I/I(n+gb).

b7 u Replace I by I x I(n+gb).

b! n Replace ‘b’ c" by 0, -n. Thie interpretive order ia
need for preparing to cycle around a loop 11 tinea.

b8 :1 Replace I(n + ‘h’ by I.

 

b8 u
bLn

81.11

d

~118-

Replace r by lrl - |I(n+gb)l.

Replace 3b’ cbby 3b + n. °b' Thia interpretive order
in need when one wiehea to atep addressee by none
increment other than +1 in a loop. If one placea

bl. 1022 in a loop, the effect will be to decreaee
addreeeae by one on each paeaage. bl. 1 will increaae
then by 2. etc.

Replace gb ch by 11, ch. where b ie the hat b-regieter

referred to by acne previoue interpretive order.

yuan 0g mornnmnmmmgva ORDERS

BI
80
84

81
85

82
83

87
86
8!
88
83‘
81.
8.1

5 eilliaeconda + e x (3/2). where e ie the umber of
ahifte required to convert A, p back to etandard fan.
2 nillieeconda

3 nilliaeconda

5 eilliaeconde
6 nillieeconda
3 sillieeconda
3 eilliaeconde
3 nilliaeconda
2 nilliaeconde
3 nilliaeconde

 

 

~119-

When an interpretive order is preceded by b I 8, add
one millioecondlto the above times.

When one wiehee to repeat a cycle of interpretive ordere
n tinee, the interpretive order bR 11 may be written before
entering the loop to act the counter cb to .11. The inter-
pretive ordere in the leap will be obeyed n times if the
loop ia terminated by b2 or b3 interpretive order to tranefer
control to the beginning of the loop. Thie tranafer of control
interpretive order will be obeyed n-l tinee and dieobeyed the
nth tine.

M Auxiliary Routinee. It ie often convenient to be
able to leave the floating decinal routine an an to Iodify
interpretive ordere or to perfore calculatione which my be
done nore effectively outside of floating point. To leave
the floating decimal routine one ueee an 8.! 11 order. (All
etandard floating decieal auxiliariee are entered in thie way.)
To return to floating decinal, one ehould tranefer control to
the left hand aide of word 29 of the floating decinal routine.
The interpretive order following the 8.! n order which wee
laet obeyed will then be obeyed and co on. In thie way, it
ia not neceaeary to plant a link in auxiliary eubroutinee.

One nay. in fact, think of the 81 11 order ae a eubroutine

 

~120

order. In case any changes are made in the floating decimal
accumulator while outside the floating decimal routine, con-
trol should be returned to the left hand side of word 19
rather than 29 so that this number may be standardized before
re-entry. ‘

Handling of Numbers. Each number is represented in the
form A x 101’ where l ) IA! ) 1/10, and 64 > p 7, -64.

In a single register of the memory, the number A is placed in
the 33 most significant binary digite (a0, a1, ..., 1132) in
the eeee'way as an ordinary fraction is placed in the entire
register. An accuracy of between 8 and 9 decimal digits is
therefore achieved. The exponent p is stored as the interger
p + 64 in the 7 least significant digits of the some register.
Ior convenience, the floating decimal accumulator uses two
registers 83 and 133 for holding the number A x 10?. The
fraction a/2 is in S3 and the interger p -* 64 is in 153.

The only exception to the above rules is the number zero
which cannot, of course, be represented as A x 10p withIAl >,10.
Ior this reason, zero is handled in a special way. It is
represented as a number with.A I 0 and p 3 -64. This represen-
tation happens to correspond exact1y*with the ordinary’nuchine

representation of zero.

~121-

After each aritt-etic interpretive order is obeyed, the
afier in the floating decilel acctmlator is standardised,
i.e., the amber in 83 representing A/2 is adjusted so 1
IAI b 1/ 10 and p is changed accordingly. To acconplieh this,
control is transferred to word 19 in the floating deci-al ~
routine after each aritlmetic order.

If an interpretive store order is atteqted when I has
an exponent greater than 63, the nachine will stop on the
order 34 p at location p, where p is word 72 of the routine.

Imrtaet words in the Routine. Word 2 in the floating
deci-el routine detereines the location of the current
interpretive order. when obeying the left hand interpretive
orderin locations, thiswordis50nI85 20Iendwben
obeying the right hand interpretive order in location 11, it is
1.5 nI 00 20I. Other words of interest are the b-registers
...... start .6 word 158 (for .0 and co) and go to 165
(g7 and c7.) These registers hold gh and ch in the fore
80 “I 00 (2048 7‘ ch) I.

Warngg. When the same nudeer is continually added to
a am, such as when an argment is being increased, the error
can be quite large, because it is additive over a decade.
Ior eeanple, if we increase 10 to 100 by nits, we can get a

eerie».- error of 90 x 2'33 because the errors all have the

-122-

same sign. If we increase 103 to 104, we can have a maximn
error of 9000 x 2"”. This can easily be prevented by writing
an auxiliary subroutine to stabilize the fractional part of

I, i.e., to replace it by the nearest multiple of say 10‘7.

 

I‘U

claret!"

34H”

~123-

NOMENCLATURE
Holes of overhead product
Holes of feed
Rnthalpy of vapor stream
5 Rnthalpy of pure amount as vapor or liquid
lquilibriu constant (y/x)
holes of liquid
Plates above feed
Plates below feed
Heat flux, enthalpy of vapor ninus enthalpy of liquid
in passing streams
Reflux ratio (L/p)
Teeperature °I
Holes of vapor
Holes of botton product

a ,b,c,d Constants

h

P
9

Rethalpy of liquid streae

Partial derivatives used in rectifying section
Partial derivatives used in stripping section

Ratio of coepoaitioe of particular component on feed
plate as calculated fro. opposite directions

Hole fraction in liquid

Hole fraction in vapor

-114-

SUBSCRIPTS

Rectifying section

Condenser

Distillate

teed or feed plate

Constant of enthalpy polynonial

Particular couponent

Constant of equilibriun constant polync-ial

Plate usher in rectifying section, nubered in Arabic
nmsrals tron condenser to feed plate

Plate nuber in stripping section. nubered in lonan
nuarals fro- rehoiler to feed plate

Ieboiler

Stripping section

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

u)

-125-

BIBLIOGRAPHY
Brown, C. 6., and Martin, R. A., Transactions of American
Institute of Chemical Engineers, 332., 679, (1939).
Colburn, A. P., Transactions cg:~ American Institute of
Chemical Engineers, _3_‘_l_, 355, (1941).
Colhurn, A. P... Transactions of American Institute of
Chemical 3 ineers, 11, 805, (1941).
Donnell, J. U., and Cooper, C. 3., Chenical Engineerm,
21, 131, (1950).
Ebister, v. C., Transactions of American Institute of
Chemical Engineers, {32, 15, (1946).
Penske, H. 3., Industrial Engineering Chemistry, .231,
482, (1932).
Cilliland, E. R., Industrial and Engineergg Chemistry,
3.2.: 260, (1935).
Gilliland, E. R., Industrial and_!ngineering Chemistry,
3;, 918, 1101, and 1220, (1940).
Harbert, W. 0., Industrial Engineering Chenistg, 2A,
482, (1932).

Jenny, T. J., Transactions ogmrican Institute of Chemical

Engineers, 3.3.0 635, (1939).

Levis, V. K., and Cope, J. (2., Industrial and Engineering
Chemistry, .23., 498, (1932).

 

12)

13)

14)

15)

16)

17)

8a)

-125.

Levis, W. 1., and Hatheson, C. 1... Industrial and
Engineering Chemistry, ‘21:, 494, (1932).

McCab’e, W. I... and Thiele, E. W., Industrial and
Engineering Chemistry, 11, 605, (1925).

Ponchon, Tech. Moderne, g, 20, (1921).

Sorel, E., "La Rectification do 1'Achol," Paris, 1893.
Thiele, E. W., and Ceddos, R. L., Industrial and
Engineering Chemistry, 22, 289, (1933).

Underwood, A. J. 0., Journal ognstitute of Petroleum
(London) §_2_, 614, (1946).

Montroso, C.F., and Scheibol, 3.8., gndustrialm

Engineering. Chemistgz, 18, 263,. (191%).

<.- ._.....

 

"'TITIiWLWIL 17111911131117! IBM/WIT! filifififlilijfi/I‘m”

03056