CA1193466A - Liquid level indicator - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE A method and apparatus are disclosed for measuring changes in relative distance between a float and both a signal source and a detector. Also disclosed is the advantageous use of such an apparatus for detecting losses as little as 0.02 gallons of liquid per hour from a tank otherwise capable of storing 1,000 gallons or more of such a liquid.

Description

~3~

~C'~;GROU~D OF T~3E INVENT~ON
FIELD O~ l`HE INVENTION
This invention r~lates to the art of detecting a liquid level. More particularly, this invention relates to the art of detecting leaks in liquid st~rage tanks.
PRIOR ART
To detect a loss of 0.02 gallons o liquid per hour from a storage tank, e.g., an underground gasoline storage tank, by determining changes in the liquid level in the tank can be very difficult~ By way of illustrating this difficulty, consider a cylindrical ~ank half full of liquid containinq about 4,000 gallons and oriented on its side having a length of 21.3 feet and a diameter of 8 feet~ If one gallon were removed from such a tank, assuming all other relevant variables to be discussed hereinafter are held constant, the level of liquid measured relative to the lowest point of the ~ank would change from 4 feet to 3.9992 feet, i~e., a change in liquid level of 7.85x10-4 feet. To observe this change in liquid level is very difficult. Note that even if there were no leaks in this tank~ a change in temper-ature of liquid, e.g., gasoline, of 0~25F causing a density change of o01139 lb/ft3 cubic feet per pound would result in a change in the observed liquid level of 7.8~x10-4 feet.
Consider also the impact of evaporation. Assume, for example, ~1) a tank half filled with gasoline at 70~C, and ~2) that the air at ab~ut one atmosphere above this gasoline in the tank has substantlally no gasoline vapor, then the level of liquid would change by o.oa738 fee~ as a result of the vapor abDve t~e li~uid changing from a vapor containing substanti~lly no ~asoline vapors ~o one saturated in gasoline vapors~

Sunmar~ Industries, a division of Sun Oil Company of Pennsylvania, sells a leak detect:ing device which relies on the Principle of Buoyancy, i~e., the principle that a body suspended in a liquid is ~uoyed up by a force equal to the weigh~ ~f liquid displaced by such a body. A sensor which extends from a sensitive, but rugged balance, and which is partially submerged in the tank ~luid de~ects buoyancy changes corresponding to either an increase or a decrease in the total amount of liquid in a tank.
The Kent Moore System is a method and apparatus for determining whether there are any leaks in a liquid storage container. One of the steps necessary in carrying out a determination of leaks is ~o pressurize and fill to excess a storage zone. Details concerning the experimental procedure are published by Kent-Moore Corporation for Model 1000, Tank Syste~ Tightness Tester~ There are several problems in the Kent-Moore System which result in readings which are not stable~
One source of these problems involves gas bubbles which become trapped within a storage tank or zone~ Since most storage tanks are not absolutely level, vapor pockets almos' inevitably form as such a tank is filled to excess.
Trapped gas bubbles tend to chanye in volume in response to changes in temperature and/or changes in pressure.
During a typical Xent-~oore test, pressure is firs~ inc~eased and then decreased~ Trapped gas bubbles first decrease and then increase. in volume in response. Equil ibrium of the ir.al si~e of these bubbles requires that the atmosphere o gas within th2se b~b~les reaches a steady state, involvinq 30 temperature and CompositiOn.
Another source o problems arises because the Kent-Moore System uses a pump that necessarily inputs energy into ~he gasoline tanX. As a result o using such a pump, tempera'cure equilibriatit~n is vQry c3ifficult to ~ehieve,, small leak ~neasured by ~he Kent Moore Sys~cem is the difference between a temperature change times ~:he coefficient c:f expansion minus the vc>lume, l~st ~y a leak.
During tests with 'che Kent-Mc~ore System, it has been found that an obserYed volLIme often fluctl~ates lin b~7th a positive as well as a negative direction. This fluctuation is believed to re~ul~ from changes irl sizes of 'crapped bubbles.
In summary, t~e main dif~iculty o~ the Kent - Moore System 10 involves the excess filling of the tank which leads to trapped yas bubbles. These gas ~uhbles, ln turn, lead to variations in reading which are not raQcessarily representative of leaXs.
An apparatus or method capable c~f detectin~ leaks as easily as that disclosed by S~nmark ~ndustries ls both desirable and useful. Further, ar~ apparatus which can del:ect leak~ as well as the method o~ the Kent-Moore System, bu~
wi~hou~ its draw backs is both deslrable and U5e~Ul,, B~IE~ DlS~:l~lQn OP THE IN-JENq`101~
It is an cbject of ehi~ ~nt~on to provide a 20 sirnple and easy to use ~pparatus and method to detect small leaks,, e.g.., ~s l~ttle ~s 0.02 gsllQns p~r hour ~n a tank otherwise capa~l~ o ~oring 1, 000 g~llons or mor~
It is ~urther ~n objecS oE this invention 'co provide ~ methud and apparal us ~apable c~f comperlsating for tempera~cure changes so as . o di~tingu~sl~ c:hange5 in liquid level which ~re due to leaks rom tho~e due to temperature charlges,.
O~her ohjec~5 o thi~ ~rsvention are ~lear ba5ed on the spec:iicatlonO
Briefly" ~he objec's~ of ~h~s inven~ion carl broadly 30 be achi~ved by an appara~us eapable of detec~inq small ~hanges in loca~ion of a fl;~a~c me~ns~, ~Sore speci~ allyp an apparatus ~af this invention comprises in combinatic~n: a signal means for providillg s~r emitting a signal having ~ characteristic; a de~ector means for de~ecting a modulated signal by producing a response signal directly related to the characteristic; a support means for positioning the signal means and the detector means; and a float means somprising a means for floating at a desired depth in a selected liq~lid and a reservoir means for holding a measuring mediumD The float means is movably connectable to the s~pp~rt means. The detector means and the signal means are fixedly connectable to the support means so that the signal when emitted by the s;gnal means will have the charac~eristic of the signal modulated by the measurir.g medium. The amount by which the emitted signal is modulated to produce a modulated signal by the measuring mediu~ vari~s with cha~ges in lo~ation o~ t~e fl~at meansO
The detector means is oriented ~o detect the modulated signalO
An exampte of a signal means is a conventional light bulb.
An example of ~ de~ector means is a ph~to resistor which, for example9 uses cadmi~m sulfideO An example of a signal i5 electromaynetic radiationy such as would be emitted by a conventional light bulb. An cxample of a characteristic of.
a si~nal is intensity, An example of a meas~ring medium is a liquid having a k value defined in relation to Beer's Law in the range of about 0.1 to l,oO0 reciprocal centimeters~ Preferably, the k value of the measuring medium has a value in the range of about S0 to ab~ut 200 reciprocal centimeters~ By interposing varying amounts of measuring medium between the signal means and detector means the amount by which the signal is modulated can be made to vary~ If~ for example~ a change in location of the float means can be made to result in a change in 3Q amount of measuring medium between the detect~r means and the signal means, then a method for monitoring changes in location ~f the float means is made possible. This i5 discussed in more det~il hereinafterO

-'I

Another embc~iment of this ~r~venl:ion is a me~hod or detecting a leak lrl a storage t~nlc containln~3 a li~yuidO
Thc method cornprises de~ermining change~ in location of the f loat means discussed hereinaboveO
An improvement to thi~ method furtheE involves locatln~ the flt)at means at a depth approximately equal to VL~5L where VL 18 he volume of he ~elected l~quid iA
whieh ~he ~l~at means i~ located and ~, is fre~ ~urface ~re~
of the selected li~llid- ~y lc~cating t)~e f loat means at this 10 depth, temperature variatit:3n of the li~uid in the storage tank does no~ cbange the depth al'c wh~-:h 'che ~loat means 10at~ freely.. In other words, a subs'cant~ally temperature invariant floating position ~ maintained by 'che float means.
In still another improvement to the method of this inventionf the Yapor above the liquid ~s saturated with the liquid in the storage tank 50 as to mirlimize evaporation during a measurement of the lc)cation of the f lo~t means.
Several methnds readily understood in the ar'c for insuring that the vapor about the liquid is saturated in the liquid include a~comizing so as t~ fill the vapor ahove the liquid with small droplets of liquid or coating wil:h a ~hin layer o the li~auid surface~ of the container above lthe liquid so as to has'cer~ saturation nf th~ v~por above the liquid.
BRIEF DESCRIPTION 0~ T~E I)R~WINGS
Figure 1 discloses a ~ide elevation viLew partially in cross section t~ a ~an~ containlng an embodiment of an apparatus o ~his lnvon~ion Figur~ 2 discloses an enlarged v ew of a por~ion of the embodim@nt of this lnvention shown in Figure lr Flgure 3 is ~ ~op srle~d als:~ng î~n~ 3-3 o Fisur~ 2~, Fi~ure 4 discl~ses a schematic diagram of elect~ical corlnec~iQns from a phol~ detec~or to a mill~vol~c (mV) sl~rip --5 ~

~3 Al 4~ -~3~

chart recorder. The electrica1 connection converts resistance across the photo detector into millivolts.
Fi~ures 5 and 6 disclose an alternative embodiment of the present inventlon employing light transmitting fibers.
In Figure 6, a schematic diagram f~r changing light rec~ived by a l~ght receiving fiber into millivol~s is shown.
~ igures 7 and 8 are millivolt strip chart traces produced during ~WD experiments employing an apparatus of this invention, ~he details concerning these experimen~s are discussed ;n the examples.
DETAILED DESCRIPTION OF THE INVENTION
Figure 1 discloses an undergro~nd tank 20 in ground 30. Tank 20 comprises a cover support 24, a heighk adj~stment screw 26, cover plate 18 and a supply opening 22. Connected to height adjustmen~ screw 2~ is a tubular support 28.
Fixedly, attached to tubular support 28 is a sigllal source 32 and a detector support 34. Float means 38 is pivotally attached to tubular support 28 by means of a hinge ~9 compris-ing: a first pivot 40, a second pivot 42, a primary lever 41 and a secondary lever 43.
Figure 2 shows an enlarged drawing of a p~rtion of the embodiment of the apparatus of this invention ~hich is shown in Figure 1~ Figure 2 discloses a signal source 32~ a reservoir 44, a photo resistor or detector means 36; a detector support 34, a hin~e 49, a float means 38~ a band clamp 31~
electrical leads 23 and 25~ an india ink solutio~ or measuring medium 19 and gasoline ~r a selected liquid 21~ 5ignal source 32 comprises a houslng 29, a Plexiglass0 window 27S a bulb 33~ and a bulb socket 51, The electrical connections of signal source 3~ are carefully insultated so as to minimize any risks as~ociated wi~h gasolin~ vapQrs. ~rther, th~
housing 29 and Plexiglas ~ window 27 form a vapor tight seal 37 to maintain the eompartJnent containing bulb 33 and bulb -G-~ocket 51 free from any explDsive vapors. ~inge ~9 corrprises a first pivot 40.. a sec~nd plvot 42, a primary lever 41 and a secvndary le~er 4~.
Siqnal sourre 32 i~ ~iacedly at~ached to tubular sul?port 28 by means of a band clamp.310 A de~ec~or ~;upport 34 is held ir~ a fixed position relative to tubular support 23. ~ one end of detector E;upport 34 is located a photo resistor 36 within a sealed compartmen ~2. A curved glass cover 35 f i~s over photo resistor 36 :sr de~ectc~r means 36 10 and keeps any in~ia ink solution lg outside seal~d compartmer 52. Electris:al leads 23 from photo resistor are attached as shown in an electric circuit schematically shown in Figure 40 One end o~ lead~ 23 is directly attached to the mV recorder input S2 ~snd the other end is indirectly connec~ed ~o the m recorder input 63 through ground 58. Electrical leads 2~
are attached at one end to ~round 58 and at the other end to a voltage source (not shown) which Jnust maintain a subs~an-tially constan~ volkage to the ilament of bulb 33 so that the inter~sity of light emit~ed by bulb 33 does not vary 20 signif icantly..
Bri fly, the s:~peration of the apparatus disclos?d ~n ~igu~es 1 and 2 is as follows.
The ~ at means 38 whach ic movably attac:hed to tl~bular slJppor 28 is capable of mov;ng rela~ive to tubular suppor~ 28~ Since flo~l: means 38 conlt:ains weights 57 ~Figure 1~, it m~intains a ~ubstan~;ally ver~cal orientation with~n g~soline 21. Because floa~ means 38 rema~ns in a ~ubstantially vertical orien~ation due ~o n~tural bl~oyancy orce~, only one hinge 49 is required although others may be used.
The first piv~ 4~ comprises a ~ 47t stainless steel tube ~3 which is attached to tubular support 28 an~ ~ primary lever 41 which ~s pivotally m~us~ted within tube 53. Second pivol~ 42 comprises a lj~ tainless steel tube 54 ~nto which ~7--~3~

primary lever 41 is inserted and pivotally mounted in a manner simila~ to that of first pivot 40, and a second lever 43 is fixedly attached to 1/4" stainless steel tube 549 The main purpose of hinge 49 is to permit movement of 10at means 38 relative to tubular support 28~ ~ther arrangements can be used which fulfill the same purpose as hinge 4g.
Reservoir 44 is fixedly attached, e.g.~ either directly or indirectly, to secondary lever 43. Similarly, float means 38 is fixedly attached, e~g.~ directly or in~irectlyt to secondary lever 43. As fl~at means 33 moves up or down in response to changiny buoyancy orces~ e.g., due to 105s or gain in the amount of gasoline 21 in tank 20, reservoir 44 changes position relative to detector means 36. Since both si~nal source 32 and detector means 36 are in a fixed position relative tubular support 28g the relative position of signal source ~2 to detector means 36 rema;ns constant throughout changes in location of flo~t means 3B~ ~or example, as float me~ns 38 moves upward, reservoir 44 fixedly attached o float means 38 also will move upward relatiYe to tubular support 28. The amoun~ of india ink 501ution 1~ above photo resistor 36 indicated by ~ouble ar~ WL~ will incre~se ~s float means 38 moves upward and decre3se as float means 38 moves downward relative to ~ubular support 2B. Light from signal source 32 provided by bulb 33 passes through a Plexi-glas ~ window 27 and between the arms of primary levex 4ll then through india ink solution 19 having a thickness of ~L"
and finally impinges upon photo resistor or detector means 36. The distance "L"-as it increases will cause a decrease in the intensity of light picked up and absorbed by photo resistor or detector means 360 Example I discusses in more detail the relationship o~ the intensity detected by photo resistor 36 and the voltage output from electric leads 23/

Figure 3 is a top view along line 3-3 of Figure 2 Figure 3 discloses tubular support 28, detector support 34, detector means 36~ first pivot 40, second pivot 42, primary lever 41, cross bar 46 and reservoir 44 containing a measuring medium 19. Cross bar 46 fixedly attached to detector support 34 is useful to aid insertion of the device of this invention by limi~ing the amount of movement around first and second pivots 40 and 42. Movemen~ around first and ~econd pivots 40 and 42 is limited because primary lever 41 contacts cross bar 46 when the maximum amount of counter-clockwise rotation around first pivot 40 oceurs~ In o~her words, as the ~evice of this invention as shown in Figure 2 is withdrawn through supply opening 22, primary lever 41 rotates in a counter~
clocXwise rotation around first pivot 40. This counter-clockwise rotation continues until primary lever 41 contacts cross bar 46. Since further counter-clockwise rotation is precluded ~ft~r pr~mary le~er 41 conta~ts cross bar ~6, the remaining portion of this invention fixealy attached to secondary lever 43 then begitls to move as tubular support 28 moves.
Clockwise rotation aro~nd first pivot 40 will be limited due to contact between top su~face 55 of reservoir 44 and firs~. pivot 40. ThLS limitation to ~lockwise rotation is necessary to m~intain the proper rela~ionship of hinge 49.
Figure 4 discloses a schematlc measuring circuit 60 which includes electrical 1eads 23 of detector 36.
~easuring ci~cuit 50, comprises a constant voltage source or batte~y 50 and a resistor 45~ Resistor 4~ and detec~or 36 are in series with one another. The voltage differences across detector 36 ~re measured and recorded b~ means of millivolt recorder 48 on strip chart 61 (not shown). Battery 50, for example, can have a volta~e of 1~5 volts when resistor 45 has a resistance of about 1005000 ohms. Detector 36 preer~bly uses cadmium sul~ide.
_9 P7eas~lring circuit 60, shown schematically, cc:nverts the resist~nce across detectcr 36 illtO a voltage difereratial across detec~or means 36~, This Volta9Q differential across detector 3~ is me~ured ~nd res:c)rded ~y m111~volt recorder 48 on a s~rip char~ 61~ The v~ltage sollrce 50 must be sub-stantially cons~an~ not only to keep the intensity rom bulb 33 substantially constant" but also to ~ceep 'che total voltage drop across both resis or 4~ and detector 36 sub~antially cons~an~ .
The apparent resi~t~nce across det~ctor 36 will vary dependinq upon the ineensî~cy of ligh~ radia ion i1npingi~g thereon. The amoun~ o transmitted light radiation reaching detector 36 from light ~ource 33 will vary, all o'cher facltors to be discussed hereinafter being equ 1, logarithmically w~th the height L c~f liquid 19 ~Figure 2~.
2n a pre~erred em}:odimerlt, 'che transm~ ttance characteristics of 3neasurins medlum.l9 will follow a simple form of Beer's ~awl, ~L.e., I/Io 3 e ~ Z o The X is ~ constan~c which cancels out as shown ~n ~n. e~sample~ Carbon black or graphite e.g~ I in an india ~nk solutior: of albout one percent ,, has been found particularly su~table iLr~ this invention.
The val ue of k in r~ciprocal cen~imeters is preferabl}Y in excess of ~0~. The larger the Yalue o~ k~ the more sen~itive is the instrumen~O ïf lc beeomes too ~ arge ~ e ~ g . ~ much above 1000~ minute vibrations can become a serious proble~n and/or the inten~ity of l:ransmitted ~ ight can become diminished to a point that makes detecticln difficult. Pre~Eerably, k ~as a value ln the range of about 50 to ~bout 200 reciprocal centim2teg s ~
Fi~ures ~ d 6 dicelose an alternative embodiment ~to ~he invenl~ion ~hown ln Figures 1 and 2. In place of sign~l source 3~ a trans~ tin~ f iber 70 i5 used ar;d in pl~ce o~ de~e~or 36 ~ rece;ving f~ber 72 i~ used~ O~her elements disclosed in Figure 8 are numbered with those numbers of the same or equivalent elements of Figures 1 and 2 Althoug!~ fiber 70 is indicated to be a transmittiny fiber~
i~ may also be a receiving fiber when receiving fiber 72 is alternati~ely a ~rarlsmi~ing ~iber. A ~ocusing lens 71 may be inserted between ~ibers 70 and 72 ~o provide a collimated beam therebetween.
Fiyure 6 is a schematic representation of the alternate embod~ment shown in Figure 5. Disclosed in Figure 6 are a battery 7~, a light emitting diode 74t a transmitting fiber 70, a collimating lens 71 (in phantom outline), an absorbing fiber 72, a photo diode 76, a means 78 for convert-ing current to vol~age and millivolt recorder 48.
The device schematically disclosed in Figure 6 operates as follows. Power from battery 75 causes light emitting diode 74 to emit light which is transmitted by fiber 70. Optionally, a collimating lens 71 collimates the beam so as to minimize undesirable dispersionO Light received by fiber 72 is transmitted to a photo diode 76. The current produced by photo diode 76 is converted into voltage by a two-step electronic circuit. The first step of the electronic i~
circuit collectively shown as box 78 is to convert current into voltage by ways well recognized and understood in the art. Devices useful as transmitting and receiving fibers with couples to transmitting and receiving photo diodes are sold by Skan-A-Matic Corporation, Elbridge, New York. A
second portion of the ci~cuit 78 converts the voltage pro-duced by the first step of converting current to voltage and ampliies such vol~age so as to pro~ide a workin~ voltage capabl~ of driving a milliv~lt recorder 48. The amount of light r*ceived by fîber 72 which passes through collimating lens 71 will depend primarily upo~ the amount of measuring medium ~r india ink solu~ion 1~ which is be!~ween ~r~nsTni~ting fiber 70 and receiving fib2r ~2. ~e o~served vol age on the millivol~c ~ecor~er ~8 will vary in ~he same manner as in Figures 1 and 2 ~I:o disc:loE;e the relatiYe movement of ~loat means 38 wi1:h respec~ ~o bo~h tubu:lar support 28 ~nd anything fixed rel3~iv~ to ~ubular suppc~rt 28.
ït is possible by varying the weights 57 to position float means 38 aJe a dep~ch ~o that c:hanges in the height of surfa;:e 56 due to tempera~ure changes of the gasolir)e will not cause float means 38 to change its posi'cion. The depth required to ma~ce float means 38 invariant to changes in tempera'cure of the gasoline andJor tank will depend upon the particlJlar linear coeffic;ients of exp nsion for the liquid 21, the tank 2û and ~he ~loat means 38~ This depth is approxima~ely equal to ~he liquid volume divided by the free liquid ~urface area 56 (Figure 1 ) . Derivation of a formula giving this dep~h is given in more de'cail in an example hereirl.

8eer~s Law for scatter c7~ light r~diation of frequenc$r f through a liquid of thickness L ~s: If~IfO
~ e }~fL where If~ is ~he ini~ial intensity of light radiation o~ a parlticular frequency i~; I i5 lthe intensity csf l.i gh~ o freguency ~ ltransmi~ed 'chrough a li~yer of liquid o~ 'chickness L; and X~ is a physical ~onstant ch~racteristi~
Qf the liqLIid., ~ oæ an ~nd~a ink ~slut~on o abou~ 1%, the k~ f Beer9s Law for ~ reguenc:l~s of l~ght fr~ a 100 watt bul~
are su~stantia~ly equal~ ~h~ vois~s any prs:~blems rom 30 using llghg having dl~ferell~ freq~encigs a~nd di~ferent ~ntensl~ies :IEor e~ch ~uch requency4 ~,e. Bee~ aw simplifies to I/I ~

~1 ~3'~

Any change in the initial intensity, I0, results in a proportional change ~n ~he transmit~ed intensity~ I~
so that the ra~io o I/I0 is unchancjed. Consequentlyt changes in the intensity of light transmitted by a l.ight soLlrce due to factors such as changes in line voltage or age of liqht source, e.g9 bulb 33, d~ not affect the ratio of I/I0 or the L value observedO
Because of the nature of a photo resistor uSili~ing~
for example cadmium sulfide, the internal resistance, RF Of the photo resistor is a constant divided by the intensity of light impinginy on the photo resistor. Therefore~ ~he ratio R2/Rl is eq~al to the ratio Il/X2.
If E2fEl is equal to R~/Rl r then any change due to system varia~les such as battery voltage changes, temperature changes and mechanical stresses which do not affect ~he value of L observed also will not affect the ratio of E2/Elo This is so because I2/Il are only affected by changes in provided k remains constant.
Demonstration that.
E2/El=I2~ R2/Rl for the measuriny circuit 60 shown in Figure 4, wherein Rl=~nternal ~esistance of detector 36 when a light of intenity Il is impinging th~reoQ;
R2=internal resistance of detector 36 when a light of intensity I~ is impinging thereon;
. El=the observed milllvolt value recorded on a strip ohart.
E2=the observed mil7ivolt value recorded on a str;p chart af ter removal of 1 quart of liquid from tank 20;
Ew-~oltage across resistor 45 and detector 36, a constant, and ~13-f~

Rczresistance o resistor 45, a constant~
E
Ew ~ ~G R2~ ~2) Ew R 2~RC
Equati~:>n~; tl~ and ~2) are derived based on Ohm~s Law, r V ~ iR~ wherein V 25 vol tage, i ~ electrical current, and R = resistanceO
from equation ~1~
~El~ C~:3 3D P~l~EW-El~ ~3) ~rom equation (2) (E2~ (Rc) ~ R~,(Ew rE;~ (4) dividins equation (3) by e~auation (4~s E2~El ' ~ R2/Rl ) 1 ( Ew-E~ Ew E~ ) ] ( 5 ) ~ince E~ is much grea~er th2n 1:2 and El W-~2 ~ W~ 5 ~e~ s~ e o 20 1, and thexefore e~ation (5~ sin~plifies to,, E 2JEl ~R:2~Rl P~lso ~inc~ I2f~ /R:2 based wpon the lnheren~ character of pho~o resis~or ~3S;D there~ore, E2/13~ R~ 2-As~ume:
}1 and I2~ tensity o~ light received by detec~or 36 at t~O and talS hrs, re~pectiv~ly.
I3~ ens~y o~E llghl: received by detector 36 be~ore ~ny gasol ~ ne i5 removed; ~n~
Idd--ln~ensi~y of light reeeived by detector 35 ~f~er 1 quart of gasoline 21 has beerl removed rom a ~an3c 20,o therl by 13eer's Law ~Eor ~n India Inlc Solution~

~ f~ ~

(Il~X~ n(E2/El~k(L2-Ll)=kh1 ln(I3/I~ ln(E4/E3~=k(L,4-L3~=kh2 Vl=Sh where: .
Vl=volume of liquid removed for a change in liquid level of ;ll~
V2=v~ me of liquid removed for a change in liquid level of h2; and S-surface area of free surface 56 in tank 20 shown in ~igure 1.

Vl ln(E2tEl) ~ k S . Z Vl = n ln(E47~E3) 5 if ~2 is a kno~n volume, say i quart and defining ~1 equal to n, th~n n is ~he number of quarts in V

ln(E2/El)=n ln(E4~E3)-ln(E4/E3)n thereore, / / ~n In Figure 7, El is 0.8-0 Y~lts, as recorded on strip ehart 61, and corresponds t~ some ini~ial intensity Il received by detector 36 at time zero; E2 is 0~32 vo~ts at some time 15 hours af~er the start of the experiment. At time zero~ it is necessary to saturate the vapor above surface S6 with gasoline or whatever the stored liquid 21 ls to avoid changes in level of liquid 21 due to evapora~ion. This problem is discussed in the Specificat:lon in a paragraph bridging pages 2 and 3.
Als~.at time zero, 1 quart o gasoline 19 was removed and .
the initial and final volts recorded on strip chart 61.
Initial E3 and E4 were recorded as 0.80 and 0.43 ~lt~, respectively. After lS hours, 1 quar~ of liquid 19 was removed and ~he initial and final vol~s recorded for another E3 and E~ Qf Oo 3~ and 0.17 volts, respectively.
~sing the formulas shown herein:

-lS~

2~

E4/E3=O.S38 and 0~531 for an average value of 0~534 There~ore, 0~32/o.~û=(o.53~n n=about 1.460 quarts in 15 hoursO
The rate o the gasoline loss is about 0.024 gall ons!nour .
EXAMPL~ II
A determina~ion of resp~nse signal stability for 10 the apparatus shown in Figures 1 and 2 was run by causing ~i the float means 38 to rest on the bottom of tank 20. In this situation~ there is no movement of float means 38 relative to detector 36.
In Figure ~, 63 h~urs elapse between an initial recorded value o~ 0.80 volts and a final recorded value of close to 0.80 volts~ A maximum drift of 0.70 from the 0.80 value initially and finally recorded occurred at some point during the ~3-hour interval~ There was no apparent preferential drift direction. Clearly depending upon the number of hours, e.g., 1 or 12 hours, between the initial value o 0.80 and the drift value 0.70, the apparent loss of li~uid would be 0.212 quart/hour or 0.018 quart/hour.
EXAMPLE III
When a floating means of this invention is located at a depth approximately equal to the liquld volume divided by ~he liquid surace area, the 10at means will remain stationary even during changes in temperature involving the liquid in the tank and the float means itself.
The derivation of the formula indicatin~ the depth at which the 10at means wi~l rema.in stationary even during changes in temperature is as followxs The foree against a 5ubmer~ed float means oE area A
shown in Figure 1 w.i11 ~e~

-~6~-(1) F = 0Ax, where F is force, 0 is liquid density, and x shown in Figure 1 is the depth of the float means below the surface. All three ~f th~s~e factors will be affected by temperature; therefore, when we differentiate with respect to temperature T:
(2) ~F~dT - 0x~dA/dT) ~ 0A(dx/dT) ~ Ax(d0/dT3 Let c~ be ~he linear coefficient of expansion of the liguid, c2 the l;near co~fficient of expansion of the tank, and C3 the li.near coefficient for ~he float means.
The volumetric coefficient of expansion of the liquid will then be approximately 3cl; the volumetric coefficient for the tank will be approximately 3c2; and the area coefficient of the pressure sensor will be approximately 2c3, The reason for approximately 3cl, 3C2 and 2c3 is as ~ollows. cl or C2 is equal to a very small constant wherein:
~l~cl) or (l+c2~x(Dimension at Tl)x(~2-Tl)=
Dimension at T2; for cl oE the liquid or C2 Of the tank, the new volume at T2 for the liquid and tan~ are respectively:
(l+cl)3x(T2-Tl)3x(Dimension at Tl)3 and (l~c2~3 h x(T2-Tl)3x(Dimension at Tl)3.
However, (l+cl~3-13~3cl+3c~2+cl3.
Since both cl and c~ are much smaller than 1, 3Cl+3Cl~+cl ~ 3Cl 3c2~2c22+c23 ~ 3c2,.
Finally, for area A~ c3~2x~Area at Tl)x(T~-Tl)=Area at T2 where (l+c3)~ 2c3+C32 Since C3 is much smaller than 1, 2c3~c32 ~, 2c3 We cal~ ~aow ex~res~; d0/~d'r, ~h/r31T,~ and dx~dT i~l ~erm~
of these coeff icierlts.
~ ~ ) dAfd~3~
( 4 ~ d0/dT=-3cl5ZI
The change ln liquid height ~bove the ~ensor dx will be the net cha2l~e irl liquld volLlm~ ided by the l~qLIid surface; the ne. s:hange of l~quid volume will be the expansion of the li~uid minus the expansion of the tank.
~ 5 ~ dx/dT- ( VL/8L ) ( 3cl--3 C;! ) lQ where VL/SL is lis[uid volume divided by free liquid surface 56 (~igur~
Substituting eq~a~ ns (3), ~4~ 3.ndl (53 ~nto ~quation ;2~O
(6) dF/dT=2c30xA~3cl0xA~30~ sL~ ~Cl C2) ~f the force actir7g on the pressure ~ensor is constant, we~can set the above expression equal to zero~ A and 0 immediately drs:~p out~ and we ean solve or the depth xO
( 7 ) X= ~L/SL ) 3Cl--3c;~
3Cl-2C3 The depth x a'c wbich the force against ~ float means is constant is approximately equal to the liquid volume 2a over the li~uid surfa~e, with only minor adjustments necessary for the coe:Ef icients of expansiorl.
In the case o~ a horizontal cylindrical tankl7 the ratic:~ of liquid volume . o l~quid ~urface may be expressed as:
8~ VL/Sh=~ 1/2 sin2,el, where D is tank diameter, h is l~quid 45 in0 heigh~, and p ~ cos~ ( 1O2h~D~ .
TherefoEe~ for a hori~on~sl cylindrical ~a~ks 30 ~g) ~D 0 ~ J2 ~a2~5 t3~1 3~ ~) 4s~n5~ 3Cl-2C3 In ~arge t~nks, particul~rly, it i~ very âi'~i~ult to measure average liquld temperature with enough ~ecura~y to know whether an obser~ed vol12me ah~nge ls dsJe 'co ~ leak or to~temperature v~r~ati~n~" For exa~ple7 gasoline expands by ab~u~c l~ne par~ per thousand ~or e~ch degree Fahrenheit 9 In 4,00D gallon ~k, thi~ means 4 gallorl~ per degree~ A
lealc of l/2û gallons per hour would be masked by a temperature ehange o~ O. 0125F per hour, averaged thr4ughout the entire volume. The larger g he ~ank ~ t~e 2;maller ~he aYerags~
10 temperature c:hange required to ~ask a given lealc rate., ~n addition~ large tanks require mt)r~ tempera'cure sens~ng points to give an adequate pic~ure of wha~c the average te~perature i5,-Specific embodiments of this ~nvention disclosed inthe examples and elsewhere are intended to be illustrative only. ~aria~ s on the ~peciic embodiments are clear to a person of skill ~n the ar~ and are intellded to be within the scope of this invcntion.

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Claims (2)

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. An apparatus which both comprises a float means for floating at a desired depth in a selected liquid and a means for measuring small changes in location of said float means, wherein said desired depth is approximately equal to total volume of said selected liquid divided by free surface area of said selected liquid, whereby a substantially temperature-independent free-floating position is achieved.

2. In a method for determining leaks in a storage tank containing a liquid, said method comprising a step of determining small changes in the location of a float means floating in said liquid, the improvement which comprises locating said float means initially at a depth approximately equal to VL/SL where VL is the volume of said selected liquid in which said float means is located and SL is free surface area of said selected liquid, whereby temperature variation of said liquid in said storage tank does not change said desired depth at which said float means floats freely in said selected liquid.