THE RICE INSTITUTE
HEAT TRANSFER COEFFICIENTS FOR CONDENSATION s' OF N-HEPTANB IN THE PRESENCE. OF METHANE BI
ALIEN N. DEFEIEQE
A THESIS
SUBMITTED TO THE EACULTT
IN PARTIAL FULFIL3MT QF THE
REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
Houston, Texas Mayy 1 118 517335 ACKIICWLEDGEMENT
l?he author -wishes to express his sincere appreciatioir to
•Dr* W, W. Akers for his helpful guidance and supervision in this investigation.
ii msLE OF COUTENTS
Suacary ...... t 1 Introduction...... 2 Apparatus ...... 9 Procedure. 9 Hcsulis ...... 13 Discussion. 16 Conclusions .. 23
APPENDIX* I. Bata...... 2U II, Method o£ Calculation of Vapor Composition ...... 39 HI. Bibliography...... 3? IV. Nomenclature. 38
iii UST OF FIGURES A8D TABLES
Figures 1. Apparatus* « , . , . , . . , * * « 8 2* Wilson Graphs for Condenser Tempera tureof 22k®F an&Averaga Cooling Water Temperature of 82-8I*°F * * . * * 25
3* WilsonGraphsfor Condanserlemperature of 2U?°F and Average Cooling Ifeter fej^erature of 82-8lt°F * . * * * 16 It* Effect of Methane Concentration on Gondenaing Coefficient of n-Heptane ...... * * * * * * * * * 17
Tables 2* Beat Transfer Bata for Ptjre Wortnal Heptane * * * ■* + + * * 2U Il-Vir* Heat Transfer'Bata forCondensation of n~Heptane in Bresence of Bothane . . # ****** * * * * 2$ VIII. Data for Total Quantity of Bethane and Heptane Present in Apparatus.. •••«.#.** *«« * * 31 IX* Data Used In Calculation of Concentration of Methane in Vapor at Condensing Temperature of 22l|bF* # * . * * * * 32 X. Data Used in Calculation of Concentration of Ifettone in Vapor at Condensing. Temperature of 2lt7°F* * * * * * * * 33 XI-XII. Eesults* ...... * . . . . * * . * * ... * . * * 3k
iv X
TVi *Bi4n - aianferMritw Iwjafc t>naiirifai» OflalficifflllB
fa* tbd s^inttaiiMisthsiid Wugyateua Pl^ ware«NF otsSlo& W^PPBi^F^Pr Qd^^BPT a PHPfmw ^^PPBBtP« MawBBHBr^PHMB,, ;,wf conceal-HB BfwBBB wWBf tratian of sotted In the vapor attffoeondraser tempera tttresj 224 ami 247%; Xt was estteated that theeffactive condenser tube surffcOe temper¬ ature was within <513 image - of 85 to $9%;' 3be condensing heat transfer Coefficients wore obtained by smsnsof the Wilson graphical sseHtod as modified' by Beatty and Shts; Bata secured fear this method of obtaining condensing beat transfer coefficients were OTer-an heat transfer ooeffi-
■ " :■ ■ .. ':"' ■ ■■ ■ '. • ■ . ■ I. . . . . ■ ' Cleats at a series of cooling eater velocities far constant condenser
. .. ■■"■;■-'■ . ' . 1 tenpsraturb# constant met&ane concentration in the tape?* and an average cooling water tearperature that varied within the naafrojr'reage @2 to 84%; ■ : ’’ ’ ; ''. '. ^ , ’ /$ • . ■ ’. . . .’ •. , :: TfateHie conditions Just enunwratea, the reciprocal of the over-all beat transfer cooiff icietnt was plotted torsos Hie reciprocal cf H» 0^8 power of Hie coolingwater velocity to obtain a straight line whiohwaa extrapolated to sero value for .the abscissa, Hie 0^8 potsr of Hie water velocity, fhe - ccnQmiBing lieat transfor coefficient vao oaloulated for the Intercept thus
; The apparatus used far Hie investigation, was a closed ooribljatlon Condenser-vaporiser - Containing a iicriwntal Condensing tube; Oxere was aC ;■ oriented bulk flew of Hie vapor-gas mlatee paBt the condensing dement. ; Methane vapor concentrations varied f?cm 0 to IQ inol percent. - She condensing beat translfer coef^l®i^ta?ied iron 100 be ffi 3t was concluded that under tie conditions Of the investigattm a single curve is obtained when the condensing beat transfer coefficient is plotted versus mol percent methane in the vapor; 2
imorocrroi?
When a 'vapor condenses in the presence of a nonccradonsable gas, the concentration of the gas in the vapor imnodistely adjacent to the condensate surface is greater than the gas concentration in the bulk of the vapor; This must “be true, since in tho inmsdiate vicinity of the condensate surface, the vapor is roiaoved frcax the vapor-gas mixture end the gas is not removed (after equilibrium conditions are established) • Therefore, there is a gone of high, gas concentration, or "gas film”, near the condensate surface. The movement of vapor through that portion of the film immediately adjacent to the phase boundary approaches a true diffusion process ! This diffusion zone is bordered by a transition region on the vapor side there the mechanism of mass 'transport changes from a true diffusion mechanism to an eddying, convec¬ tive mechanism. Partial pressure, gradients of the vapor and gas in the true diffusion zone are many times greater than the partial pressure gradients in the transition zone. The same thing can be said of tho temperature gradient! There are several difficulties in deriving an analytical solution to the case under investigation, lie;, condensing heat transfer coefficients in the presence cf a nmccndcnsable gas with no bulls movement of the vaper- gas mixture past the condensate surface and constant gas concentration in the bulk of the vapor; Consider the case of a constant vapor temperature, constant surface temperature, and varying gas concentration in the bulk of the vapor-gas mixture! It is probable that the properties of the true diffusion film change markedly as the proportion cf nomcondsneable gas in it increases! At relatively low gas concentrations in the bulk of the vapor the properties of the film should approach the properties of a pure vapor film under similar conditions! Also, at relatively high gas concentrations the properties of tho film, should correspond more nearly to those of a pure gas 3s' film. According to this reasoning, atransition region would be expected in which the properties of the film should be intermediate between those of a pure gas film and those of a pure vapor film. It is probably not possible from theory to predict whether this postulated transition region is relatively "narrow” or relatively "wide" with respect to gas concentration in the bulk of the vapor*rgas mixture* Consider the case of constant gas concentration in the bulk of the vapor, constant surface temperature and varying condenser temperature. It can be reasoned from general heat transfer, general diffusion theory and practical experience that the convective heat transfer properties of the film probably do not change rapidly with temperature level. The work of Iangan on the air-water system tends to substantiate the general observations that are made in the foregoing discussion. Iangen used an equation derived by Nusselt as a starting point in his study of the condensing heat transfer coefficients of steam in the presence of air; The Nusselt equation (8) states that the quantity of vapor that diffuses through the gas film is the product of: a “diffusion constant”, the area of the condensing surface, the difference in the partial pressure of the vapor in the bulk of the vapor-gas mixture and the partial pressure of the vapor at the phase boundary (condensing surface), and the ratio of the density of the vapor to the total condenser pressure; The Miffusion constant" in the Nusselt equation is really a modified mass transfer coeffi¬ cient which is defined by the equation. Iangen replaced the Nusselt equation with an empirical equation which is applicable only to the steam-air system under the conditions of the experiments. The reader is referred to the original paper. li
Colburn and Hougen (2) give a seml-theoretical method for ths design of commercial condensers which must condense vapor in the presence
of a noncondensable gas* The method is based on the analogy between heat
transfer and mass transfer* A Jakob (7) discusses the problem under investigation. The Jakob discussion is based on the similarity of the general differential equations for heat and mass transfer. The discussion,, by implication* suggests a method of correlating large masses of data on different systems. $
Apparatus A diagram of the apparatus is shown In Figure 1. The diagram is self-explanatory. The body of the condenser-vaporized vas constructed of two steel I-beams which were welded together. The vaporizing element was a trass finned-tube! She condensing element was a copper pipe having the following dimensions: &3)., 0.&1 Inches? O.D., 0!8t0 inches; condensing length, 4.03 ft. The thermometers for measuring the inlet and outlet temperature of the coding water were ASW. thermometers of the type used in gas calorimeters and had Owl*# divisions. The stainless steel thexmometer wells in which they* were installed projected approximately six inches into the cooling water Stream. These thermometer wells were partially filled with mercury so that the thermometers would respond quickly to changes in temperature! It was found that mercury in stainless steel wells gave a greater rapidity of response than oil in copper wells. Mercury could not he used in brass or copper because of its dissolving action. A copper-constantan thermocouple was used to measure the condenser temperature. The thermocouple was soldered to the inner mod of a copper well which projected apprcxinatoly 3 inches into the condenser. The potentiometer millivolt scale was such that the condenser temperature could be estimated to the nearest 0.23?. The manometer used to measure the condenser pressure was of the U-tube type and could be read to the nearest 0*5 mm Hg. A platform scale and stop watch were used to measure the coding water flow rate I The scale had § lb* divisions! MOst of the difficulties encountered in the construction of the apparatus arose from the fact that the body of the condenser had to be capable of sustaining a high vacuum for a period of at least eight hours! It was 6 found that In the construction of this particular apparatus serened steel joints were not very trustsrorttiyi This was true even when new fittings,, machine-made nipples, and good quality joint sealing substance (litharge and glycerin) ware used. Some of the difficulties encountered with screwed joints were due to the relatively thin sides of liie apparatus. However, as it has been stated above, difficulties were encountered when the joint consisted of a machine-made nipple end new fitting. The filial solution to this problem was to eliminate all joints that were not absolutely necessary and to weld the remaining onesi'
The condensing element was sealed into the apparatus by means of a packing gland on each end of the apparatus. Two types of paoldng were used.
One typ8 was a graphite-impregnated commercial variety for use with hydro¬ carbon materials ^ This typo was placed next to the hydrocarbon Side of the glands. The other type was a dry asbestos variety which was placed in the gland after the type mentioned above TO in placed The dry asbestos packing held the hydrocarbon type packing in place when the packing gland was screwed tight; that is* the hydrocarbon type packing had a tendency to "ooze” when the dry asbestos packing was not used in the manner described.
Ordinary brass globe valves were used. It was found necessary to use rubber valve washers instead of the composition type washer usually- found in new valves. As might be expected, it was not possible to achieve an extremely high vacuum which could be maintained for long periods of time
{2k hours) without the use of the vacuum pump. The vacuum requirement was deemed to be satisfied when the manometer reading declined by 1.5 mm. from a value equal to the barometer reading (to 1he nearest mm of Hg) in a sixteen hour period. This requirement was met when the apparatus was tested at the beginning and end of the experiments. 7
8 .Wia CneSNSOl^BP BT ^PPBP ^^BBBBWB A^TrtanntrtngBPBBBBtoiBP^'BMBBIwBBP'BWiPPPPB^ oS^|BBW tjhft ^^VVfB^BPBBrWlBpiJP BoMBF" to^^^OrtpiBrt t*gn*0OwP.^pBBB WF BFBpBPBJftBArnm^iimfail-tr agB least!*, 48 icsHoai trt&tti, 3*3 tooliosi liel^it, 213 taebaa* Sfo ipeveat tto
9dflAfb^1ir'of. 4&cs»aL@S3i^te ;tel3dsit330 £Secm .tb0..rpof .of ttofcc&csxfco tto ecEfonoffiP tube, 12i0 boKoaa piwfcod on on© of t&o longofigoaeo thattbo roofcf tbo e^sae&iM: W^klS^^htsm tho cco&enBoa* pipe m .tooliaed at m ssogte of ■.
ftyp«wgjTiw.'tei^Ty fcgO .4iT»fl ftfliyi
©lo apparatus tms iiisulatoil-?ritli ^ uagnoeia* *Fm aflafeaura tMcfcnass of tit© Insulatioa i?as 3/4 Inclu $hd satire apparatuo Induains the theramater wlls (”B° ln Flgtnre I)-i^© insulated* C2A A CodingWaterThermometer D CondensingPipe B CodingWaterThermometerWe// £ Peceptac/eforCoo/ingWate^ T P!atfcrmSca/e H MethaneCy//nder K TinneciTubeforSteam L Conc/enserTubePackingGZands C Conder>serBox(shownr/if/cofinsodiiorj Q ConstontPressorePegu'crting\/ofve for Steam / SL PROCEDURE
The n-heptane and methane used were obtained from the Phillips
Petroleum Company and ware assumed to be pure. Initially, the air was
pumped from the apparatus and a measured amount of normal heptane was intro¬
duced. The quantity of n-heptane introduced -was determined to the nearest
gram. The procedure used for the n-heptane-methane runs will be described.
The procedure for the pure n-heptane runs was essentially the same except,
of course, that methane was not introduced into the apparatus.
After the pure n-heptane runs, the apparatus was allowed to coma
to room temperature. Methane'was always introduced into the apparatus while
it was at room temperature. There were two reasons for this* (1) manometer
readings could be made more accurately at room temperature and (2) the
solubility of methane in heptane at room temperature and pressures below
2^0 mm Hg is negligibly small, according to the solubility data of Erolieh
and co-workers (?) on hexane and octane at 2?og. This data showed the sol¬
ubility of methane (expressed in volume of gas at 2?og and 1.0 atmosphere per
volume of liquid) in hexane and octane to the very nearly linear with pressure
(Henry*s law relationship). Yftien this data was extrapolated from pressures above 1.0 atmosphere to pressures below 1 atmosphere, a negative methane
solubility was obtained, which is, of course, impossible# However, the
extrapolation indicates that it is very probable that the methane solubility
is small enough to be neglected;. Frolich and oo-workers estimate the accuracy
of their data to be within 4 ?$• As a further check on the solubility of
methane in heptane at the conditions at which it was introduced into the
apparatus, methane at a partial pressure of 212 mm was allowed to remain in
contact with heptane at 31°C for a period of sixteen hours; There was no
observable decline in the partial pressure of the methane. It is extremely 10 unlikely that equilibrium between the methane and heptane could have been instantaneously established (6).
Essentially, the procedure used for the introduction of methane into the apparatus was: ¥ _ “* 1. Vapor and gas were pumped from the condenser until the condenser pressure uas very nearly equal to the vapor pressure of n-heptana at the condenser temperature* a* Data recorded after this step were condenser pressure, J’ . ' temperature and length of tine that vapor and gas were being removed from the apparatus* 2* Methane was introduced into the condenser*
a* Data recorded were condenser temperature and pressure*
3* The partial pressure of methane was then determined by differ-' ence. The length of pumping time required for Step 1 wad usually about 10 minutes* The pumping tine was recorded so that the n-heptane loss during the pumping process could be proportioned over all runs* This was deamed more accurate than weighing the n-heptane after each run* The loss of n-heptane due to pumping was very small* See Table VIII, Appendix I*
During Step 1, the condenser temperature lowering caused by evaporation during pimping was always less than 1°F* The condenser was allowed to reach a constant temperature (no observable temperature change within a l£-minute period) before the introduction of methane* See Table VI3J for data obtained when various quantities of methane were introduced into the apparatus* The vapor pressures of pure n-heptane are given in Table VIII so that the thoroughness of the evacuation can be easily seen* The condenser temperatures were controlled by a constant pressure valve on the steam inlet line*. See Figure I. The source of the steam was a small boiler that , is used for experiments in the Mechanical Engineering 11
Department. This boiler had. no automatic steam pressure regulating mechanism.
As a zresult, there were minor variations in the condenser temperatures due to the fact that the constant pressure valve for the steam shown in Figure 1 did not entirely eliminate steam pressure variations. It can be seen from
Tables I through VIII that the variation of condenser temperature during the runs was generally on the order of * 1°F.
The quantity of water collected during the Wilson runs was never less than 100 lbs. Generally, two runs were made at a given setting of the inlet water valve* During a run, the cooling rater inlet and outlet temper¬ atures were read at half-minute intervals* The inlet and outlet temper¬ atures recorded were generally an average of four or more thermometer readings»
At a given mass of methane in the apparatus, the manometer was calibrated at two or three temperatures in the range of desired temperatures
(over a 30-ijO mm Ug range on the manometer). Then, at a given water veloc¬ ity, the condenser temperature could be quickly obtained by interpolation on the manometer scale. For example, with a given mass of methane in the apparatus, the condenser temperature was brought to within 1 to 2°F of the desired temperature (either 22l*°F or 2l47°F) and the manometer reading corresponding to a given temperature was determined. The condenser temper¬ ature was then changed 1 or 2°F and the corresponding manometer reading f' obtained. Then* within the calibration range, condenser temperatures at a given water velocity could be obtained directly from the manometer. This procedure was necessary because of the relatively short time required for a run at a given water velocity and the relatively long time required for accurate potentiometer readings* 12:
At the end of the experiments * the condenser tube was removed from the apparatus and closely examined for scale formation on the outside and inside# At the beginning of the experiments, there was a very thin oxide coating oh both surfaces of the pipe* When a sample of the pipe tiias polished to a bright luster, the oxide coating would develop, as would be expected, Within a very short time (one to two hours) upon exposure to the atmosphere# This is a normal characteristic of copper pipe. . The con¬ denser pipe was installed in the apparatus with its normal oxide coating present on the surfaces. Ho change in the condition of the surfaces could be observed at the end of the experiments. Since no change in the condition of the surfaces could be observed, it was deemed not necessary to check for its presence. It has been the experience of other investigators (l) that no change in the scale factor could be detected over such a short period of time under similar conditions* If there had been any scale formation during the experiments which was sufficient to cause any appreciable error in the results, it is very probable that it could have been observed* At the end of the experiments the amount of n-heptane present was determined by weighing it on a balance which had 1 gram divisions* Data- on the quantity of heptane present in the apparatus are given in Table VIII* Also, at the end of the experiments the volume of the apparatus was calculated from the weight of water required to fill Itj the volume was *938 cubic feet* 13
RESULTS
The data obtained consist of over-all heat transfer coefficients at a series of water velocities for a constant condensing temperature and
constant methane concentration in the vapor. The average cooling temper¬ ature, tjjg, varied over such a narrow range (82-8l4°F) that it could be
termed constant. The Wilson method (10) as modified by Beatty and Kata (1) was used to obtain the condensing heat transfer coefficients from these data. Essentially, the Wilson method of obtaining individual condensing
heat transfer coefficients consists of a plot of the reciprocal of the
over-all heat transfer coefficient, !«., versus the reciprocal of the 0.8 Uo power of the cooling water velocity, 531 . Extrapolation of this line to zero value of the abscissa, .1 t gives an ordinate intercept which is - w.o ■ equal to the sum of the heat transfer resistances of the pipe wall, scale and condensing film, Since 1 is the over-all heat transfer resistance referred to unit outside area of the pipe* the heat transfer resistance sum mentioned In the previous sentence is also referred to unit outside area of the pipe, According to the theory of resistance in series, the resistance of the pipe wall and scale can be subtracted from the sum of
the pipe wall, scale, and condensing film resistances to obtain the con¬ densing film resistance. Since all resistances have been referred to unit
outside area of the pipe, the condensing heat transfer coefficient is the reciprocal of the condensing film resistance thus obtained. If the outside and inside surfaces of the pipe are free of scale, as was the case in this investigation, it is, of course, not necessary to consider scale resistance
in the calculations.
The Wilson type plots from which the condensing heat transfer
coefficients were obtained are shown In Figures 2 and 3, The data for the Wilson plots are given in Appendix I, Tables I through 17 and VI through
VII. At the two highest concentrations of methane in the vapor (lli and
18.3 mol percent) the cooling water temperature rise was too small to obtain an accurate Wilson plot} therefore, for these two methane concentrations the water side heat transfer coefficient was calculated from a Hinton-type
(11) equation and the condensing heat transfer coefficient was calculated from the over-all heat transfer coefficient data in the usual manner.
Beatty and Kata (1) show that the accuracy of the Wilson method for determining condensing heat transfer coefficients is improved by high cooling water velocity and low cooling water temperature rise. The range of the cooling water temperature rise is shown in Tables I through VII.
Generally, the range was 1 to li°F. Hie linear cooling water velocities in most cases were within the range 5 to 10 ft/sec, which is within the li to
2J> ft/sec range used by Beatty and Katz (1). It was necessary for the investigators just mentioned to use higher cooling water velocities because the over-all heat transfer coefficients in their investigation were two to eight times greater than those encountered in this investigation.
A graph of the condensing heat transfer coefficients (calculated from the ordinate intercepts of Figures 2 and 3) versus vapor composition is shown in Figure It. The calculated results from which Figure A was obtained are summarized in Appendix I, Tables XI and XII. The data from which the composition of the vapor was obtained are given in Appendix I,
Tables VIII through X. Hie manner in which the vapor composition was calculated is given in Appendix II. The methane equilibrium constants of
Sage and lacey (13) were used in the calculation of the vapor composition.
AB shown in Appendix II, the method used to calculate vapor composition is insensitive to errors in the equilibrium constants. 15 hUOtNt DJtTZGtN CO 20 * 20 PER INCH 17 18
Discussion
' It would have toon desirable to maintain the average temperature of tho outside surface of the pipe wall at a constant value for a given condenser temperature and vapor composition "because far the case under investigation, this temperature is the remaining fundamental independent variable after condenser temperature and vapor composition are fixed.
That is, it would have "been desirable to have directly measured the temper** ature of tho outside surface of the pipe. Langen (8) in his study of the ' steam-air system concluded from experience that the measurement of tube wall temperatures by the use of thermocouples Is not very satisfactory. The Langen method of measuring tube wall temperature involved the use of eight equally spaced platinum resistance thermometer elements placed in longitudinal, milled grooves around the periphery of the condenser tribe; Tho grooves containing the platinum vires were covered with brass strips and the condenser tribe surface was restored to its smooth, initial condition. Each of these resistance thermometers directly measured the average tube wall temperature on a line throu^i the tube parallel to Its longitudinal axis. On a cross section of the tubs perpendicular to the longitudinal axis, it is interesting to note that Langen found (under the conditions of his experiments) that the average tube wall temperature as Indicated by the resistance thermometers mentioned above varied over a range of approxi¬ mately k°Q in some cases. La this investigation, it was not feasible to use the elaborate Langen method of measuring average tube surface temper-* ature. Initially, a heater for the inlet cooling water was incorporated in the design of tho apparatus! One of the purposes of the heater was to vary tho cooling water temperature by an amount determined from preliminary experiments so as to maintain the average tube vail temperature at a constant (calculated) value* ibis would have involved obtaining a set of approximate preliminary condensing heat transfer coefficients over the range of methane Concentrations studied. Tho heater and procedure mentioned above were not used because of practical considerations. Since the pressure of the steam supplied to the apparatus varied somewhat and since it was necessary to measure the inlet and outlet cooling water temperatures to the nearest oIoi^F, it is probable that even minor variations in the temperature of the outlet water from the heater (inlet water to the condenser) would have caused considerable inaccuracy. That is, sudden variations in the inlet cooling water temperature as great as 0.5°!? would have made it extremely difficult to obtain an accurate average value for the difference between the inlet and outlet cooling water temperature. Also, it is somewhat doubtful whether the procedure Just given would have improved the accuracy of the results obtained;
j?or condensation of pure vapors, Beatty and Khtz (l) show that if Wilson plot data are obtained under conditions of constant average cooling water tenperature and reasonably high cooling water velocities, the condensing heat transfer coefficient obtained from. the extrapolated value of Jk will be very nearly equal to the condensing heat transfer . tJ0 coefficient that would exist if the average condenser tube surface temper¬ ature were the same as the average cooling water temperature; Stated in other words, the condensing heat transfer coefficient for pure vapors obtained from the extrapolated value of-~ (data obtained under conditions of constant condenser temperatures and constant cooling water temperature) Is not a condensing heat transfer coefficient that existed during the tests; 20 ratter, It 1B the condensing coefficient which would exist If the average
condenser tube surface temperature were the same as the average cooling water temperature* It should he emphasized that the foregoing statement has been proved only for the case of the condensation of pure vapors* It
could not he proved for the case of condensation of a vapor in the presence
of a noncondensahlo gas because no general equation is available for the prediction of heat transfer coefficients under these conditions* The
fact that the condensing heat transfer coefficient for a pure vapor
obtained under Hie conditions enumerated above corresponds to the con¬
densing heat transfer coefficient which would exist if the average condenser
tube surface temperature were the same as the average cooling water temper¬ ature existing during the tests has a practical hearing on the present
Investigation* It means that probably the condensing coefficients
obtained at low methane concentrations in the vapor would tend to
correspond to condensing coefficients which would exist at condenser tube
surface temperatures near the cooling water temperature * At high methane
concentrations in. the vapor, the over-all heat transfer coefficients were
relatively law as compared to the water-side heat transfer coefficients*
Consequently, the temperature drop across the water film would tend to
he small! therefore, the condenser tribe surface temperature would tend to
he near the cooling water temperature* *Ehe purpose of the foregoing dis¬
cussion is to show that the average condenser tribe surface -temperature-
range far the data represented In Figure k would tend to he rather narrow*
It Is not possible to give an exact eatirate of the range! however, with .
due consideration being given to the tendencies mentioned above, the writer
estimates the range to be 85 to 95^* • 2i
Emphasis has teen given, to the matter of average condenser tube
surface temperature because any eventual practical solution of the problem
Of predicting heat transfer coefficients of vapors in the presence of non-
condensable gas will probably involve condenser tube surface tes^eraturev
If this variable is fixed, vapor side heat transfer phenomena are' divorced
from the heat transfer phenomena occurring on the coolant side of the con¬
denser pipe. It should be noted that for the case under investigation
under conditions of a given vapor composition and given buUc vapor temper¬ ature the temperature at the interface between the vapor-gas mixture and the liquid condensate is fixed when the condenser tube surface temperature
is fixed.
It should be noted that a cooling water temperature correction factor (1) could have been included in the abscissae of the Wilson plots,
Figures 2 and 3v' The correction ms not used because it ms found by trial that it did not cause an error within the accuracy of the drawings.
It can be seen from Figure 4 that the relatively small difference in the two condenser temperatures did not result in two curves for the condensing heat transfer coefficient. Shis would probably be expected
since the range of condenser pipe surface temperatures for the two cases ms approximately the same. Apparently, for a constant mss of methane in the apparatus idle major effect of raising the condenser temperature from
224% to 247% ms to decrease the concentration of methane in the vapor ^
The condensing heat transfer coefficient for pure heptane calculated from the Husselt equation ms 206 and 209 BTtf/flr/Ft^/% for the hitter (247%) end lower (224%) condenser temperature, respectively^
The condensing heat transfer coefficients for pure heptane at the higher ayid lower condenser temperatures as obtained from the Wilson plots are 177 and 180 BTO/aSr/Ft2/^, respectively* These values are well within the accuracy that can he expected from the Hussolt equation* The natural con¬ vection heat transfer1 coefficients of methane at 2kJ and 22k°F at pressures
of heptane at these temperatures, ancalculated from the empirical actuation recommended by McAdams (ll), are 3*2 and 2;6 respectively*
Although the condensing heat transfer coefficients of the methane- heptane system were not studied at high methane concentrations, it should ho noted that the curve shown in Figure k approaches these values at very high methane concentrations •
The method of calculation of the concentration of methane in the vapor : is given in Appendix 111* This method of obtaining the concentration
of methane in the vapor at the two operating temperatures was deemed more
accurate than partial pressure measurements at these two temperatures*
The method of calculation is relatively insensitive to errors in temperature
or pressure measurements at the two operating temperatures and takes advantage of data that could he obtained under the most constant conditions
(room temperature)* The method also tabes advantage of the relatively large partial pressures of methane at room temperature and is relatively
insensitive to errors in the values of the methane equilibrium constants;
This is discussed in Appendix H. 23
CONCLUSIONS
For condenser temperatures of 22b and 2b7°F and an average cooling water temperature of 82 to 8b°F, it can be concluded that Tinder the con¬ ditions of this investigation a single curve is obtained when the condensing heat transfer coefficient is plotted versus mol percent methane in the vapor* 2h
%iiti K sfsesss&sss O O O O H rl 01 01 ri H H H H H rt rf H -ft %8 MMssussas. &a$£m5&$ lit? V0V)\0V0V0V0\0V0V0V0 \OVOVOVO\OVO\OVO\OVO
I « oMM H O\O rno oco t- uvqmo cnco inotoo .It8 1 I
3 § 0 *3 g* 3 m to coin corn rococo corn 8 o H* t* •:* * •■'* * * •* «* ■% **§£ A • f’l; ’• r|: f| :■ r tp"t -‘ #*|: f( • f**| .• H o +» «3 I w q«c\oj«> t~o\\qo}1 o '©Hi-Jco.si-vo rnc-oj o\ ,J% ~ ’ •»• •>• •»-. •' •• •« •>■ • ' #1 • ■ 'V •5-- *v; •> •*!■ «i ♦:*#!- OI • 8 I §J>8‘ mmtm ssss&i&g 88888 888 888 8888 ■a6 J no *Of2r2*&,l2*st ^Sf&„s hgs $1 OJ|> 8CVI«S 80\0S SS§§SO HHH ssssg&aft®® 4^H 9 ^M OJ^ CVICO % 0\0«| n O4^ HHfH% 41 ^ H 0\O3 ‘ (nvo.. _ _ H _ comes cncncncn5 ••«* ^ % n ■ «* «*w m i'S3'S^S3 S3 SISiSiSi IH 2$ 3 OOOOCO o o cu cvi cnto COUPON© 8 - •: • R• *8 SS«<8 SrSS ■• = • #i© •'8 • ‘H H ci^cQ qcqvQ-rf- ir\ir\tr\ ■3' m-sr *KT «sr -4- -srvb co fr-co o o o H H ci cn cu** cn M ■ ?V •< #i' • << «t- •;■t-co *7 #* • •«: • Hle? C^OVOVD O ONC\0 Cl O trvO cuoD H o\cu o\ci o • *- •? #C- #-v •. •> •)- «(• ft: ft t•> •!' •■*• *> *i • K®33R®R«I®R .SSS % * Si ©tntntntntntncntntn HH HHHHHHHHHrt trw *£> H t>*VO H O H H ONCO-S* m.4*v0 ovo^tco ftf • ft^ ft ®«®®®®s®®<3 HHHHHHHHH HHHHHHrlrtrtrt cr\co-a- C\C\O\0M*! COOJ \0 o tocfvo HOD 0\O ir\ •»• ft* • *'.•> • <• ft; ft; ft'. ftr #r ft r ft; ft*'- • >• ft;- fti ft* ft-- ftv ftt ft *4* CO 00*4* ^ lf\ lC\^Sr cu cu cu cu cu cu cu cu cu cu oooooooooo oao H^2Jg«flOoSo2 o ON© t-CO-sf CNCU ON 8g§! % *V <* «V «k- % % «k «k n . A «<* •* IIS% «\ * % OOOOO 0\0\0)0\0\ Sf$r^i*1 *#3 1*1^ i1*1S 3f*i ir*l8 »fl CU 01 CU CU Cl H H H H H >vo 5>S8.feSS^®S'a ft» •»• ft?/ #9- ft-:- ft! ft Siiw .4* .4-.4*-4* IA tf\V0 VD b-* © Jx IH w 0?© a&i&CO lololo CO CD CO W CO CO CO CD CD CO ©8&&sass8® &&»B:&a§§!RS i‘ mv •>■ #-'• •»-#t •. •) • •>.#»• «v #v «v •:> #-«' •-• #1-. «1 . • ■aifat ^ii UNifNrffjt'm tncnoTcu cu ir\«fMc\tf\rfr^t* 65 Q ISISSSIfl 8181811881 26 a H t;.,#i*\#v. #•*:..#•;;•. ••»•;>•» • * *r. *i .+ ^#»^*v •i-.ns. rl H HHkrlrlHri rl H H H H ‘H *H H H ■a a ino •i CO#r •» «v; •» #t$3888 #K # :i'R&8-sai3»aiRR •;• > •! M 0 ON CVOY0N OYOVOYOYO OY l> t-00 CO CO CX) CO CO CO CO HIID H ■4» ■ ^ *Hg > o o cu ram coco on o o t-co ovo H O O tno lC\& roHCJVOcviQ^^t > £>H H ro rooorocQ^ rn£vJ 2? 2? O OOO O O OOO O .■<* «*.*.* * * * * % % H • «* H DTA «h H HHH rlHrtrirlH HrlrlHH H H riHH O O if\*zt CO b~(N'Jfr to o rl o fr^co co vo o co co :'i’. #!••:• •* •»■, m- _•».>.• •Vm- •r-.nt* «t-'•v.,nr. H H trf HHHHrfHHHHH CVJ CU H 0\b-rOO\in O O O O O O O o o o «If Jj, If if fulfil I OJ-^HOCOCO-4*^COCO «ES | asaasaaaasi SSSSfrfmWSS■ «i ** «v * «t * * by©Sri coriCO s* rifflVOtryiryco S*to trysr1T\ CO •V-' •l\’ •*• •*»;. • »- •; • »• • * ■ • n SScS^ co » co c&c&eo c8 vo o ON cuO 0coco^5* a ON _ o 'i'iidd&idid SSSSSSSS^S 1114ttf jfc| P3 © ir\trvr***<* •»«»•»%•=** wmpww « * * * oi P5 siamasisissi n OS X « CBBftft fe ■*» 6§ 3, w fia £ ft* §» Vi m sci *'w • **m «* •» i•* ■ rirlrlri ass« |a £1 **§. tit ' .4-VOjfr O v> HHH% ** *» *«%*«* IA M& & HHH H H H H OVD CVl O^t, .. '1-••!' •! « • tW s SSS HSS HrtrtH t & «?6* CVl CU CU OJ CVl CVl CM 113*4 mu sum„ cn > > «* .-* -* •'* a. 9>6> 1 ^ S!gS$_ . ©I... - .*•!•»•; #i: « ■ • III58*6 | e 333 a a a a •g (D O gr *3.2? Cv Sc^SRi? 3*8 H H{3R w »ss « CO H!*! §la fill* • * ■ n * CVl cn CVl 04 m *°3§ fr-O Mol psr cent jnotijano in vapor m «< «s li ri 49 fill <■ ®|o S in J^assMSRi3i§s**fi»Rn a Ig-I^S aassssss©©©©as©©©©©©© w E 4» \s0M©O0-0.0 ■P H(3teta^w-«k.-p*» >j«k ^■*•,:k•%«i Sc ID JT&-pScucoi?\!r\coSio'coiR UPPBBDIX X - POUT'D. rnn® vm lata fcg Octal Quantity off Itettiaaa • ana B&ptom Broeoat; ±a Amua^tua SBWflL;'; Ooa* Absolute Tapm? J«j3caufco Bartiel Total Quantity Ocnco^ CoE&cnce* Ereseuro Ccofleasar Breastae© Qisaatity Eun Sco?iQ3 Hoptaas Eswsmas _ ef Ifc&aeia?© <£ of Hatlsac© ' to ••• Safes© E<3$teae 82tea?' ^Mbam. . . Ereeaafc ‘ Coa&anser ASMMtxa at M&iUesi in ;. ia . of ■ peacteTOsaf .0* CoEtoesp CcQctensea? (Ebs) (°oj (mBg) (TOSS) (TOSS) (llolo K X04) ■ X&&B io;38 31*0 0 2A &3 10,27 31I2 63i6 ■6&& ; u?.io ' lil4 3& 8>B XO3L8 643 62*5 a^ls 86.8 1*99 ■ ; k&s 10*07 . 3i|3 6^2 ; >?43; 1323 3*04 5&&B .:9;97 30*3 APfSHDXX I -CONT’D. TABLE IX Data Used in Calculation of Concentration of Metliane in Vapor at Condensing Temperature of. 22I40P ~ Average Average Uol Methane Quan¬ Concen- Run Total Condenser Average Equili¬ tity Volume Quantity tration Series Con¬ Teaper- Compress¬ brium of of of of denser ature ibility Constant Liquid Vapor Vapor lie thane Pressure, Fa ctor in Vapor z ■ K L ' V (mm Pig) (of) (Ho. (Ho* (Hols) (Cu Ft) (Hols x (Hoi %) Units) Units) 103) 2A 99k 22b.5 ♦939 226 •1007 .668 1.06 b. 95 % ‘ 1,0355; 1 22lj,2 .9b3 219 .0998 . .671 1.9b 8.35 hk 1,075 : ■ 22b .6 213 .0985 ,676 2.03 12.2 ; 5A v 1,138 22ij.3 .950 198 *0975 .679 2,15 18.3 6k ’ 1,068 ' 22b.0 •9b6 211i .0959 .681 ; 2.02 11.7 7A ;,oiii» 22ii.3 .9b3 218 •09iilr .688 2.00 9.0 33 APPENDIX I - CONTtp. TABLE X Data Used in Calculation of Concentration of Methane in Vapor Condensing Temperature of 247QP Average Average Mol Methane Quan- Concen- Total Condenser Average Squill- tity Volume Quantltytration Bun Con- Steeper- Compress- hrium of of of of Series denser atur© ihillty Constant Liquid Vapor Vapor Methane Pressure Pactcr in Vapor *t % Z K L - V (zm Eg) '(<*) (BO: (Bo: (Hols) (CuPt) (Mods (Mol #) Units) Units) X103) SB 1*359 246.8 ;9l4 166 ;iooi .666 232 3:65 3B i,4oo 246.8 :915 160 i0992 :66r 2.60 6:19 to 1,435 247.0 :918 154 :0981 2.68 945 5B 1,500 24r;o ;923 152 :O9TI :w 239 i4:o to 1,430 246.8 .919 155 :0954 .679 2:68 848 7B 1,435 247.1 ;9i5 154 :<^38 ‘684 234 63 3ii BESULTS Table XI Condensing Heat Transfer Coefficients for n-heptane-methane System at Average Condenser Temperature of 22li°P Concentration Condensing of Heat Series Methane Transfer in Vapor Coefficient (mol %) (BTU/Hr/Pt2/oF) 3A 0 180 2k h'9$ Ui8 % 8.35 117 lift. 12.2 Ul.7 & 18.3 6.7 6k 11.7 Ii8,0 7A 9.0 100 Table XII Condensing Heat Transfer Coefficients for n-heptane-methane System at Average Condenser Temperature of Concentration Condensing of Heat Series Methane Transfer in Vapor Coefficient (mol %) (BTU/Hr?Ft2/0F) IB 0 177 2B 3.65 199 3B 6.19 139 liB 9,19 103 9B 1U.0 23.U 6B 8,78 107 7B 6.6 126 3* APPENDIX II Kothod of Calculation of Vapor Composition Tha mol percent methane in the vapor at the two condenser temperatures 'was calculated by utilising the expression * g F K f (1) l l 4 7 7 S v V * Kx 4 £/V K7 4 I»/V Actually, the first term on the left gives the quantity of methane in the vapor. If I*/V and V can be determined accurately, the mol fraction of methane in tha vapor can bo calculated from the expressions , . Kl$l . 1 (2) nx^prm ~rv It was deemed more accurate to use aquation (2) and'take advantage of the fact that L and V could be accurately determined by a trial md error process utilising the following known information! (1) volume of apparatus, (2) total mass of methane present in apparatus, (3) total mass of n-hoptane present, and (li) total condenser pressure and condenser temperature * The methane equili¬ brium constants used are from the data of Sage and Iacey (13). Tha procedure for calculating yx at known values of Fx is given below. First, it was Assumed that at a given condenser temperature the quantity of heptane in tha vapor will be the same as if the system consisted entirely of heptane, A reasonably accurate value of L could be obtained immediately because (1) the quantity of heptane in the apparatus was relatively large and (2) the quan¬ tity of methane in the liquid was extremely small (on tha order of l x 10*^ mole). After this approximate value of L was obtained, the volume of vapor could be obtained by subtracting the liquid volume from the total volume of tho apparatus. The total mole of vapor could then be calculated from the expression H - FV . A molal average Z was used* The Z for methane was taken > 36 to bo 1*0# The Z for heptane was calculated from tho thermodynamic data of Goull, Stuart, and Yu (3). In obtaining a nolal average 2, it was necessary to assume the composition of tho vapor* For tho range of variables studied, the value of 2 was relatively insensitive to vapor composition* After a value of V ms obtained, a close approximation to the composition of the vapor could be obtained from equation (2). The procedure given above was then repeated in order to obtains more accurate vapor composition. It ms usually not necessary to repeat the procedure more than twice, This method of calculation has the advantage that a relatively large error in tho value of K does not cause a large error In the computed vapor composition* At the higher condenser temperature, for example, if the true value of Kwore 1,2 times the Sage and lacoy value, the true vapor composition would be approximately 1*03 times as great as that calculated*. 37 it Beatty, S; Q. and D. I*. EOtz, ^"Condensation cfVapars oa,Outsid0 of ginned ffufcesVCIiagu Kig.BroaresB 44, 55-68 (1948). 2f Colburn, A. P. and 0. A. Housen, "Design of Cooler Condensers for. Mixtures of'Vapcxrs with Hanoondenslng Gases’1, Bod; Bngt Cheat; 26, 3#' B.Stuart aafl. K. $; 1U, "^imoajfmnlf rropertios rtf' Cheatsgng; BroiegesB 46: 311 (1950). 4. Eckert, 25. B. GZ, antoodubtlah io ■fee aggeaggeo? c^Bratandffasa. /'■' Chapter V, Yccrlt (l930)i 5't Ifcoliclii1 $’• %* ■ <3>. #« HCssa, ®«;: J. ®mch end A. A. "Bolufcillties of Cases in Liquids at B&& £ressuroBM. Lad#: Eng. Cheaa^ 23* 548 6. BUS., E; S* and )f. H. Lacey, *Bate of Solution, of Ifel&an© in Quiescent Liqiiid Hydrocarbons 33r,:ihdl'Bhgt Chen. 26.1324-27 (1934)V 7*‘ dSkcifr. M;y Beat transfer» yfot I» 5934 John ffiley and Sons* loot, (1949). 8* Langen, E;, "BerEirtfluss dest, lufteehalieet 3auf (§enaffarc!iffuJ)erssns Bel . famdensiegSatlan S«aicgf a g 15. Shegvood. g. L«. Absorption and Egtapaotion. Chapters 1 and Il/ lfoGraw HiH Book Company, Iw York (1937). 30 mm m ho “ Condensing heat transfer coefficient, BT0/Hr/ft£/°F K - Equilibrium constant, ratio of mol fraction of substance in vapor to mol fraction in liquid, no units Xi ~ Quantity of liquid, mols P - Total absolute condenser pressure, mm % q - Beat flow rate, BTU/Hr ti - Inlet cooling water temperature, op t2 - Outlet cooling water temperature, °F tc - Condensing temperature, °F UQ * Over-all heat transfer coefficient based on outside surface area of condenser pipe, BT0/Hr/Ft2/°F 7 - Quantity of vapor, mois W - Cooling water flow rate, lbs/hr yj_ - Mol fraction of methane in vapor, no unite Z Compressibility factor, no unite at - Arithmetic average temperature difference between bulk of vapor and cooling water, °F •$£ $MA iieiifuimm'mm ! *■ ^~ B S5* t*t fo S& - „ © e ;* ii 4» jb ■a L m ! igggggMfs*mmm fl s D0rtaJM53 , ■ HIHH*Hif*?H| . rtM0JCUW#*tHrtrtrtrtrtHrtHIWW «s!;,e^ o^coccvo»n.s*m^c|c^o’Sc§<8 ffiSiifill illifl'tfff gM&UUEBfll jMiW '.H'.'°.^ ^:-.®T"i^...i".- 88g&$)££s!g3 ITMTVCVI