A MATHEMATICAL mvasmmou or m: EFFECT OF was: spAcma,‘ excess AIR, AND BRIDGEWALL ' .AND smcx tweuwaes upon pups; STILL DESIGN Thai: for flu) Douro. of M.- S. MICHIGAN STATE UNIVERSITY ' William Vere .D'A. Saunders 1961 THESIS 0-169 This is to certify that the thesis entitled A Mathematical Investigation of the Effect of Tube Spacing, Excess Air, and Bridgewall and Stack Temperatures Upon Pipe Still Design presented by William Vere D'A. Saunders has been accepted towards fulfillment of the requirements for M.S. degree in Chemical Engineering ' Ma'or r iessor V// 1 P 0 Date March 11+, .1961 LIBRARY Michigan State University ABSTRACT A.MATHEMATICAL INVESTIGATION OF THE EFFECT OF TUBE SPACING, EXCESS AIR, AND BRIDGEWALL AND STACK TEMPERATURES UPON PIPE STILL DESIGN by William Vere D'A, Saunders A.mathamatical model is presented for use in the design of petroleum furnaces. This model includes the requirements of heat load and pressure drop. A program for the solution of the design equations has been prepared, and solutions were obtained for specific furnace requirements by varying tube spacings, per cent excess air, and bridgewall and exit stack temperatures. . In order to predict pressure drop in the presence of two- phase flow an equation similar to the Fanning equation was develOped. It is difficult to judge the reliability of this equation because data was not available. Furnace designs obtained were correlated in terms of the distribution of heat loads to radiant and convection sections, and were plotted as functions of the bridgewall and exit stack temperatures. Radiant heat transfer rates were related to the fraction of the total heat input absorbed in the radiant section. This correlation included the effect of tube spacing. The principal significance of excess air is its effect on the fraction of total heat input absorbed in the radiant section. At a fixed bridgewall temperature and normal conditions of operation, this fraction can be increased by a factor of approximately 1.5 with a 50 per cent decrease in the excess air. A MATHEMATICAL INVESTIGATION OF THE EFFECT OF TUBE SPACING, EXCESS AIR, AND BRIDGEWALL.AND STACK TEMPERATURES UPON PIPE STILL DESIGN By William Vere D'A. Saunders A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Chemical Engineering J 1961 ACKNOWLEDGEMENT The author wishes to express gratitude to Professor J. W. Donnell for his help and guidance during the course of this investigation. Appreciation is also given to the Computer Laboratory staff, particularly Dr. M. G. Keeney, for their patience and help in making MISTIC available to the author. -11.. Abstract . . . . . Acknowledgement . List of Figures List of Tables . . List of Appendices . Introduction . . . Tube Still Heaters TABLE OF CONTENTS History and Development . . . Development and Selection of Radiation . . Equations Convection . . . . . . . . . Heat Balances . . . . . . . . . . Continuous Balance Vaporization — Physical Properties of the Crude Calculation of the Density of the at any Temperature . . . . . Thermal Conductivity of Petroleum Pressure DrOp Calculations . . . Statement of the Problem.. . . . . . . Restrictions and Limitations . . Results of Calculations . . . . . . . Discussion of Results . . . . . . . . Conclusions and Recommendations . . - iii - Crude Liquids . . . . . 21 ée 22 25 25 27 33 LIST OF FIGURES Figure 1 Box Type Furnace . . . . . . . . . . . . . . . . . . . 2 GUILT" 10a 10B 10C 10D 11 12 Types of Pipestill Heaters . . . . . . . . . . . . . . Radiation Between a Plane and One Tube Row Parallel to the P 1a n8 0 O O O O O O O C O O O O O O O O O O 0 Variation in Qr/QC With Exit Stack Temperature . . . . Variation in Qr/Qc With Exit Stack Temperature . . . . variation in Qr/QC With Exit Stack Temperature . . . . ”Per Cent Excess Air Versus Fraction of Total Heat Absorbed in Radiant Section . . . . . . . . . . . . . Fraction of Total Heat Absorbed in Radiant Section vs Qt/QA O O O O O O O O O O O O O O O O O O O O O O 0 CP Calculations Flow Around One Thbe Increment Flow Diagram-Convection Section . Flow Diagram-Convection Section . Flow Diagraeradiant Section . . . Flow DiagrameRadiant Section . . . True Boiling Point Curve and Gravity Flash Curve . . . . . iv Profile for Crude 13 35 36 37 38 39 h8 5h 55 56 57 67 68 Table I. II. III. LIST OF TABLES Mean Length of Radiant Beams in various Gas Shapes Service Requirements of FUrnace . . . . . . . . . Results of Calculations . . . . . . . . . . . . . Results of Calculations . . . . . . . . . . . . . Polynomials for the Evaluation of q! . . . . . . . Molar Heat Capacities of Flue Gas Components . . . 105 107 Bibliography . . . . . Nomenclature . . . . . Program.Abstract . . . Description of Program Sample Calculations . . Fixed Point Orders . . Floating Point Orders . Furnace Design Program Polynomials . . . . . . LIST OF APPENDICES vi 105 INTRODUCTION The design of modern petroleum furnaces is tending toward larger and more efficient units, sufficiently flexible to adapt to wide variations in physical characteristics of the charging stock, and more responsive to accurate control of the finished product. It is the current trend in design practice to increase the ratio of heat receiving surfaces to refractory surfaces and to increase the radiant heat transmission rates. These increases. affect the size and duty of the convection section and, unless a suitable distribution of heat is obtained throughout the furnace, uneven heating and inefficient units result. There is also a tendency to increase the fraction of vapor discharged from the still to the fractionating tower because increases in efficiency are obtained under these conditions. It is the purpose of this investigation to study the effect of the tube spacing, percent excess air, and bridgewall and . exit stack temperatures and to propose a suitable means of allowing for their effects in the design of tube still heaters. The successful design of a tube still heater must include the requirements of heat load to the furnace and pressure drop of oil through the tubes. This involves the calculation of (1) flash vaporization data to determine the sensible and latent heat required as well as the fractions of liquid and vapor present in the tubes; (2) suitable heat transfer rates in the radiant and convection sections; (3) the tube length and diameter best suited for the type of still and discharge conditions required. The mechanisms of heat transfer in combustion chambers are complicated by the phenomenon of radiant heat transmission; as a result, the design of tube still heaters has developed on an empirical basis. Based on the fundamental principle of _ l _ _ 2 _ radiation postulated in the Stefan-Boltzmann equation, Eb = STA, and with the aid of certain generalizations, an equation was develOped by Lobo and Evans (1), h h - T2 ] ashpw q = 5 [T1 which is extensively used in the design of heaters. Calculations for pressure drOp were made using the Fanning equation, with a correction for added frictional loss caused by continuous vaporization of crude throughout the still tubes. By arbitrarily dividing the tubes into a number of zones, the problem of obtaining heat balances and pressure drops over these sections can be solved but necessitates an elaborate trial-and-error calculation. These calculations not only involve the simultaneous solution of heat transfer equations, but also the evaluation of sixty third degree and seven fourth degree polynomials. This has been accomplished with the aid of a digital computer. A.program for the computer was prepared whereby changes in tube spacing, per cent excess air, and bridgewall and exit stack temperatures could be made in a design. The results of these calculations have shown that the distribution of total heat loads to both sections of petroleum furnaces is an important factor in determining their design. Various distribution ratios can be obtained by changing the bridgewall and exit stack temperatures and the per cent excess air. However, the choice of a specific ratio can only be made after the economic permissible heat transfer rates have been determined. TUBE STILL HEATERS One of the most important commercial applications of radiant energy transmission is encountered in petroleum refinery furnaces. These furnaces, or tube still heaters, are extensively used in atmospheric or vacuum crude distillation, high temperature gas processing, and thermal cracking, as well as in various heating, treating, and vaporization services. History and Development "The early stills used by the oil-refining industry were of the simplest kind. Holding but a few barrels, they were set directly over a coal or tar—fired furnace. The ascending vapors ‘were condensed in a coil submerged in water with no attempt at fractionating further than the gravity indication of the over- head condensate." (2) The stills were generally potshaped and, owing to their construction, were often called shell stills. In the early years of the petroleum industry, progress was slow. The only attempts made to improve the design of the shell still were increases in its size, leading later to the "cheese-box" still. "The cheese—box still with its eventual capacities up to 1,000 barrels replaced the shell stills at a number of refineries, starting in the late sixties. These cylindrical stills usually had what was termed a 'vapor chest' connected to the still by vertical pipes. The still had a dome—shaped top and a double curved steel plate bottom. The still was supported by a series of arches." (3) The increased heat efficiency and capacity of these stills reduced the costs per barrel of throughput in comparison.with the earlier shell stills. However, the small effective heating surface and the large volume of charged stock caused them.to be very inefficient and to have low rates of heat input. With the advent of the fractionation art and the introduction of cracking operations, it became necessary to construct heaters that could withstand the high temperatures and pressures of the -3- _ h - cracking process. These requirements resulted in a continuous operation permitting the greater use of heat exchange and the steady improvement of design and operating efficiency. An early attempt at continuous operation involved construction of a battery of shell stills connected in series, with the first still emptying into the second and then in series on to the number of shell units in Operation. "Comparatively successful application of tubular heaters on a small scale for dehydration and refining of emulsified oils led to the gradual adoption of tubular heaters for general refining purposes and eventual substitution for shell heater for large-scale refining operations." (4) The earlier tubular heaters were similar in design to the shell stills, but the stills were displaced by a bank of tubes. This improvement, in some instances, doubled the heat transfer rates from 3000 Btu/fte-hr with the shell type batch Operation to 5000 or 6000 Btu/fte-hr with the tubular heater. Increases in heat load to the furnace led to localized heating of the tubes and created zones with excessively high transfer rates of 15,000 to 20,000 Btu/ftZ-hr, called "hot spots." Coke formation and tube failures occurred at these points. As these furnaces were designed to obtain the major portion of heat transfer by convection, hot spots were attributed to radiation from flames in the fire box. Furnaces were then built with tube banks shielded from the flame by perforated or solid walls to protect the tubes from its radiation. This resulted in a more uniform heat distribution within the furnace, 'with higher overall heat transfer rates. It was then discovered that, even with the shield, the tubes first exposed to the combustion products became easily overheated. Unless the gas temperature was reduced below a certain minimum, hot spots would still occur. This reduction of gas temperature was accomplished either by diluting the fuel with excess air and then with recirculated flue gas, or by installing tubes in the combustion chamber to cool the hot gases by absorbing radiant energy from the flame, the gases, and the refractory surfaces of the chamber. -5- The basic construction Of most tube-still heaters is similar. Such units almost always consist of a radiant section, where the major portion of the heat supplied to the process stream is by radiation, and a convection section, where the major portion of the heat is supplied by convection from the gaseous combustion products. Heaters vary widely in shape and size, and are designed to meet various requirements for such variables as charging stock, heat distribution, thermal efficiency and time-temperature effect. Because thermal decomposition is a rate process, the degree of decomposition is a function of both temperature and time and is described as the time-temperature effect. Petroleum heaters have been divided (5) into three main groups according to the amount Of decomposition obtained. (1) Heaters used only for heating, with little or no decomposition; (2) Heaters where, in addition to heating, substantially all of the decomposition desired for the refining process isoMmhmm (3) Heaters where only partial decomposition is obtained in the heater, the remainder in the reaction chambers or soaking drums which are usually not heated externally. Heaters of the first group are employed in operations where no chemical change is desired in the charged stock, as for nondestructive distillation processes. These heater are designed to obtain a minimum time-temperature effect with a maximum temperature. Heaters Of the second group are used primarily in cracking Operations where the decomposition of the stock takes place within the heating coils. These heaters are designed to give maximum time-temperature effect at the highest Operating temperature allowable. Heaters Of the third group, used for thermally sensitive residual cracking stocks, must be designed for a time-temperature effect that will permit the highest outlet temperature without excessive decomposition from soaking within the heating coils. -6- A number of typical furnace arrangements are shown in Figures (1) and (2) to illustrate diagrammatically the arrangement of tubes and the direction of fluid flow in the basic types Of tube still heaters. Figure 1 shows a typical box type furnace fired from the end walls. Radiant tubes cover the side walls, roof, and bridgewall (partition between radiant and convection section) surfaces. The tendency in modern furnace design is to fill the radiant section.with cold tube surfaces; to accomplish this tubes may also be placed on the floor surfaces. In cracking Operations, Oil is preheated in the upper and lower rows Of the convection bank then passed through the radiant tubes. After reaching an elevated temperature conducive to the cracking process, the oil is passed through a large number Of convection section tubes wherein it is maintained at a high temperature for a sufficient time to accomplish the desired degree of cracking. n \\\\\\\\\\ a cw\\\I\\\ FMJZ. 1:0 ~ Emir—.30 i=0 PUDO m<0 wDJu r it 89.00 00000 L\\\\ If VV//K//r////V///d/M/ \\ 0009 QOQO @099 9.09.0\ 9.909 .\\\\\\\\ \\\\\\\\ @000 @080 \ \ 809% O mfiuszm OOOO \\\\\\\ 99999999 20:.me «wh4uI b2<.0<¢ 98889009880988 m m w w % MW H \\\\\ \\\X\\&\\\ F J ///////W/ V/////////////////// / tr“ FIGURE 1 I I _A_ "_""x-"“" 'X L ‘1‘ U uuuuuuuuu - I]; A ; it 7‘ E! k V lVVF/irV I‘ai IL J;-\ Loafers. -ipestill Types of FIEURE 2. DEVELOPMENT AND SELECTION OF EQUATIONS Evaluation of the rate of heat transmission to the cold surfaces in tube still heaters is accomplished by considering the extent to which each.mechanism Of heat transfer influences the overall rate. Transfer Of heat energy liberated by the chemical union of molecules in the flame takes place first in the radiant section to the surrounding tubes primarily by radiation though some convection Occurs. As the gaseous products Of combustion progress through the convection section, heat transmission is principally caused by the mechanism of forced convection accompanied by small amounts Of gas radiation. Thermal energy transferred within the furnace enclosure must be equated to the change in enthalpy of the entering and exit streams. To accomplish this, the following equations must be Obtained: heat transfer by radiation, heat transfer by convection, and heat balances about the Oil. Radiation Radiation in a combustion chamber originates from three distinct sources (6): (l) the chemical union Of molecules in the flame, (2) the hot products Of combustion, and (3) the luminosity or soot content of the flame. The magnitude Of radiation emitted from the first source is dependent on the composition of the fuel, the maximum temperature attained, and the absorbing characteristics of the flame for its own radiation. However, in muffle furnaces where the flame is shielded from the surfaces of the combustion chamber, heat from this source is transferred to the combustion products by conduction and convection. Radiation Of greatest magnitude originates from the combustion products and is dependent on composition, temperature, and shape -9- -10... and size of the gas mass. 0f the gases comprising the combustion products, carbon dioxide, carbon monoxide, the hydrocarbons, and'water vapor are the only ones With emission bands Of sufficient energy to merit consideration. Gases with simple symmetrical molecules, such as N 2’ H2’ total gas mass, show no absorption bands in the region of import- and 02, which also comprise the ance in radiant heat transmission. MOreover, carbon monoxide and hydrocarbons are present in such small amounts as to be negligible compared with water vapor and carbon dioxide. Finally, the third source of radiation from the flame, its soot content, is dependent on the degree of combustion and the design of the combustion chamber. Using data Obtained from investigations on the infrared spectra Of carbon dioxide and water vapor, Hottel (7) has presented charts for use in calculating the quantity of heat transmitted from these gases. He has also shown that the energy emitted from a gas mass to a unit area Of bounding surface is a function of the gas and surface temperatures, the absorptivity Of the surface, and the product PL, where P is the partial pressure in atmospheres Of the radiating constituents, and L is the average length Of a blanket Of flue gas in all directions for each of the points of the bonding surface Of the furnace. values of L for furnaces of various shapes were determined by Hottel and Table I presents a digest Of these values for furnace calculations. Incident radiation is not completely absorbed by its ultimate heat receiving surfaces immediately but is reflected and absorbed in an infinite series Of interchanges between source and surface. Consequently, radiant interchange between the surfaces of an enclosure must involve consideration of the view the surfaces have Of each other as well as their emitting and absorbing characteristics. The absorptivities of bodies are generally dependent on the wavelength of incident radiation and also on the factors affecting their emissivities. Absolute values Of the emissive power of bodies are not readily obtainable, however, the ratio of the actual emissive power to the black body emissive power, TABLE I Mean Length of Radiant Beams in Various Gas Shapes Dimensional Ratio LB (length, width, height in any order) Rectangular Furnaces 1. 1-1-1 to 1-1-3 2/33IVFFurnace volume 1-2-1 130 l-2-Llr 2. l-l-l-l to 1—1-00 1 x smallest dimension 3. 1-2-5 to 1-2-8 1.3 x smallest dimension 11-. 1—3-3 to 1—00-00 1.8 x smallest dimension -11- _ 12 _ defined as the emissivity, has been determined for many materials and data are presented in most textbooks of heat transfer. In systems such as furnaces composed of walls and pipes, it becomes difficult to evaluate the manner in which radiant energy falls on these surfaces. The next flux between source and surface occurs by a complex process involving multiple reflection from all surfaces forming the enclosure. The new concept necessary here is F, and has been defined by Hottel (8) as the direct interchange factor, dependent on the angle factors between the refractory surfaces and the surfaces surrounding it, together with the emissivities of the source and sink surfaces. Since heat receiving surfaces or heat sinks in most industrial furnaces are composed of a multiplicity of tubes disposed over walls, roof, and floor of the combustion chamber, it is necessary to evaluate the effective heat transfer area. The development of Hottel, almost exclusively used in design work, assumes that the heat source is a radiating plane parallel to the tube row. The effectiveness factor,<3, is the factor by which the surface of a plane replacing the tube row with assumed emissivity of 1.0, must be multiplied to obtain the equivalent cold plane surface. For a detailed development of 0:, reference should be made to Hottel (9). Figure 3 presents values of<3 for radiation to single rows of tubes with refractory behind them. In view of the complexity of the problem, numerous investigators have correlated furnace performance by means of empirical and semitheoretical equations. The most acceptable of these, is the semitheoretical equation proposed by Lobo and Evans (1). Using an equation of the Stefan-Boltzman type in correlating data from 85 tests on 19 different petroleum furances, they developed the following equation: A u q = a (Tg - TS ) a Acpw + hcA'r(Tg - Tr) + hcAc(Tg-TS) (1) (T‘ r“ 0.7; 0.4. 0.3- 0.2. 0.11 "1 l. (_ . I .. mull- A C f‘ F4- ‘FLi :tatf' wrw» ' xi «3 LIL: rt ".4 ; J I -. . 4K) t. I. A 1.11:. l L l l l r’ I I ." I 3 4 D O { Caviar tn Center Dista on f “"93 Wow Outside Diameter cf Ru.es -13- _ 14 _ 3&1 this equation the direct interchange factor, F, has been replaced by an overall exchange factor, t. W includes, in addition to direct interchange, the contributions due to multiple reflection at all surfaces as well as such contributions by reradiation from zones at which the net radiant-heat transfer at the wall surface is zero. Since both the external losses from the furnace and the net heat transferred to the refractory by convection, given by the term hcA'r(Tg-Tr), are usually small, the two may be assumed equal without appreciably affecting the results. Equation (1) may be rewritten q = o [Tgh - TquOACP* + hcAc(Tg-TS) (2) By making the following assumptions, Lobo and Evans further simplified their equation: 1. The convection coefficient lies normally between 2 and 3 Btu/hr sq ft - ’F; 2. In most furnaces AC equals (aaAcp) approximately; 3. The overall exchange factor #‘has a value of about 0-57- Therefore, the terms he and Ac in Equation (2) can be expressed in terms of and W, thus: hcAc = 2 2 = 7 O cpv 0-57 or hcAc (Tg-Ts) = 7(0Abpv)[Tg-TS] Making the substitution in Equation (2), h 5h:g - TBA] + 7 (TgeTs) (3) 2.2.237" CP In the combustion chamber Tg’ the mean temperature of the hot gases in the furnace and the temperature of the exit gases will undoubtedly differ. However, the assumption of complete mixing in the furnace and that Tg could be replaced by the exit gas temperature was Justified by satisfactory results. The exact evaluation of t is tedious and complicated, thever, their development included a plot of W versus the ratio with r aA CP the flame emissivity as a parameter. Results indicate that the -15- W plot represents an accurate and simple method of simultaneously allowing for the effect of flame emissivity and the amount of refractory surface present. Hottels' charts giving the values of the radiant heat transfer flux due to CO2 and water are most conveniently used in calculating the emissivity of the flame. The radiant flux of H20 and 002 are additive, although a small correction must be included to allow for the influence of one type of molecule with radiation from the other. The flame emissivity is given by the equation: (qc + qw)Tg - (q0 + qw)TS (qb)T _ (ab)T g s (t) E = g Radiant heat transmission in the convection section is particularly significant to the uppermost tubes or "shield tubes" in the convection bank where the temperature of the gases is still high. In spite of the small beam length, Mbnrad (10) has shown that radiation may account for 5 to 30 percent of the total heat transfer in the convection section. Evaluation of the radiant heat coefficient was accomplished by adapting the method of Lobo and Evans and the simplified charts provided by Hottel. The mean length of the radiant beam for exchange between tubes, given in Table I, is based on the center to center spacing (fi-fi), and the outside diameter of the tubes (DO). LB = o.u [(¢-¢) - 0.567] DO (5) q” z 65 We + ”Te ' (01. Wis] A (#0015096 <6) since q _ rc hr - AAT hr = 63 “(1c + qfl)Tg - (qc + qw)TS] (lOO -- %> (7) T _ T 100 g s where the emissivity of the surface es is assumed to have a value of 0.95. (11) _ l6 _ Convection Heat transfer by convection varies widely with gas velocity and size of gas passage, somewhat with temperature of the gas, and very little with gas composition. Although there are numerous relationships available for obtaining convection coefficients, little work has been done to develop a satisfactory relationship for furnace design work. The empirical equation by Monrad (10) is the only comprehensive formulation of convection transfer rates. For direct convection from the gases he prOposes the relationship: = 1.6 G2/3 TO'3 h c 13.13 0 (8) The equation applies to any conventional arrangement of the tubes in the convection section. However, the coefficient hc is the pure convection coefficient and it does not include radiation from.the hot gases or from.the walls. Monrad has made a study of these factors. The first of these is designated as hrg or the coefficient of heat transfer from the gas by radiation. A formula for the evaluation of this coefficient was presented in the previous section on radiation. In his calculations, Monrad also included a correction for the increased thickness of the gas layer at the tOp of the tube bank. His assumption was that this radiation could be approximated by that of a plane equal in area to the top tube bank at PwL = PcL = 1.0, between the temperature of the gas above the bank and the temperature of the tube. He reasoned that since radiation had already been calculated for PwL and PcL based on the center to center spacing and the tube diameter (hrg), the added gas radiation would be equivalent to that at the top gas temperature between PcL = PwL = 1.0 and PcL and PwL based on the center to center spacing and the diameter; consequently, the correction: h’ = h(at PL = 1) - h rs. rs This however, appears to be too severe a correction as PL values for the gas layer above the bank could hardly approach a value of unity. water vapor, the radiating constituent of highest concentration in the gas mass rarely exceeds a partial pressure -17- of 0.20 atms. Consequently, the average beam.length would necessarily have to be greater than 50 feet (for lower concentrations of water vapor) to cause values of PL = 1.0. For this reason, it was concluded that sufficiently accurate results would be obtained without including this correction. The area of the walls surrounding the tubes comprise a fairly large fraction of the tube area. These walls pick up heat from the gases by convection and radiation, and reradiate to the tubes by black body radiation according to Stefans' Law. With the assumption that factors such as reabsorption of heat and the differences in heat transfer coefficients to the wall and tubes are negligible, the following equations were presented: [hC + hrgHTg - Tw] Aw heat to walls = [hrbMTW - Tt] At heat from the walls = heat to tubes from walls Therefore the per cent increase in heat absorption by tubes above that received directly: h [Tw - Tt] A“ x 100 hrb [Tw - mt] Aw x 100 rb = z - The + hrglng - TtT At Atllhc + hrgILTg - TWJ + 1hc + hrgTLTw-Ttlf (9) h may be approximated by: rb T 3 hrb = 0.00688 es [1661 (10) Es = 0.95 T = Temperature of the tube surfaces The complete coefficient of heat transfer in the convection section was computed from the preceding items as follows: _ (100 + 74» wall effect) hu - 100 (he + hrg) (ll) In considering radiation from the walls to the individual rows of tubes in the bank, the correction for the wall effect becomes less pronounced as the gases cool on their way to the stack. The wall effect then, will be of most significance to the tubes in the shield section. If a correction is made for the shield section (suppermost rows surrounded by gas at a temperature of l300°F or above) only, it will be necessary to _ 18 _ evaluate the fraction of the wall surface that will "see" the tubes in the section. An approximation was made by assuming that the area of the walls surrounding the shield tubes would be the only surfaces that could see that section. Corrections for the wall effect and gas radiation were made only for tubes in the shield section, whereas the effect of radiation was neglected in calculations for the film coefficient for the rest of the tubes in the convection bank. In general, the coefficient of heat transfer on the gas side is controlling; although the resistance of the liquid film may be assumed negligible, approximate values were estimated using a modified Dittus-Boelter (ll) equation. 232—133 = 0.027 (13%)”8 (91%)”3 (33911" (12) w“ Based on the outside pipe diameter, the overall coefficient of heat transfer (U) is given by: l U ii. : $0331? g? (13) m o i i i and the heat flux to the oil evaluated using the following equation: qc = U (itDOAL)(At) (11+) Heat Balances The energy balances made throughout these calculations involving the physical properties of the crude oil, can only be fair approximations due to the complex nature of the hydro- carbon mixture. Calculations based on the heat content of the charged stock will involve some error since the difficulty of obtaining the accurate specific heat of the oil, its vapor and its latent heat of vaporization is quite large. The difficulty in estimating external heat losses from the furnace is another source of error. The liquid heat content of Mid-Continent source crude oils 'was calculated using the equation obtained by weir and Eaton (l3). _ 19 _ (H - Ho)L = (15d - 27) + (0.811 — 0.h65d)t + 0.000290t2 (15) H = total heat continent above 32°F. Ho = heat continent at 32°F. t d = sp. gr. of material at 60°F. The heat content of liquids do not vary appreciably with temperature °F . pressure, therefore, Equation (15) was used to calculate the liquid heat content over the entire range of pressures encountered in the pipesflill. Like the liquid data, Weir and Eaton found it possible to incorporate the vapor heat content versus temperature relationship in a single recommended equation. (H - Ho) = (215 - 87d) + (0.u15 - 0.10ud)t . v 2 (16) + (0.000310 - 0.000078d)t It is necessary to include a correction for the variations with pressure. Using the equation of state proposed by Linde to predict PV data, and the constants as obtained by Baklke and Kay (1%) an equation for the total heat content of the vapor was developed. 0 + EP T3 + V:§E-E.__E_P+D+FP (17b) P r3 T = °R v ft3/1b P #‘/in2 A, C, D, E, and F = constants dH = deT - [T(—§§¥)P - v] dP (a) PV = AT - P + P(D + FP) (17) Differentiating Equation (17) ._ELY P( EDT) Q. '94 ... a a.) *3 + U) Q 4.. UL) T<-%t’> =-%— - 20 _ Substituting (b) and (17b) into (a) and simplifying _ 19 is: dH — deT - [ T3 + T3 - D - FP] dP integrating T 2 2 1 FF #0? 2EP H - Ho = f c dT +-————-— [DP + ___ -.___ -.____] (18) 32 p 9331-7 2 T3 T3 and T ‘ I32 deT = (215 - 8Td) + (0.h15 - 0.104d)t + (0.000031 - 0.000078d)t2 The constants, as obtained by Bahlke and Kay are: .A = 157 c = 723A x 107 D = 20 E = 102 x 107 F = 0.52 Energy balances on the gas side were obtained from heat capacity equations for constituent in the combustion product. These equations were summed according to the total moles of each constituent and evaluated as a single equation. These equations are presented in the appendix. Continuous Equilibrium vaporization - Per cent Vaporized In most cases of distillation of such complex mdxtures as crude oil, continuous equilibrium vaporization is used. It is then necessary to know the relationship between equilibrium vaporization temperature and per cent vaporized for any given pressure if intelligent design calculations are to be made. Piromoor and Beiswenger (15) have established a widely used correlation which enables the flash curve of the crude (flash zone temperature versus per cent oil vaporized) to be estimated from the true boiling point curve of the crude. These correlations were later modified by Maxwell (16) and are based upon the empirical facts that: I l. The True Boiling Point curves (TBP) of many commonly encountered crudes and fractions are nearly straight lines between their 70% and 10% vaporized points. - 21 _ 2. There exists a fairly close relationship between the lepe of the TBP curve (straight position) and the flash vaporization curve. 3. There exists a relationship between the 50% distillation, TBP temperature and the 50% distillation point of the ' flash curve. An example of the use of these relationships is outlined in reference 17. To correct flash curves to other pressure, the flash curve is displaced parallel to itself at a higher or lower temperature (depending on whether the pressure is higher or lower than atmospheric) as determined by the vapor pressure versus temperature chart (Cox Chart). The vapor pressure versus temperature relationship with an atmospheric temperature corresponding to that at the 50% distilled point on the flash curve is chosen. Physical Properties of the Crude The physical properties of an oil are found to vary gradually throughout the range of compounds that constitute the oil. The properties such as specific gravity and viscosity are found to be different for each drop or fraction of the material distilled. The rate at which these prOperties change may'be plotted as mid per cent curves; i.e., a plot of the desirable property versus percentage diatilled. A mid per cent yeild curve was used to determine the specific gravity at 60°F of the crude at its different stages of vaporization. The viscosity was obtained using the relationship obtained by Nelson (18) for the high temperature viscosities of hydrocarbons. Calculation of the Density of the Crude at any Temperature (19) It is assumed that the thermal expansion of any sample may be represented by an equation of the form: 2 _ + _ + - t DT A(t T) B(t T) density at any temperature t. U I UU III - density at a standard temperature and.A and B are based on the change at 25°C. Since the specific gravities of most materials are given at 15.56°C (60°F), this temperature is chosen as standard. Then, - 22 _ SG60 = so + [QT + 2s(t-25)][t-15.56] + s[t-15.56]2 (19) converted to degrees Fahrenheit -60 B so = so + [t ] + T [3t-217] (19a) 60 1.8 aT TB Values of at and 3 were obtained,from.charts as functions of the specific gravity of the material. Thermal Conductivity of Petroleum Liquids (20) The thermal conductivity of the crude is given by the following equation: K =-i%i§%g% [1 - 0.0003 (t-32)] (20) Pressure Drop Calculations The problem of calculating pressure drop in tube still heaters cannot be solved by the conventional Fanning equation; since vaporization of the crude with increasing temperatures, results in the presence of two phases, making the equation inapplicable. Pressure drops encountered in two-phase systems are higher than those resulting from single phase flow for a number of reasons. The energy change of the phase transition, the frictional energy remaining in the system due to the internal shear at the boundaries of each phase, and the reduced cross- sectional area of flow for one fluid produced by the presence of a second fluid all affect the pressure drOp. Consideration must also be given to the Hydraulic Energy (PV) of the fluid mass which not only changeS'with temperature and pressure, but also with the composition of the liquid and vapor phases. The complex conditions of multiphase flow and the number of variables involved has been the subject to intensive survey, and relationships (21, 22, 23) have been proposed which correlate two-phase flow data. These investigations have been restricted to isothermal conditions and no attempts have been made to propose a correlation for non-isothermal systems in which there is a continuous change of phase. Therefore it was assumed that each section of pipe would behave isothermally at the average volume fractions and physical properties of the crude. The data -23- of Reid, Reynolds, et al (22) was chosen because their investigations were conducted on pipes of similar diameter to those encountered in tube stills. By a proper definition of terms, pressure drop calculations for two phase flow could be predicted by a Fanning type equation; 2 AFTP = i ng (21) c i 1 = pseudo density of the two phase mixture. ¢ = pressure coefficient analogous to the friction factor of the Fanning equation. In order to calculate X, the following assumptions were made: 1. The volume occupied by the liquid plus the volume occupied by the vapor, at any instant, must equal the total volume of the pipe. 2. The linear velocities of vapor and liquid phases are equal. 3. Flow is sufficiently turbulent to cause complete mixing of both phases. W = Wi W; From (2) ”312 9132: pp2 L L v v 2 2 _ 2 From (1) DL + D - Di wL Wv -—-2 =--——- Substituting for D PLDL P D 2 v v v 2 wLevDi _ D 2 QLW +PvWi L w _ WL 2 2 XDi 9 WLPfDi ] + L P§Wi PtW§ X = WLPLPV + WvPLPv ————:7—-—- . Pva vaL PLWv+ Pva The liquid volume fraction (LVF) = Wva W P tW P L v v L -2h- W The vapor volume fraction (VVF) =1w-F-Zgéwggr L V L X 3 c3.. (LVF) + cV (VVF) = LVF (eL'ev) + ev (22) . Since dyis an empirical constant it must be obtained from a correlation of two phase data. Reid, Reynolds, et. al. (23) have shown that for liquid volume fractions above 10 per cent, one follows the relationship:' APIP = APL (LVF).1 (23) In this equation the following assumptions are made: (1) single phase friction factor correlating charts are applicable to two phase flow problems; (2) the superficial average densities and velocities can be employed. APL is the liquid phase pressure drop as calculated from single phase correlations if the liquid were flowing alone in the pipe at the same rate as the two phase flow. If the assumption is made that X = LVF (PL), a comparison of the two Equations (21 and 23) indicates that, ,1 may be approximated by the friction factor of the liquid phase. For Reynolds numbers, Re>2.5 x 106 Perry (2h) recon-ends the following equation for friction factors: 1‘ = 0.0011, + 0.09 (fig—9°27 Hence if = 0.00111 + 0.09 (£40.27 Where 0.1 5 LVF s 1.0 (211a) At liquid volume fractions below 0.1 the vapor can be assumed to behave independently of the liquid. Therefore values of ¢'were approximated from the single phase friction factor correlating charts at vapor Reynolds numbers greater than 2 x 105. These values varied from 0.001b to 0.005. It was also observed from two phase data that d'decreases as the LVF decreases, and increases as the Reynolds' number of the liquid phase decreases. In view of this, it was concluded that the following equation could.predict sufficientLy accurate values of fi'at low liquid volume fractions y! = 0.0011, + LVF (%)0'27 Where LVF < 0.l (2th) STATEMENT OF THE PROBLEM Restrictions and Limitations This investigation was initiated to study the effect of the variables of per cent excess air, center to center spacing, bridgewall and exit stack temperatures on the design of Petroleum Furnaces. Based on a semi-theoretical equation prOposed by Lobo and Evans for the calculation of heat transfer rates in the radiant section of tube still furnaces, and on an empirical equation developed by Monrad, a series of design equations were written. These equations were solved for different values of the variables and their effect on heat transfer rates and furnace dimensions studied. The Equation of Lobo and Evans was developed for applications only to already designed or completed furnaces. However, as it was used for the actual design in the investigation, certain assumptions were necessary. These are: 1. View factors to individual tubes can be calculated using the empirical relationship of Lobo and Evans. 2. The mean.beam.path to the individual tubes can be approximated by the average beam length of the furnace. The furnaces considered in this investigation were limdted to the conventional box-type with the width equal to the height, single rows of tubes in the radiant section and with equal center to center spacing in the convection and radiant sections. Four tubes per row were placed in the convection bank and the length of the furnace arbitrarily fixed and equal to the length of tubes. Calculations for the inside film.coefficient of the tubes were based on dualiquid phase only. The errors caused by this approximation are very slight as in most cases the outside film coefficient controls. Errors in the tube temperature calculated from this coefficient do not appreciably affect the heat transfer rates as the difference between the fourth power of the gas and _ 25 _ _ 26 - the surface temperatures are extremely large. The reliability of the final design is limited by the accuracy of the physical prOperties data, and the validity of the assumptions used in obtaining the design equations. Perhaps the most severe of these restrictions is that encountered in the approximation of friction factors used in pressure drOp calculations. RESULTS OF CALCULATIONS The results of the calculations are summarized in Tables III and IV. Table II gives the service requirements used in the investigation, as well as the furnace characteristics. The results presented in Table III were obtained without considering pressure drop requirements. Table IV shows the results obtained when the diameters are calculated to satisfy the requirements. - 27 _ - - - m.a om o.osm com oo: - o.ooo.ow a mm ma.o mm m.H om o.o:m com 00: . o.ooo.om m or ma.o mm m.H - o.oam oom oos - o.ooo.ow m om ms.o mm o.m - o.oam cm» 00: - o.ooo.ow a om ma.o mm m.a - o.oam om» co: - o.ooo.om m Om Ha.o om o.m - s.eaa oer oaa mma a.mmm.mm m om Ha.o om m.a - s.eaa one OH: mma a.mmm.mm a .sm .sa .ssam seam seam a. a. ss\manm ss\oa has: Hfi< maze . 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When a distribution ratio has been chosen, the design of a petroleum furnace can then be established on a basis of the permissible average radiant heat transfer rate. The results illustrated in Figures IV and V show the heat distribution ratio to be a function of bridgewall temperature; exit stack temperature; and furnace capacity. These curves include the results obtained using two tube spacings, indicating that the heat distribution ratio is independent of this variable. Figure VI is presented in order to permit visualizing the effect of excess air on the distribution ratio. At a specific bridgewall temperature a greater percentage of heat can be distributed to the radiant section by decreasing the percentage excess air. USing the bridgewall temperature as a parameter, this effect was correlated in terms of the fraction of the total heat input absorbed in the radiant section, and plotted versus the per cent excess air. These results are shown in Figure VII. In the preceeding discussion, emphasis is placed upon available distributions of the total heat load between both sections of the furnace without considering the transfer rates per unit area of cold surfaces. It is quite difficult to generalize regarding allowable rates of heat transfer as this would naturally depend upon the rate at which the 011 removes heat from the tubes and the maximum temperature to which the tube may be heated without causing corrosion, distbrtion of H the tube, thermal cracking of the crude and coke deposition inside the tubes. It should not be concluded however, that a choice of the maximum allowable rate results in the best furnace design, as this maximum may only be attainable in one section of the furnace. The choice, should be based upon rates in both sections which will yield the lowest total tube surface area. -33.. - 3h _ The results of these calculations indicate that this situation is accompanied by high bridgewall temperatures and small quantities of excess air. In the interests of economy, it is the current trend to fill the radiant section with cold tube surfaces. Figure VIII gives an indication of the relationship between the cold plane area in the radiant section and the fraction of the total heat input absorbed in this section. These curves show that this fraction, although independent of the tube spacings used, varies with excess air and furnace capacity. These curves are also significant in that they give an indication of the Optimum.size of the radiant section. For example, if the maximum allowable| rate of heat transfer was found to be 20,000 Btu/ft2 for Furnace l (illustrated by curve 1 in Figure VIII), then a design could not be made such that the fraction of the total heat absorbed in the radiant section is less than 0.32. Also, if the permissible rate were close to the maximum, for example 18,000 Btu/hr ft2 then the resulting small radiant section would be obtained at a loss of economy. This, however, can be avoided by increasing the per cent excess air and thus increasing the fraction absorbed for a specific radiant rate. it) L)€: :nxec‘10n Absor ed in 4 u .. i'.L“(L‘ h.0 ‘ 3.2“ 2.8- 2.0 - 106‘ 102‘ 0.8 I F films 1+ Variation in Qr/Qc With Exit Stack TempeTature LU ID H LN ‘ l)rgi' k)L1k~'V-x Furnace Data: Flow Rate = 39,262.4 r1 7 3 1'1 .1 PINK.) 0 .. 830 9‘30 1030 1301/th Inlet Temp. L “10 °Y Exit Temp. = 6770 °:" L“ ‘ )L ‘— l J l T (‘1 j I' “ Lxccss Air 1300 13-00 1500 1'00 *rbigc-Wall Taiperature -35- .. r-s J «J ._—-< ’ I \ . . +4 k-’ I ' I- C; U J 1;! , ,n 4 \4 J -—< .‘—‘ 'r“, . , +4 '. f C) ‘r ’ Q) .-. K (j .4- ,u‘ 4 I. “ I < -- ,4 .\ >- ‘ J r \J . . .4 ‘ 5-1 'r“. '7" b '15 (3,) , . #1 .. (.J SH r“ 1" ... _ J‘ ,A. [D .4 a (V ,J (a ‘s .. L... , -2 (I . .1) i , (g *Litfl ‘L ALA i 4.: 4:- y6a [‘0 if) 2JH 2.0- 1.6-L 1-2... 0.8 FIGURE 5 Variation in Q .Q_ With a,,g _ 7 f. c , .nxli,fitach.5knnpeitltdre \ Curve Temperature °E 1 it 2 95C 3 IO}; Furnace Data: Flow Rate = .C,OOL 1: hr Inlet Temp. : wtO 1 Exit Temp. : 755 °F 50% Excess Air 3 ?ridge-Wall s {D i 11b lmt rat are °F 4.0 3.6 3.2 R) U0 2.h 2.0 1.2 (N CU ‘ 11 T 4 FIGURE 6 I l . at], A: (‘:r .4! , . 2. 25¢ hxcess Air, 7" I LXlL Temperature = 1 1L 1 "‘ - . ’. Y7 . . ‘I fi ‘ 7‘ fl, _ 1" ...‘..(:’:‘b-‘3 Ii- L ) L-‘ l.\lL:’l .LF‘ I 5‘ m . .n . .. r‘ ’ ' 7 stack Temp. 300 °F = '35:- 1:- J . I ’/\I 1300 1&00 r V T 1500 1(00 Brid’e-Eall Temperature -37- to U) (V '- 5-. c. u g) AA» a 1 ‘_D C‘ txc ‘5‘. \ I"; ‘ but, j 5 I‘CGII \ 1f) 1 l FIGURE 7 V“, ;ereent Excess Air Urn? Fraction of Total heat A -<.\‘ r ' ‘v’fit‘. C \ rdlotrzbrhi 1i} Enid-.tut, Urn. L"; 11-36." .7" UI‘IJLCP 3 1. Average Tridgews‘i twinperettuml'" 150C) 2. Average jridgewuil temperature - 1400 3.. Average ;_l"id;_:(," 511‘ temperature > 130? l l i of Total Le 0.4 0.5 0.6 rbed in Radiant Section ectiou (s, U radiant h A Ti in , 3 CL (W ’eat Absorb , J Tet :ll (.2 f 'actiOL {1 I .L FIGURE 8 .1 ‘ 1— -~ - e " I‘ L . ELM; -iml. - }‘ .11 I-CLCe 2. .frre Farr "- O.8 .m- . I“ “‘3' EtuGo TX 0.6+ 005-1-— 0.1m. 0.1-L U.) C) .p‘ 0 \fl 0 O'\ O -\1—.— C CD . at -39- CONCLUSIONS AND RECOMMENDATIONS .Accurate furnace designs can be obtained using mathematical models similar to that employed in these calculations. Although these models are useful in determining the effect of various phenomenon in furnace characteristics, they cannot be used to directly determine optimum designs. In order to obtain the best design for a furnace, models must includeénonomic considerations as well as those factors included in this model. The factors most significant in determining the ultimate design of furnaces are the distribution of total heat load to the radiant and convection section, and the average heat transfer rates. The heat distribution ratio of a furnace is dependent upon the per cent excess air and bridgewall and exit stack temperatures. Increases.in any of these characteristics will result in a larger distribution ratio. Average heat transfer rates in the radiant section are almost entirely dependent upon the fraction of the total heat input absorbed in this section and increases as the fraction decreases. This fraction is dependent on the per cent excess air and bridge- wall temperatures and will increase as either variable decreases. The total tube area required for a furnace with a specific duty is usually lowest when the bridgewall temperature is high and the per cent excess air is low. The number of calculations made throughout this investigation was severely restricted by the size of the computer available and the type of programming employed. Should a similar investigation be attempted, it should be conducted on a larger computer using a faster method of interpretive programming. It is also recommended that a:more accurate method of predicting pressure drop in the presence of two phase flow be obtained. APPENDIX ES -ln- 10. ll. 12. 13. 11+. l5. l6. 17. 18. 19. BIBLIOGRAPHY Lobo, W. E. and J. E. Evans, Trans. Am. Inst. Chem. Eng., 32, 5 (1939)- Bell, H. 5., American Petroleum Refining, p. 1A1, D. Van Nostrand Company, Inc., New York, 1945. Petroleum Panorama, 1859 to 1959, Oil and Gas J.; 1959. Dunstan,.A. E., Science of Petroleum,_3, p. 2223, Oxford University press, London, 1938. Ibid, p. 2228. 'Wilson, D. W., W. E. Lobo, and H. C. Hottel, Ind. Eng. Chem., g, 1186 (1932). Hottel, H. 0., Trans. Am. Inst. Chem. Eng., _1_9, 173 (1927). MeAdams, W. H., Heat Transmission, 3rd ed., p. 63, MeGraw- Hill Book Company, Inc., New York, 195M. Hottel, H. c., Trans. Am. Soc. Mec. Eng., 2;, 265 (1931). Monrad, c. c., Ind. Eng. Chem., git, 505 (1932). Kern, D. Q., Process Heat Transfer, p. 708, McGrawaHill Book Company, Inc., New York, 1950. Ibid, p. 103. Weir, H. M. and G. L. Eaton, Ind. Eng. Chem., _2_l_+, 211 (1932). Bahlke, w. H. and w. B. Kay, Ind. Eng. Chem., 23,291 (1932). Piromoor, R. S. and Beisnenger, A. P. I. Bulletin, 19, No. 2 (1929). Maxwell, J. B., Trans. Am. Inst. Chem. Eng., 17, 59 (19h). Nelson, W. L., Petroleum Refinery Engineering, p. 113, McGrawaHill Book Company, Inc., New York, 1958. Ibid, p. 180. Density and Thermal Expansion of American Petroleum Oils, U. S. Bureau of Standards, Technologic Papers, No. 77; 1916. Thermal Properties of Petroleum Products, U. S. Bureau of Standards, Miss. Publications, No. 973 1929. Lockhart, R. W. and R. C. Martinelli, Chem. Eng. Progr., £5. 39 (191s). -l+2- 22. 2A. 25. 26. -113- Reid, R. C., A. B. Reynolds, A. J. Diglio, I. Spiewalk, and C. H. Klepstein, Am. Inst. Chem. Eng. J., 3, 3 (1957). Chenoweth, J. M. and M. N. Martin, Pet. Ref., g9, 51 (1955). Perry, J. H., Chemical Engineers' Handbook, 3rd ed., p. 383, McGraw—Hill Book Company, Inc. , New York, 1950. Donnell, J. W., and C. M. Cooper, Unpublished Notes. McCulloch, c. E., 011 and Gas, 2, 93 (193A). :p O 3: a: a" 03> o "d U *d ‘2 UU in u: :2 Ft «5 *a‘gs :1 O WNWD‘ H 835 b *d "U refit. m’d O NOMENCLATURE total outside tube area, ft2. effective refractory area, ft2. actual refractory area, ft2. total wall area, ft2. area of plane replacing tubes, ft2. heat capacity, Btu/lb °F. - pipe diameter, ft. pipe diameter, ins. equivalent diameter: of liquid phase. equivalent diameter of vapor phase. fraction distilled. black body emissive power, Btu/hr ft2. geometric factor. overall exchange factor. Fanning friction factor. superficial mass velocity, lb/hr ft2. enthalpy, Btu/1b. heat absorbed by crude per node, Btu/lb. pure convection coefficient, Btu/hr ft2 °F. radiant coefficient, Btu/hr ft2 °F. thermal conductivity of crude, Btu/hr ft2 °F/ft. thermal conduetivity of tube, Btu/hr ft2 °F/ft. mean length of radiant beam, ft. length of radiant section, ft. length of tube node, ft. pressure, lb/in2 partial pressure of CO , atms. 2 partial pressure of H 0, atms. 2 heat transferred to the oil, Btu/hr. specific gravity. temperature, °R. temperature, °F. _ Ah - 5:: _ A5 _ overall heat transfer coefficient, Btu/hr ft2 ° mass flow rate, lb/hr. height of furnace, ft. F. factor by'which.AcP must be reduced to obtain effective cold surface, QACP (effective tube area). gas emissivity. pressure drop coefficient. viscosity, lb/ft hr. pseudo density of two phase mixture. center to center spacing of the tubes. Stefan—Boetzmann constant, 0.173 x 10'8 Btu/hr ft2°Ru density, 1b/ft3. p = Subscripts b = black body. c = convection. S = gas. 1 = inside. m = arithmetic average. 0 = outside. r = radiation. 8 = surface. 'w = wall. 1 = inlet. 2 = exit. PROGRAM.ABSTRACT TITLE: Pipe Still Heater Design. AUTHOR: William v. Saunders. DESCRIPTION The program calculates the dimensions, number of tubes and their diameter in the radiant and convection sections of the furnace. The method used includes the correlations of Lobo and EWans for the evaluation of radiant heat transfer rates and those of Mbnrad for calculating convection coefficients. COMPUTER MISTIC, ioeh cathode-ray tube memory locations, perforated tape input and output. PROGRAM.LANGUAGE Fixed point and floating point coding. RUNNING TIME . Six to ten hours depending on the accuracy of initial estimates of the guessed quantities. COMMENTS The engineer can have the calculation stop after any of the two sections: radiant section, convection section. Program has been successfuly used over {forty times in designing furnaces. AVAILABILITY A.manual for the description of the codes used in this program is available in the Computer Laboratory library at Michigan State University. This program is available from the Computer Library in the Chemical Engineering Department. _45_ DESCRIPTION OF PROGRAM Description To handle the lengthy calculations involved in designing the tube-still furnace, a procedure was develOped for use with a small sized digital computer. The machine routine is such that a choice of tube length, flow rate of crude stock, center- to—center spacing of the tubes, percentage excess air, and bridgewall and exit stack temperatures may be varied in considering the different designs. The furnace may'be calculated in any increment of tube length desired; however, as the computer routine used was an extremely slow one, it was necessary to shorten the calculations as much as possible in order to have expediency of calculation time. Such being the case, an increment of four tube lengths was chosen in the convection section and two tube lengths in the radiant section. The flow of calculations around a tube increment is shown in Figure 9. At the inlet of the tube, the temperature, pressure and liquid volume fraction, (t, T, P, LVF) is known from the previous tube, or if the first calculation from the inlet conditions to the furnace. The inlet conditions (t2 and P2) are guessed and their arithmetic averages computed. Based on these average values, new values of t2 and P2 are calculated. The calculated values of the outlet temperature and pressure are compared.with the assumed values. If the difference between calculated and assumed values are not within tolerance, new values for the exit conditions are chosen and the procedure repeated until the outlet values are within tolerance. These values are then used for the next tube. When the gas temperature above the tube reaches a certain maximum, which is set as the highest allowable bridgewall temperature, calculations for the convection section are stopped and calculations for the radiant section commences. When the exit temperature and pressure from a tube increment compares _ M7 _ (‘l LT'PC‘ C 111D __ . V , 1 ,‘ . . . \J /l_n)\_)i.: L'.Wh, pH LAWCTLAIED , TIL". I BE. IT’S DE 2 ‘2 t P I' l 1 :1-1 C/‘L' C'ILA‘T’E "“"C"?A;' :' C 17“" .L [4.11.] CI) - ._J( ". ‘ “"6, 'F'I"AILE :5 and t l P and -’ 2 I2 CONVECTION NODE 2 iEX L‘ REVISE AID RECAT .Cfi ATE TOLERAKCE C“. ._ l 1 '2 , .rn Ci RE t2 :1 t2 . 1 . r2 .515. 1’2 RADIANT NODE .T-‘if Z';";"_E 9. C'th':l"etions 1101.; Around one '71:. Zi'::creme:1t -h8- P) _ 49 _ with the desired discharge conditions, the dimensions of the furnace are calculated from the number of tubes in this section and compared with the assumed dimensions. If the discharge conditions do not check within tolerance a new diameter is assumed and all calculations repeated. Calculations within the radiant section are repeated when the assumed dimensions do not compare with those calculated. Finally a heat balance is made about the furnace and the fuel rate modified until the heat liberated equals the heat absorbed plus the heat lost from the furnace. Method of Fitting Equations to Data The numerous charts necessary to the solution of this problem had to be programmed so that they could be interpreted by the computer. The most convenient and accurate method of doing this is by fitting the curve to polynomials. Polynomials were obtained by reading a set of points from each curve and by fitting these points to a polynomial of the form F(X) = 1/2 2:: ASKS The criterion of excellence for each polynomial'was that the sum of the squares of the deviations nrl 2 f = oints from the curve (Xi) P Should be a.minimum.with respect to arbitrary variations of the coefficients.AS. Two library routines, K3 and L78, were available for the evaluation of these polynomials. The constants, as obtained for the curves used in these calculations are presented in Table 5. MACHINE REQUIREMENTS The automatic computer used for the furance calculations ‘was MISTIC, a binary, fractional, single address computer with a word length of hO'bits, a.memory of lO2h‘words, and which puts - 50 - two instructions in a word. MISTIC like most digital computers is composed of five units: input, memory or storage, control, arithmetic, and output. Input This unit includes as an input medium a S-level perforated Teletype paper tape by which the problem is communicated to the computer, and as an input device a photo-electric reader which is able to pull the tape past a light. The light shines through the holes activating a photo-sensitive surface which converts the spots to electrical impulses, equivalent to the number represented by the coded character on tape. These impulses are sent directly to an assembly register. meory The numbers received by the assembly register are sent under the control of the computer to memory. The memory is an electronic device composed of 40 vacuum.tubes. On the face, or gird, of each tube 1024 spots can be stored. Each spot is assigned a certain address or location, and corresponds to a binary digit from every word. Each tube represents a different binary digit, that is, a power of two (referred to as a bit) to camprise a total of 40 bits, or one word. Information stored in memory usually consists of a series of instructions (a program), directing the machine to execute certain Operations and a set of data on which these operations are performed . Arithmetic The instructions and data held by memory are used both by the arithmetic and control sections. The arithmetic section is that section of the computer in.which mathematical and logical Operations are performed. These Operations include: addition, subtraction, multiplication, division, and the comparison of two quantities and are associated with three #0 bit registers and an adder. These are the A.register (accumulator), the Q register (quotient), the R register and the adder. In an addition, A.holds one of the terms and the result, Q holds the quotient -51- of a division and has no additive properties. The adder is a register on which the number in.A is added to the number in R. Control The control section of the computer directs every Operation executed by the computer. MISTIC stores the program provided by the Operator in memory, and before any Operation can be executed it must be summoned from.memory by the control section. This section is comprised of an instruction register (IR) which holds the instruction currently being executed by control and a control counter which holds the address of the next instruction pair to be sent to IR. Output When the result of a calculation has been obtained which must be transferred to the operator, it is sent to the output section. The output section is similar to input in that electrical impuses are converted to a suitable code and trans- lated by an electro-magnetic devise and presented to the reader on tape.Teletypewriters are available and are used for printing on paper the symbols represented by the punched tape. Subroutines RUSTIC operates in binary, and in.vieW'of this, special attention must be given to the location of the decimal or binary points of numbers before every arithmetic Operation. Its arithmetic unit necessitates the binary point to be fixed so that any number X used in computation must be in the range -ISX<1. It is necessary then, that each number at every stage of a calculation be scaled within the capacity of the Machine. Many problems encountered in engineering calculations involve numbers Of various magnitudes making scaling an additional inconvenient complexity. For these calculations floating point routines may be used. These routines represent numbers as x = a x 10b and store a and b. Thus they can represent numbers in the range of 10-63‘5 xi< 1063. The floating point routine used in the preparation of this program was a standard library routine designated as A1. - 52 _ Running Time and Accuracy The running time for a complete computation cannot be predicted exactly as this would depend on the accuracy of the initial estimates of the guessed quantities and the number of increments chosen. The running time necessary for an increment of tube length to converge was approximately three minutes and that for a complete computation averaged to about five hours. A.conservative estimate of the time required to perform a complete computation by hand, would be 110 hours. The accuracy for each arithmetic Operation is set by that of the Al Routine which provides an answer to at most nine decimal digits. However, the elaborate trial and error computation involved necessitated a choice of limits-of-convergence which resulted in an accuracy within 0.8 per cent of the correct answer for the exit temperature and 1.5 per cent for the exit pressure for each tube increment. Error Stops During the necessarily lengthy calculation periods, the operator was kept informed of progress and possible errors by special features included in the program. At the end of each calculation cycle, print outs showed; (1) dimensions of the furnace, (2) difference between the desired and calculated pressure drOps and also tube diameter, and (3) number of tubes in the radiant section and the fuel rate. Obvious errors in any of these values could eaSily be detected however, the less obvious mistakes could only be detected in the final answers. Diagrammatic Flow Chart The backbone of the automatic computation system consists of two separate but complementary computer programs for the solution of the design problem. The first program treats the convection section as an independent unit and makes calculations around tube increments until the gas temperature above an increment reaches a certain maximum. This:maxtmum is set by the bridgewall temperature desired in the radiant section. The second program.utilizes this temperature and the exit conditions from the convection section to solve the problem of furnace di- mensionsb number of tubes required, tube diameter and also the heat balance about the furnace. nt'x. O -53- The calculation procedure is diagrammed in Figure 10. With the exception of the preliminary calculations (box 1), each step in the diagram corresponds to a series of calculations listed in the smaple problem given on the following pages. In order to shorten machine running time as much as possible certain quantities were evaluated at the beginning of the program to avoid repetition during any cycle for which these values do not change. These are the preliminary calculations and include the evaluation of 1.6Gl/3/D'O(2/3) from the convection coefficient, Equation (8); the mean beam path of the gases between banks of tubes, Equation (5) and the ratio AW/At. PIELDKIIJARY CALC THATI O T :3 AISt) JA'E P )t2 ‘ . @ CALCULATE P t 18 m m izAs mass arm AIIY VAPORIZATION? YES NO CAICT Unit's - J ‘ D 7, PER cm )4- — 5 IE1\ 0441.... YAi’Of-IIZED C VAPORIZED = o cucumcs: CRIIDE‘ s E :‘SICAT .1, a r .JCE‘is V R' IEb FROM AH CALC'ILATB, Vfi’hc YES IS THIS I WC“ 3% A SHIELD T's" JR? J - FIGURE 10A. Flow Diastram. Convection Section. -51.- DIFI OAS PL“W RATE ASSURE 3" . U CAI’C 3: Av—‘VE 1:8 PM I D ES h cage cum? 6% 1 Eéz A: . SEW “ h CA: 0 m: U u {Elm o CAIN APEq }_@—[DESq-A' D”ES CAlpqlAmE ts "' .. e D ‘ ’4 . .L 1 L1 A; ‘2 .‘:ES )J." (“EITLWCAT r IS ”Vi 7' 1‘ [1,; $- r f ‘ I I y I) A V 2 “IO ‘ CHUVVT A ‘ fDE . - i -' v ND REPEAT ~ ’“R 15 'T‘ 15 7'1: .ADJL- A: Twas ’ AS? S IIEID l’TEIE SE as, FIGURE 10?. Flow Diagram. Convectio: Section. 55- MD itg AND ‘I’ DIH 1w ‘ ‘ 2 A‘JD REI'IZAIL‘ L. 04 w :3 :5 0 ASSw T? 'E DH III'TS I03: C0 CALCLTA '13, PT, I. @fi J 1531-3131;": sms 2 T'RLIH IL. 6 ’ {4“- U L, . 1 35le 10C. 10103. SE 0 CA: .0: .A'I‘E “3303f é] CI'LLCé ”.0 ll CALC'II ATE A P CALCULATE (3} T'low Di -'.2;-§I‘.’:.m . -55- I‘ ldi? ' t L Lb AXD f Section. @ 9 7 1'1 _ ' * 1‘10 , ,, n--- . MJD"F7 DuES L% EQUAL CHER“*LCATE DT ENS, 'S ASS,§ ? IEw VALUE Ta * “L“ “ ”ED (PEMRR D C/;W -;CA E DxES Z q MQDT}? GAS do as EQ A” ,EAT {:3} T' REEEAv A“; DESFJH CA;C7:A:*‘XS SAMPLE CALCULATIONS The following computations serve to illustrate the flow of calculations around a tube node in the convection and radiant sections. It should be clearly understood that this illustration represents only a small fraction of the computations necessary to complete a solution of the furnace design problem. Furnace data: Inlet temperature = #00 OF. Inlet pressure = 2H0 lb/in2. Stack temperature = 870 OF. Tube spacing = 1.5 tube diameters. Fuel - CHH fired with 50% excess air. Crude data: Flow rate = 80,000 lb/hr. API gravity = 35.7 True boiling point and mid-gravity curves are presented in Figure ll. From the true boiling point curve, a flash curve is drawn at 238 1b/in2 and is shown in Figure 12. Calculations Tube increment= 100 ft. (2) Assume: Exit temperature = h09.517 °F. Exit pressure = 236.29 OF. Tube diameter (inside) = 0.u1 ft. ' tm.= 40h.76 OF; em = 238.15 lb/ine. (3) Calculate per cent vaporized: t - t _ b . d — lOOm (equation for the flash curve) t(b) = t(p) - 50m. t(P) is the vapor pressure-temperature equation for a hydro- carbon with an atmospheric boiling point corresponding to the 50% point of the flash curve. t(p ) = #26. 58 + 3. 2P - 0. 0113 P2 + 15 h x 10 Solving for t(P at p= 238.15 1b/in2 , t = 759 7% OF t(b) = 379.7h F. Since t(b) < MOM.76, vaporization has occurred. d = (h0h.76 - 379.74) f (100) (7.6) = 0.033 This result can also be obtained by reading the fraction distilled -6P3 from the flash curve Figure 12. -58- .. 59 .. (6) Calculate the liquid volume fraction (L.V.F.): Wt L.V.F. = W: + Wv pL w p" [ .014 1600 L F We "' (l'd) [ — ] pc 6OOF we = 80,000 lb/hr (SG)c = 0.847h The specific gravity of the liquid can be obtained from the mid- gravity curve (Figure ll) , or from the following polynomial at d = 0.033. (so)L = 0.599 + 0.965d - 1.h87 d2 + 1.017 d3 = 0.63 .z'wL 57,h50 lb/hr WV = 22,550 lb/hr = 1728/{ig—7—T - =13- [ 7231+ + 102P]x 107 + 0.52}) + 20} T <:|l—' u pv T : 864.76 OR P = 238.15 1b/in2 3 = 2.6 lb/ft3 opv L = (so): + <—f—‘f—§£){ 0T + [ST [31; - 2171} '178 2 0.00122 + 0.00276(SG)E — 0.0079(SG); + 0-0046(SG)E 6 “T BT 1.92307 x lO-6(SG)E - 1.5538 x 10’ (8G): = 0.63 . pL = (SG)L 62.4 = 29.95 WLpL LVF = WLQV'+ vaL .°. LVF = 0.018 CalculateOH: HL = 15 (SG)L - 26 + [0.811 - 0.u65 (SG)L]t = 0.00029t2. 11V = [215 - 87 (SG)L] + [0.415 - 0.10M (SG)L]t + 2 -h 1 _ 60 - _.3_ T3 AH = [WLHL + wvliv]2 - [WLHL + WVHVJl t1 = h00°F; Ii = 240 lb/in2; t2 = 409.517 °F; P2 = 236.29 °F. [20.h7p + 0.258P2 (28.970 + 203.AP)x107]} AH = 5.35 x 105 Btu/hr. (7) Calculate Tg' (Gas temperature above node) T 13H = f 2 c dT T P l _ LI' '5 2 0 0p — 1.9xlO + 1.7T - 9.l2xlO T Btu/ R 5.35x105 = 1.9x10h['1'2 - 1330] + 0.85[T22 - (1330)2] — 3.0hx10'5[T23 - (l330)3] Newton's method is used to obtain the nth approximation of T2, T _ f T _ 2 T — T -l 214-8117 where f(T) — f deT AH n n T1 Following this procedure, T2 is solved for by trial and error. T2 = 923 °F. (9) Calculate q(= UA At) A = «DOAL; fte; At = [tg - tm] D (D -D ) D l/U = I__ + o o i + o + hu (DO DiSKh Dihi Km, the thermal conductivity of the tube, is assumed independent of temperature. Km = 26 Btu/ft2 °F/ft. = 1.6 G2/3Tgo°3 D,1/3 O J hu G = (gas flow rate)/(minimum cross sectional area) = 8.3ux10 /LDO(¢-¢-1)3600 1b/rt2 sec. D3 DO/12; Tg = (923 + 870)/2 + #60 = 1356.5 °R. 2. 7.8 Btu/hr ft F. D‘ 5:: II 0.8 C p 1/3 1 i = 0.023 (33—9) (41%) “ L L -61- 0.81 0 K1 ='i§T§%7 [1 - 0.003(t-32)] = 0.095 Btu/hr ft2 F/ft C..AF p — At = 0.75 Btu/lb °F. “K (kinematic viscosity) = 5.995 - 0.023t + 3.93xlO—ht2 - 2.32x10'6t3 u = “K (SG)(2.u2) = 1.0T lb/ft hr. Solving: h1 = 806.9 Btu/hr ft2 °F u = 7.66 Btu/hr ft2 °F. q = 7.66 (m)(0.h66)(100)[896.5 - hoh.76] q = 5.5x105 Btu/hr. Since q and AH are approximately equal, the assumed t2 is correct. However, if qaé AH, within tolerance, another value of t2 would be calculated using the following relationship: t: = t2 + (q— AH) (t2-tl)/(AH). and all calculations repeated. (16) Calculate AP. _2pALG2 AP- inq0M) i = LVF (pL a pv) + pv = 0.18(29.95-2.6) + 2.6 = 7.52 1b/ft3 ‘ 0.27 ¢ = 0.001h + 0.09 G%é) - 0.00h9 L A L Solving AP Since P2 4' AP =3 P1 the assumed pressure is correct. For P2 + AP aé Pl repeat calculations using 1 = + , P2 P1 AP (10) Shield Section . For tube nodes in the shield section h = (100 + % wall effect) u 100 II 100 + equivalent length of A return bends = 220 ft. u.2 1b/in2 (hc + hrg) Btu/hr ft2 _ 1.6 G2/3Tg0'3 hc - D'l/3 o hrg = e [(qc +"Wig (qc q'w)Ts] (100-5.) 8 (Tg-Ts) 100 hrb x Aw x 100 [hc + 3hrg = hrbIAt % wall effect = hrb = 0.00688 es LICCJB and es = 0.95 This necessitates a trial and error solution since the tube surface temperature,t , is unknown. .A solution is obtained by approximating hu and calculating tS . = + 13$ tm AtS DO/Dihi + DO(DO-Di)/(DO+D1)Km At = ]At s 1/hu + Dofnihi + DOTDO-Di)/(DO+DiTKm At=tg-tm From.ts, hu is calculated and compared with the assumed value. If their difference is small, the calculated hu is used as the correct value. If their difference is not negligible, another value of hu is assumed and the process repeated. When a tube node has converged, the calculated values of t and P2 are used as inlet conditions to the adjacent node and calculations repeated until Tg is within the temperature range assigned to the bridgewall temperature. At this point, calculations for the radiant section begin. The method of evaluating exit conditions from tube increments in the radiant section is similar to that employed in the convection section. However, q, previously the heat transferred by convection, 2 must be replaced by qr, the heat transferred to the oil by radiation. The evaluation of qr is illustrated in the following example. Length of tube = 25 ft. Length of node = 50 ft. Bridgewall temperature = 1391.8h 'F. Inlet temperature = 797.83 9F Inlet pressure = 51.35 lb/in2 Per cent excess air = 125%. (1) Assume: Dimension of radiant section = 16 x 16 x 25 ft. _ 63 - Exit temperature = 803.85 °F. Exit pressure = 53.99 lb/ine. (2) Calculate (previously illustrated). 12 vaporized = 79J+2 ‘1». 34.086 1b/ft3. 0L = pv = 0.497 lb ft3. WV = 6.187x10LL lb/hr. w: = 1.822xlO lb/hr. LVF = 0.00429 A H = 4.0839x10 0.0556 Btu/hr ft2 °F/ft. 5 Btu/hr. K1,: “L = 0.48 lb/ft hr. 0p = 0.83 Btu/lb °F. (3) Calculate tS AH = u at DOAL [ts-tn] 1/u = l/hi + DO(DO—Di)/(DO+D1)Km 0.8 1 3 -2191 = 0.023 (29) (CP“) K'L “LT D = 0.46 ft.; D = 0.42 ft. 0 1 Solving tS = 815 °F. (1+) Calculate q_r qr = aAcpir {0.1735(108 [Tgu - T84] + 7 [Tg-TSJJ LB = 2/3 [25 x 16 x 1611/2 = 12.28 ft. PCO2 = 0.0466 atms. PH2O O .0892 8.th . PL(002) = 0.5493; PL(H2O) 1.099 atm. ft. A tube spacing of 1.5 tube diameters corresponds to a = 0.97 (Figure 3) . _ _ 2 ..aAcp—a L759! DO— 33.5 ft -64- 2G = [ (qc + qw)Tg — (qC + qw)TS 1 [EL—9%?) Btu/hr. To Obtain qc and qw at their respective PL values, it is necessary to interpolate between two polynomials. The following interpolation formula is used. f() =f< )+P'P1 X Xl P _ Pl [ f(x2) - f(xl) ] Pl < P < P2 and f(x2) > f(xl). P * desired parameter (PL value), f(xl) and f(x2) are the polynomials corresponding to parameters P1 and P2 respectively. Emission due to CO molecules: 2qc (at PL = 0.4) 4823.29 - 12.153t + 0.0097198t2 - 7.351 x 105t3 2qc (at PL = 0.6) = 7588 - 18.258t + 0.013484t2 - 1.1916 x lo‘ht3 Emission due to H20 molecules: 2qw(at PL:l.O) = 622.9 - 1.6958t + 0.0043397t2 + 1.848 x lO-ht3 2qw(at PL=1.25) = 2283.7 + 5.2497t — 0.000627t2 + 3.4113 x lo’l‘t3 Black body radiation: 2qb = -5926 + 27.632t - 0.03172t2 + 2.550 x 10'3t3 Polynomials are also available for the percent correction. These polynomials are identified by the parameter S = PCL + PwL’ and evaluated as functions of R = CO2/(H20 + C02). Interpolation is again necessary. P + P = 1.648 cL wL R = CO2 = 0.334 00;"? H20 2(%), (at 3:1) = 2.5018 + 49.2874R - 92.454R2 + 102.165R3 - 52.967OR 2(%), (at s=2.0) = 4.232 + 51.983R - 101.885R2 + 111.444R3 - 5h.63ORy Solving for eG: EG = 0.394. 2Z Z + 2L AR/cmcp = ol.(2Z + f) -1 If tubes are placed on the Bridge wall, f = 2/3z. If not, f = O. The first iteration through the radiant section is made -65- with f = 0. After convergence to the correct discharge temperature, f is calculated from the number of tubes in this section. The magnitude of f determines whether tubes should be placed on the bridge wall. 2 x 16 [16 + 2 x 25] /oA = - 1 = 1.72 AR CP 0.97 x 25 [2 x 16 + 0] 2W: (at 6G = 0-38) = 0.7336 + 0.3505 Qgg— ) - 0.0495 §§%— )2 + AR 3 CP cp 0.0024 (——_ ) oAcp AR AR 2‘19 (at €G = 0'50) = 0°7671 + 0.3792 (EA— ) - 0.06946 (EAT )2 + AR CP cp 0.0037 Qflf')3 CF Solving v = 0.6152. q1. = (33.5) (0.6152)§ 0.173 x 10'8 [(1851.4)1+ - (l275)h] + 7 [1851.14 - 1275]} = #22 x 105 Btu/hr. Since qr 4— AH, t2 will not be recalculated. Calculations for [LP are similar to those performed in the convection section. Calculations are repeated until the exit temperature, t2, from a tube node is equal to the desired discharge temperature from the still. (12) Check furnace dimensions: N8‘ = number of tubes calculated from assumed dimensions Na =-§§2:Bf = i5 lg.h6) = #6 tubes. In this example, #8 tubes were counted in the radiant section. Since N8‘ = #8, the assumed dimension Z is approximately correct and will not be recalculated. If Na f 48, Na in the above equation would be replaced by 48 and Z calculated. This Z could be used during the next iteration through the radiant section. Calculate f. f = 48 (¢¢) DO - 2z. -55- (a) If f < L/2, tubes are not placed in the bridge wall, consequently f is set equal to zero. (b) If f > L/2, tubes are placed in the bridge wall and f is set equal to 2/3Z. Since f = 48 (1.5) (0.46) - 32 = - 3.2 < L/2, the initial assumption, f = O, is correct. Calculations will not be repeated. When case (b) exists, the iteration is repeated using Z = 3/8 [NC £2 DO]. Nc = number of tubes counted in the radiant section. (15) Heat balance: In this example heat absorbed in the radiant section = 1.06017 x 107 Btu/hr. heat absorbed in the convection section = 1.2835 x 107 Btu/hr. total heat lost = 2.75988 x 107 Btu/hr. total heat liberated = 5.10355 x 107 Btu/hr. From the flow rate of the fuel and its net heating value (584.2 Btu/lb. gas) (83354.9 lb./hr.) = 4.85 x 107 Btu/hr. Since the total heat liberated as calculated from the heat balance and the net heating value of the fuel are almost equal, it will not be necessary to repeat the calculations. (18) Tube diameter: Finally, P2 If their difference is not within tolerance another tube diameter is assumed and all calculations repeated. The assumption is made is compared with the desired discharge pressure. using the relationship: Di — Di [4559 11/5 n n-l APa APC = calculated pressure drOp after n-lth iterations APa = desired pressure drop ' Din = diameter assumed for the nth iteration D1 = diameter previously used. n-l {300 dr- 600 db 500 -A— 300 In)— 200—.)— FIGURE 11 Tl? Curve and ilurritj'.firLiW_Lc for Crude 100 «In—- ur— “[- [— 4k w— 10 20 30 40 50 60 Volume Percent Distilled lOO [_ )0 IO Q) , Ncmperaiur T ‘9 I‘ r- . i .L. also) . (00 - 330 -‘ 400 - 100- .L 10 I ’r’ 20 l I l l 30 40 63+— ] L l I I T 60 70 80 90 100 Percent Distilled FIGURE l2 ORDER L5 n 50 n LA n LO n 75 n LO n 55 22 n 32 n 26 n 36 n F5 n FIXED POINT ORDERS OPERATION Transfer contents of location n to A. Transfer contents of location n to Q. Add contents of n to A. Subtract contents of n from.A. Multiply Q by contents of n. Transfer contents of A to n. Transfer contents of Q to A. Transfer control to right order at location n. If contents of A43 0, execute 22. Transfer control to left order at location n. If contents of A12 0, execute 26. Transfer contents of n to A and increase the address digits at the right side by l. FLOATING POINT ORDERS: Let F be the floating decimal number in the floating accumulator and let F(n) be the floating decimal number in location n. ORDER 80 n 81 n 82 n 83 n 84 n 85 n OPERATION Replace F by F - F(n) Replace F by -F(n) Transfer control to the right hand interpactive order in n if R2 0 Transfer control to the left hand interpactive order in n if F: 0 Replace F by F + F(n) Replace F by F(n) 69 7O ORDER OPERATION 86 n Replace F by F/F(n) 87 n Replace F by F.x F(n) 88 0 Replace F by one number read from the input tape punched as sign, any number of decimal digits, sign, and two decimal digits to represent the exponent. 89 n Punch or print F as a sign, n decimal digits, sign, two decimal digits to represent the exponent and two spaces. 8Kn ReplacerynifOsn<2OO 83 n Replace F(n) by F 8N n Replace F by /F/ - /F(n)/ 8J n Transfer control to the fixed point order at the left side of location n 8F n Give a carriage return and line feed and arrange to print a block of numbers having n columns. If the first function digit of a floating point order is O, 1, ...7, it refers to one of a set of control registers, or b-registers in the floating decimal routine which are similarly numbered. These are used to count the number of passages through loops and for increasing the addresses of these orders on successive passages. These addresses are increased only if the function digit of the order corresponds to that of the control register currently used. ORDER LIST WITH b /8 The index Cb is used for counting purposes to determine the number of passages through a loop. The index gb is used for advancing the address of floating point orders. ORDER OPERATION bO n Replace F by F — F(n + gb) bl n Replace F by -F(n + gb) ORDER b2 n b3 n bh n b5 n b6 n b7 n bk n bN n bL n 71 OPERATION Replace gb, Cb by gb + 1, Ch + l 7 Then transfer control to the right hand (if b2 n) or left hand floating point (if b3 n) order in n if Cb +1 <:0. This transfer is used at the end of the loop. Replace F by F + F(n + gb) Replace F by F(n +gb) Replace F by F/F(n + gb) Replace F by F.x F(n + gb) Replace gb, Cb by 0, —n. This floating point order is used for preparing L cycle around loop n times Replace F(n + gb) by F Replace F by F — F(n + gb) Replace gb, Cb by gb + n, Cb. This order is used when one wishes to change addresses by some increment other than +1 in a loop. If one places bL 1022 in a loop, the effect will be to decrease addresses by two on each passage. LOCATION O\U1.l:‘w N 10 11 12 13 14 15 16-19 20—157 158—270 635—660 271-379 380-449 450-508 509-546 547-589 590-634 665-678 72 FURNACE DESIGN PROGRAM Program Outline CONTENTS Specifies Floating Accumulator Specifies Al routine Specifies A3 routine Specifies 8A3 (Natural Log) routine Specifies SA2 (Exponential) routine .Specifies routine to calculate physical properties Specifies routine which selects correct polynomials to be used in evaluating W Specifies location of data Specifies location of generated data Specifies location of data Specifies location of routine to calculate €c. Specifies location of routine to calculate AP Temporary storages Convection section routine Radiant section routine Continuation of radiant section routine Subroutine to calculate physical properties Subroutine to select correct polynomials Data Data (depending on type crude) Data (generated) Polynomials for y Routine to calculate (c, 73 LOCATION CONTENTS 679—70h Routine to calculate AP 705-738 Storages for selected polynomials and their parameters 739-7h3 Answer storages 739 Counter for shield section 7&0 Number of rows in convection section 7hl Heat absorbed in convection section 7h2 Heat absorbed in radiant section 7h3 Number of tubes in radiant section 7AA Heat lost from furnace 003K 00F 007h5F 00F 00830F 00F 0077312 00F 00800F 00F 00747F 00F 00271F 00F 0038013 00F 00509F 00F 0051771r 00F 001.501: 00F 00651F OOF 00665F OOF OO679F LOCATION 0020K O OOSSSK ORDER 22 50 26 OK 88 03 83 22 50 sh ASP 59OF 2L 999F 74 PROGRAM Directive Specifying Location Routines Floating accumulator Al A3 SA3 SA2 Calculate physical properties . Select correct polynomials Data Data Data Calculate cc. Calculate AP NOTES Read in and store constants for This routine is later overread Transfer control to continue reading and storing program. LOCATION 1 OO2OK ORDER 26 OK 88 OS 03 0K 88 OS 03 0K 88 OS 03 8K 8K 83 24 85 84 85 0K 05 OS 02 OK 85 87 05 02 8J 8J sh 23F F lOOF 2L 59F F SN AL 38F SK 6L 1F 20F 5551i SZSN SK SBSN 5F lSK lSS 2L 2F ASSN SS 215K 2888 8L 8L 75 NOTES Read in and store constants Transfer control to location 20 Start executing program at location 555 Program for the Convection Section Preliminary calculations Calculate PL of C02 and H20 for the con— vection bank LOCATION 8 10 ll 12 13 14 15 16 17 l8 19 20 21 22 23 24 25 ORDER bl 739F F5 8L 2h S9 0K AF 8K F 88 198K 87 38K 0h 168K 03 11L 83 7A4F 8K F as 36SS 85 65K 80 lSN 87 SS 87 78K 8S SF 85 158K 86 5F 86 SN 85 5F 87 SF 86 SS 86 36SN 8J so 86 3SN 8J S7 8? ism 8S 15F 8K 1F 8K 1F 8h usK 86 1bSK 87 65K 86 hiSN 8S 32SS 76 NOTES Entrance to subroutine to select correct polynomials for at Transfer control to subroutine LOCATION 26 27 28 29 30 31 32 33 3A 35 36 37 38 39 A0 A1 A2 A3 ORDER 85 ASS 8A SSS 86 2SN 85 888 85 188 8A 288 86 2Sn 8S 7SS 0K AF 8K F 83 198K 8? 3SS 0A 168K 02 31L BS 17F 81 3AL 22 3AL F5 3AL 26 88 85 2158 8A 17F 88 5F 81 5F 8S 19SK 0K 3F 1K F 05 168K 17 3SN OS 8F 1L 1023F 03 39L 0K 3F 8K F 87 20SK 0A 8F 02 A2L 77 NOTES Assume P2 Store P m Assume T2 Store t _ m Entrance to subroutine to calculate physical properties Transfer control to this subroutine Calculate temp. of flue gases above nth tube (Tg) Assume T 9 78 LOCATION ORDER NOTES AA 88 5F OK AR AS 8K F 87 208K A6 0A 165K 02 ASL A7 85 6F 85 2ASN A8 8N 6F Is this the correct temperature? 82 52L 'Yes: Transfer control to 52L No: Modify T A9 85 6F g 86 5F 50 88 SF 85 205K 51 80 5F ‘ 88 208K 52 82 AlL Repeat calculations using new T9 85 208K Calculate hc 53 8A 3SS 86 2SN 5A 85 26SS 8d S6 55 87 AASN 8J S7 56 87 15F 8S 2758 57 85 2658 80 lOSN 58 88 3155 ' 8O lOO9F IS this a shield tube? Yes: Transfer control to 6AL 59 82 76AL No: Continue at lOOL'without including 8K 1F calculations for a Shield tube 60 83 l20F 8S ASS These orders are used in the radiant section P1 — Pg 2 0 ? 61 8O lOO2F 8A lOO8F LOCATION 62 63 6A 65 66 67 68 69 7O 71 72 73 7A 75 76 77 78 ORDER 83 250R 89 AF 85 SK 89 AF 83 6A5F 8A 1F 84 739F 88 739F 85 55 8A SK 8? 21511 85 5F 85 SS 80 SK 87 SS 86 5F 85 5F 85 SS 86 5K 86 2555 8A 5F 85 5F 8K 1F 86 235K 8A 5F 85 6F 8 5 3 155 80 755 87 5F 86 6F 8A 755 85 3055 8 5 3 155 3055 80 79 NOTES Yes: Continue calculations for another node No: Point out their difference and also the tube diameter. Then change the tube diameter and repeat all calculations. Go to 6A5 to change diameter. Calculations for shield tubes begin Increment counter for shield tubes Calculate TS Assume h u LOCATION 79 80 81 82 83 8A 85 86 87 88 89 9O 91 ‘92 93 9A 95 96 ORDER 85 16F 81 80L 22 80L F5 80L 26 SF 85 10F 86 16F 87 A6SN 85 13F 8K 100F 85 5F 85 3055 8A lOSN 86 5F 85 6F 87 6F 87 6F 87 A65N 87 A7SN 85 6F 8A 13F 84 2755 85 7F 85 6F 87 3255 86 7F 8A lSN 85 8F 85 13F 8A 2755 87 8F 85 3ASS 80 23SK 85 5F 85 39SN 8N 5F 80 NOTES Entrance to subroutine to evaluate [(q + ) - (q + q ) 1 [ lOO-%] C q’w Tg C W TS [ W] Transfer control to subroutine Evaluate hrg Evaluate h rb Evaluate percent wall correction Is the hu assumed equal to hu calculated LOCATION 97 98 99 100 101 102 1., 10A 105 106 107 108 109 110 111 112 113 11A ORDER 83 99L 85 BASS 85 235K 83 66L 85 ASS 85 2755 85 55 8A SK 87 25K 85 5F 85 55 80 SK 87 55 86 5F 85 5F 85 SS 86 5K 86 2555 8A SF 85 SF 8K 1F 86 2755 8A 5F 85 5F 8K 1F 86 5F 85 3555 87 SS 87 75K 87 A15N 85 5F 85 3155 80 755 87 5F 85 5F 80 2155 Yes: 81 NOTES Transfer control to 99L No: Modify hu repeat 2788 2738 calculations using new hu h if nth tfibe tube is not a shield (wall correction)(hc+hr ) if nth tube is a shield tube 9 Calculations for 11 Calculate q = uAAt Does q = AH? LOCATION 115 116 117 118 119 120 121 122 .123 12A 125 126 127 128 129 13G 131 132 ORDER 85 6F 85 100AF 8N 6F 83 126L 85 255 80 155 87 6F , 86 2155 8A 255 85 255 BR 1F 8A A055 85 A055 80 1008F 83 126L 85 225N 80 739F 83 A8F 85 739F 8O 15N 85 739F 83 A8F 85 75K 86 1ASK 85 3855 85 ASK 85 3955 81 3F 10 130L F5 139L 26 SL 85 205K 85 355 85 955 85 3655 85 2183 82 NOTES Yes: continue at 126L No: modify t2 If t2 does not converge after the 7th iteration use last calculated value of t2 as the correct value No convergence after 7th iteration, proceed 126L Was this a shield tube? _ No: repeat calculations using modified t2 Yes: reset counter Repeat calculations using modified t2 Reset counter for number of iterations t0 t2 Transfer control to subroutine to calculate AP at this point the tube node has converged Make a summation of the AHn's LOCATION 133 13A 135 136 137 00158K ORDER 8A 7A1F 8.8 7A1F 8K 1F 8A 7AOF 85 7AOF 85 65N 80 739F 83 26L 8K 2F 85 3955 A1 A055 26 1A9F 85 205K 80 lOSN 85 3155 85 155 85 655 85 ASS 85 3755 8K. F 85 7A2F 85 7A3F 85 655 85 155 85 3755 85 A55 85 3855 87 1000F 87 1000F 81 56 86 3SN 81 57 83 NOTES Make a summation of the number of rows (n's) Was this the last tube in the shield section? No: repeat calculations for another tube Yes: Proceed to the radiant section. Reset counter for the number of iterations of t2 to zero. Program For the Radiant Section Store Tg as the bridgewall temperature Store t1 as the cross—over temperature Store P, as the cross-over pressure Set counter for AHR and nR = 0 Assume Z, and calculate LB LOCATION 10 ll 12 13 1A 15 16 17 18 19 2O 21 22 23 24 25 26 27 ORDER 87 2SN 86 3SN 85 5F 87 215K 85 2855 85 5F 87 225K 85 2955 8K 2F 87 1000F 85 5F 8A A2SN 87 3855 87 1001F 85 6F 8K 2F 87 3855 8A 1000F 87 5F 86 6F 80 15N 85 3255 85 3855 87 3955 87 lOOlF 87 55 87 65K 85 A155 85 55 8A SK 87 25K 85 5F 85 55 80 SK 87 55 86 5F 8A NOTES Calculate PL of C02 and H20 in the radiant section Calculate AR/clAcp for the radiant section Calculate dAcp per node LOCATION 28 29 3O 31 32 33 3A 35 36 37 38 39 A0 A1 A2 A3 AA ORDER 85 19F 81 29L 22 29L F5 29L 26 S9 85 A55 8A 555 86 2SN 85 855 85 155 8A 255 86 2SN 85 788 81 35L 22 35L F5 35L 26 58 8K 1F 86 2555 8A 19F 85 5F 85 2155 87 5F 86 55 86 A15N 86 3955 86 3855 8A 755 85 3055 81 A3L 22 A3L F5 A3L 26 5F 2K 2F 85 NOTES Select correct polynomials for e. Assume P2 Calculate Pm Assume t2 Calculate tm Calculate percent vaporized, HL, H etc. Calculate TS from q = uA[ta - tm] V) Calculate [(qC + qw)TB - (qC + qw)T ][lOO-%% Calculate (qBB)TB - (qBB)T S LOCATION A5 A6 A7 A8 A9 50 51 52 53 5A 55 56 57 58 59 60 61 62 ORDER OKAF 8K F 27 3055 0A 95M 03 A6L 25 5F 23 A5L' 80 5F 85 6F 85 10F 86 6F 85 10F‘ OK 9F 1K F 15 59OF 80 10F 83 59L 85 7 18F 3K AF 15 591F 35 710F 1L 1F 32 5AL 1L 1F 03 52L 85 A65N 85 3355 83 72L 85 719F 3K AF 15 591F 38 71AF 1L 1F 33 60L 2K 2F OK F 86 NOTES Evaluate 50 Select correct polynomial for q: Interpolate between the polynomials with values of 6‘... closest to £6 LOCATION 63 6A 65 66 67 68 69 7O 71 OO23OK O 87 ORDER NOTES 1K AF ‘ 8K F 87 3285 0A 710F 0L 1F 13 6AL 28 8F 23 63L 80 8F 88 7F 85 7l9F 80 718F 88 5F 81 718F 86 5F 87 7F 8A 8F 88 3388 Store 4! 2K 2F Evaluate qr 25 3088 8A lOSN 8J 86 87 AOSN 8J S7 28 5F 22 L 80 5F 87 1018F 88 6F 85 3188 80 3088 87 1008F 8A 6F 3358 am 1“. M_ LOCATION 8 10 11 l2 13 1A 15 16 17 18 19 2O 21 22 23 2A 25 ORDER 87 A15N 80 2155 85 6F 85 100AF 8N 6F 82 lAL 85 255 80 155 87 6F 86 2155 8A 255 85 255 82 19OF 81 15L 10 16L L5 15L 26 SL 8K 2F 8A 7A3F 88 7A3F 85 7A2F 8A 2155 85 7A2F 82 80F 85 1003F 80 155 82 188F 8K 2F 87 1000F 85 5F 85 7A3F 87 65K 87 55 85 9F 80 5F 87 2SN 88 NOTES IS q = AH? Yes: proceed to lAL N0: modify t2 Repeat calculations using new t2 Calculate AP At this point the tube node has converged. Make a summation of n 's R Make a summation of the AHR'S Transfer control to location 80 is t - t2 >0 x Yes: Repeat calculations for another node N0: Stop calculating nodes and test for convergence of furnace If 2f-dL<0 usef 2f - dL )’0 use f O 2/3 2 89 LOCATION ORDER NOTES 26 80 3888 83 30L 27 8K F Use f = O 88 A288 ' 28 85 9F 86 ZSN 29 83 9F 82 33L 30 85 9F Use f -- 2/3 2 8? AASN 31 86 A2SN 88 9F 32 87 2SN 86 38N 33 85 A255 85 lOOOF Does Z assumed = Z calculated? 3A 80 9F 8N A25N 35 82 639F No: proceed to location 639 85 7A1F Yes: Is the assumed flue gas flow rate correct? 36 8A 7A2F 8A 7AAF 37 86 100AF 8S 12F 38 86 155K 80 lSN 39 88 5F 8K 1F A0 83 635F Continue these calculations at 635 83 635F 00635K 0 85 39SN 8N 5F 1 82 6L Yes: Continue at 6A1 8F 2F No: print out N last calculated and flue gas flow rate last used IOCATION 2 10 11 12 ORDER 85 7A3F 89 3F 85 12F 89 6F 83 351 85 9F 85 1000F 89 5F 82 161F 85 A55 80 lOO2F 89 3F 85 5F 85 1008F 8N 5F 82 8L 85 ASK 80 A55 86 1005F 81 S6 86 1006F 81 57 87 5K 85 SK 82 751 85 1000F 89 8F OK 6F 05 739F 89 8F 03 10L 81 12L OF F OF F NOTES Proceed to modify flue gas flow rate Modify Z Print out modified 2 J. Repeat calculations in radiant section using Does Pz-PX - 0 within limits? 1 new 2 Print out difference Yes: Furnace design complete, proceed to 8L No: modify tube diameter Using new diameter, repeat all calculations. First, reset all counters to zero at 781. Furnace design complete. Print out answers. Stop all calculations LOCATION 13 1A 15 16 17 l8 19 00271K 86 88 OK 05 87 02 85 OK 8K 03 83 ORDER 158K lOF 3F 168K 10F 168K 1AL 12F 158K 739F 18L 20F lO6L 54 268K 2L 5F 8SK SSN 6F 5F 6F 738 SF lO7L 5F 91 NOTES Modify gas flow rate (BSJ) Set all counters to zero Repeat all calculations from beginning Subroutine for Physical Properties Calculate percent vaporization Was there any vaporization in this node? No: Go to lO7L. and pick up previously calculated percent Yes: Is the amount of vapor negligible? LOCATION 9 10 11 12 13 1A 15 l6 17 18 19 20 21 22 23 2A 25 26 ORDER 86 6F 86 2SN 85 955 85 95K 80 955 83 15L OK AF 8K F 87 955 0A 305K 03 13L 82 16L 8K F 85 955 85 105K 85 1055 85 1055 87 _ 115K 8A 125K 86 65N 85 5F 85 755 87 3SN 80 7SN 87 5F 85 5F OK AF 8K F 87 1055 0A A85N O 3 23L 8A 5F 85 5F 85 85K 80 755 86 65N 92 NOTES Yes: Set percent vaporized = O No: Evaluate the specific gravity as a function of the percent vaporized. Set percent vaporized = 0 Calculate the density of the crude at tm J LOCATION 27 28 29 3O 31 32 33 3A I 35 36 37 38 39 A0 A1 A2 A3 ORDER 87 5F 8A 1055 87 9SN 85 1155 85 lSN 80 955 87 138K 87 1055 86 105K 85 1255 85 138K 80 1255 85 1355 85 755 8A lOSN 85 5F 87 115N 86 855 85 8F 85 855 87 13SN 8A 12SN 87 1751\1 86 5F 86 5F 86 5F 85 7F 85 855 87 1ASN 8A 155N 8A 6F 80 7F 85 6F 85 16SN 86 6F 85 1ASS 93 NOTES Calculate wL Calculate wy= w - wL Calculate the vapor denSity. LOCATION A5 A6 A7 A8 A9 50 51 52 53 5A 55 56 57 58 59 6O 61 62 ORDER 85 1355 87 1188 86 1ASS 8A 1255 85 6F 85 1255 86 6F 85 1555 85 185K 87 1055 80 195K 85 10F 85 '2OSN 87 HES 80 215N 85 9F 85 22SN 85 8F 1K 2F OK 3F 8K F 17 155 0A 8F 02 55L 15 1655 12 54L OK 3F 05 23SN 87 1055 85 6F 05 26SN 80 6F 08 8F 02 58L 1K 2F 0K 3F 9A NOTES Calculate the liquid volume fraction Calculate HuandHv LOCATION 63 6A 65 66 67 68 69 7O 71 72 73 7A 75 76 77 78 79 80 ORDER 8K F 17 155 0A 8F 02 63L 15 1855 12 62L OK 2F 85 30511 O7 855 811 29SN O7 855 85 6F 85 32SN O7 ass 88 3lSN O7 855 87 175R 85 7F O5 155 88 lOSN 85 8F 85 7F 86 8F 86 8F 86 8F 85 9F 85 6F 80 9F 86 335K 0A 1855 05 1855 02 66L 85 755 80 37SN 87 3ASN 85 6F 95 NOTES Calculate the thermal conductivity Of the crude. 96 LOCATION ORDER NOTES 81 BK. 1F 80 6F 82 87 355N 86 365K 83 86 1058 8S 2058 BA 85 1733 Calculate AH 80 1685 85 87 1258 88 6F 86 85 1955 80 1888 87 87 1355 8A 6F 88 8S 2183 85 258 89 80 155 85 6F 90 85 1758 80 1688 91 86 6F 85 2288 92 OK AF Calculate the viscosity of the vapor 8K F 93 87 788 oh 3ASK 9A 03 93L 87 1188 95 86 9SN 87 3851\1 96 85 2355 85 AOSN Calculate (Re)L 97 87 1288 86 AlSN 98 86 SK 86 2338 LOCATION 99 100 101 102 103 10A 105 106 lO7 108 OOBBOK 97 ORDER NOTES 8S 2ASS 8J S6 Calculate hi 87 AZSN 8J S7 8? A35N 8S 5F 85 2258 87 2355 86 20SS 8J S6 86 BSN 8J S7 87 5F ' 8S 2588 8K 1F 82 [ ]F Transfer control to main routine 85 3683 8S 9SS 8K 1F 82 10L A2 50 26 3K 35 8J 22 F5 Program to Select Correct Polynomials for This program will select, from tape, two polynomials with PL values closest to poly- nomial desired. It will also interpolate between these polynomials to Obtain ea, 26L 5A 2F 2F . 2888 Store PL C02, and then PL.H20 706F AL LOCATION 5 IO 11 12 13 1A 15 l6 17 18 19 20 21 22 ORDER 26 AOBF OK AF O5 71OF 25 72OF 05 715F 25 72AF 2L 1F O3 6L 85 7O9F 3S 736F 2L AF 32 2L 85 2855 8A 2955 85 7O6F 8J AAOF 85 25N 80 7O6F 83 16L 85 65N 85 7O6F 83 16L 85 2855 86 7O6F 85 10F 8J 18L 22 18L F5 18L 26 A08F OK 5F 8K F 87 10F 0A 715F O2 20L 85 5F 8K lOOF 98 NOTES Transfer control to A08 Store polynomials in the locations designated for them. Repeat to select and evaluate qCOZ' At TB and T5 Calculate parameter for percent correction Parameter = PLCO2 + PLH20 T. C. to AAO If2- (PL88 EZOWPLH <0 let + PLHy = 1.8 Select polynomial Evaluate LOCATION 23 2A 25 26 OOAO8K 10 ll 12 ORDER 85 6F 80 5F 86 6F 85 738F 8J AA2F 8K 1F 8K 1F 82 [ JF A2 12L 50 L 26 5A 8J AA6F 85 707F 8O 706F 82 5L 85 7O8F 8J A21F 8K 1F 82 1L 8J A29F 8J AA8F 85 585m 8O 7O5F 82 9L 8J A36F 8K 1F 83 ' 6L 85 708F 8A 706F 8O 7O7F 86 708F 85 7O9F 8K 1F 82 [ ]F 99 NOTES Transfer to AA2 Transfer control to AA6 IsPL -PL>O? m Yes: Proceed to 5L No: Store difference and proceed to A21 _Read in and check another polynomial Transfer to A29 Transfer to AA8 Was this the last polynomial in the set? Yes: Use the two polynomials in memory No: Proceed to A36 Interpolate between the PL'Values available. Transfer control to 385 lOO LOCATION ORDER NOTES OOAAOK 0 F5 5L Prepare to operate on Ath degree polynomials A0 5L 1 26 298A OOIF 2 L5 5L Reset to Operate on 3rd degree polynomials LOAL 3 A0 5L. 26 298A A OOF OOIF 5 00F OOAP 6 81 AOF Read a sexadecimal character from tape A0 707F (representing a value of PL) and store in 707 7 22 7L 26 29SA Transfer control to the order following last 8J order executed 8 81 AOF Read in and store the next PL on tape A0 705F 9 22 9L 26 293A Proceed to order following the last 8J order executed OOA2IK O 22L L5 6L 1 A2 2L A1 7L 2 81 AOF Read in and store a polynomial AO 7lOF 3 F5 2L A2 2L A F5 7L A0 7L 5 L0 AASF ‘ 36 298A Proceed to last 8J order executed 6 26 2L OO 7 lOF LOCATION 7 10 ll 12 13 1A 15 16 17 18 101 ORDER NOTES 00 F 00 F L5 9L Read in and atore polynomial associated A2 10L with PL last checked A1 7L LO 715F 81 AOF AO 715F F5 IOL A2 lOL F5 7LT A0 7L LO AA5F 36 298A Proceed to order following 8J order last executed 26 lOL 26 lOL A1 7L 81 AOF Read in and dump a polynomial F5 7L A0 7L L0 AA5F 36 295A Transfer to order following the last 8J order executed 22 15L 22 15L Subroutine to Evaluate Polynomials for and to interpolate between them A2' 13L 50 L 26 SA OK 2F 1K F 2K 2F 3K 2F AK AF 8K F 07 BOSS 102 LOCATION ORDER NOTES 5 1A 72OF 1L 1F 6 A2 AL BS SF 7 32 3L 80 5F 8 26 736E 8A 5F 9 23 8F 23 BL 10 8A 8F OS IOF ll 03 2L 8O IOF 12 87 738F 8S 10F 13 8K 1F 82 [ ]F 00679K Subroutine to Evaluate AP 0 A6 22L 50 L 1 26 5A 85 2A55 2 8J S6 87 101AF 3 8J 57 85 5F A 85 1558 80 1015F S 83 19F 85 1555 6 87 5F 8A IOI6F 7 8? 37SN 87 135K LOCATION 8 10 ll 12 13 1A 15 16 17 18 19 20 21 22 23 2A 25 103 ORDER NOTES 87 138K 0K 5F 86 SK 03 9L 86 lOl7F 8S 5F 85 1185 80 lASS 87 1555 8A lASS BS 6F 85 lOlIF 87 SK 8A 38SS 8? 3955 87 5F 86 6F 8A 5SS Does P2 assumed = P2 calculated? 80 ASS 8S lOF 8N 39SN 82 22L No: Modify P2 and repeat calculations Yes: Replace P1 by P2 85 5SS 8S ASS 85 2S8 Replace t1 by t2 83 183 8A AOSN 83 285 82 [ ]F Transfer control to program 85 555 80 10F 88 588 BA A55 86 2SN 85' 855 82 188 10A LOCATION ORDER NOTES OOl9K O 85 10 15F 83 685F DflfleS. 105 Polynomials for the Evaluation of w Per cent Correction: 2% = a + bR + 8R2 + dR3 + eR4 3 R = 002/7002 + H20) Piramegif a b c d e 0.01 0.3857 A.3900 20.1857 —33.8957 9.7907 0.25 0.3558 21.932A —16.2A91 5.5128 -8.609A 0.5 A.5758 7.352A 18.9710 -19.1826 -6.A339 0.75 1.0A23 51.705A -98.6A57 106.291A -53.2739 1.0 2.5018 A9.2875 —92.A5A3 102.16A9 —52.9669 1.5 3.2912 55.1680 -109.93A6 120.0117 -58.3A93 2.0 A.2321 51.983A -101.88A7 111.AAA6 -5A.6296 Radiation due to Carbon Dioxide: 2E = a — bt + th — dt3 Parameter = PL.CO a b c x 103 d.x 107 2 0.001 51.7010 0.1513 0.2078 -0.2919 0.002 5A.0670 0.1802 0.3150 0.336A 0.003 211.8020 0.5723 0.6A1A 0.7937 0.00A 173.6900 0.6191 0.8155 1.0992 0.005 30.0980 0.373A 0.73A9 0.8113 0.006. 35.6890 1.0696 1.2016 1.A618 0.008 252.8100 0.9766 1.2920 1.A689 0.01 651.9700 1.953A 2.0A23 2.6610 0.015 75A.5600 2.2AA6 2.33A7 2.7522 0.02 1278.9000 3.5058 3.2896 A.2098 0.03 1503.5A00 A.1913 3.9372 5.0236 0.0A 1103.5000 3.3869 3.5666 3.7936 0.06 13A6.5700 A.1166 A.25A3 A.3270 0.08 668.AA00 2.57A9 3.2179 1.AA70 0.10 1817.8000 5.3986 5.3289 5.2A98 0.15 3927.0900 10.0878 8.3592 9.587A 0.20 3990.AA00 10.23A2 8.A211 8.169A 0.30 5781.0000 1A.3987 1.1211 11.8823 0.A0 A823.2900 12.1531 9.7198 7.3506 0.6 7588.0000 18.2576 13.A8A3 11.9161 1.00 62A6.9900 16.0636 12.7290 8.7AAA 2.00 8057.2900 19.8252 15.1587 9.2603 A.00 6090.0000 16.05A3 13.1966 1.7166 Radiation Due to Water vapor: 2E = a — bt + ct2 - dt3 106 Parameter == PIT-120 a b c x 103 d x 107 0.01 55.5228 0.120A 0.2066 0.0937 0.015 -110.9520 -0.2520 0.0261 -0.A1A2 0.02 25.6710 0.09A0 0.3523 0.1163 0.025 321.7550 0.7316 0.7960 _ 0.7295 0.03 265.0900 0.6268 0.81A1 0.6336 0.0A 229.8A30 0.5751 0.8985 0.5156 0.05 1A30.1100 1.0786 1.3918 1.1563 0.06 25.3160 0.2532 1.0233 0.10A6 0.08 288.6660 0.7717 1.3913 0.35A1 0.10 139.8600 0.3633 1.2072 -1.1A28 0.15 537.3800 1.3519 2.2078 0.610A 0.20 1908.1100 A.3802 A.AA17 1.7536 0.25 8.A300 0.372A 2.2078 -3.A239 0.30 1196.2760 3.17A1 A.A30A -0.5380 0.A0 A53.3800 1.1607 3.0303 -0.6590 0.50 —90.2000 -0.01AA 2.559A -9.9998 0.60 631.0A00 1.933A A.1A33 -9.2052 0.80 2025.3000 A.6138 5.8862 -11.A3A2 1.00 622.9000 1.6958 A.3397 -18.A798 1.25 -2283.7000 5.2A97 -0.6273 -3A.1129 1.50 1A08.0000 0.0252 3.87A6 -31.9589 2.00 55A8.0000 10.9A6A 8.7011 -32.9599 3.00 1362.3000 -0.3637 —0.50A6 -6A.A918 Black Body Radiation: 2EB = —5926.00 + 27.632At — 31.72A1t2 + 255.0130t3 Overall Exchange Factor: 2: _ 2 3 _ 28” a+bR OR +dR3R-AR/CLACP Parameter a b c x 102 d x 104 0.2 0.3875 0.3009 0.3655 0.1787 0.22 0.393A 0.3569 0.5188 0.2995 0.2A 0.A655 0.3292 0.A177 0.2023 0.26 0.A981 0.3A67 0.A726 0.2A80 0.28 0.5A60 0.3A80 0.A765 0.2A37 0.30 0.5827 0.363A 0.5380 0.2990 0.32 0.6170 0.37A0 0.5750 0.32811 0.3A 0.6583 0.3651 0.5726 0.3032 0.36 0.6830 0.3818 0.6028 0.3A86 Table 5 (cont.) Parameter a b c x 102 d x 104 0.38 0.7336 0.3505 0.A950 0.2AA7 0.A0 0.7671 0.3791 0.6236 0.3728 0.A5 0.8699 0.3668 0.61A8 0.3657 0.50 0.9567 0.3A72 0.5738 0.3290 0.55 1.0559 0.3379 0.6076 0.3765 0.60 1.1AOA 0.32A5 0.6003 0.3765 0.65 1.2232 0.3068 0.5993 0.3929 0.70 1.2863 0.2976 0.6122 0.A172 Table 6. Molar Heat Capacities of Flue Gas Cnmponents CP = a + bT + 0T2; T = OK Compound _ a b x 103 c x 106 Oxygen 6.095A 3.2533 -1.0l71 Carbon dioxide 6.3930 10.100 -3.A05 Water vapor 7.219 2.37A 0.267 Nitrogen 6.AA92 1.A125 -0.0807 “7111131117177“ 7177171111“